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

Percentage Accurate: 95.0% → 98.0%

Time: 8.7s

Alternatives: 21

Speedup: 0.9×

• 36.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

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 (+ (+ (fma -2.0 b z) (fma (- b z) y x)) a))))

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 = (fma(-2.0, b, z) + fma((b - z), y, x)) + a;
	}
	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(fma(-2.0, b, z) + fma(Float64(b - z), y, x)) + a);
	end
	return 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[(-2.0 * b + z), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.4%

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

Alternative 2: 91.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-9} \lor \neg \left(y \leq 0.125\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.2e-9) (not (<= y 0.125)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b (fma (- z) y z)))
   (fma (- t 2.0) b (+ (fma (- 1.0 t) a x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.2e-9) || !(y <= 0.125)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, fma(-z, y, z)));
	} else {
		tmp = fma((t - 2.0), b, (fma((1.0 - t), a, x) + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.2e-9) || !(y <= 0.125))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-z), y, z)));
	else
		tmp = fma(Float64(t - 2.0), b, Float64(fma(Float64(1.0 - t), a, x) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.2e-9], N[Not[LessEqual[y, 0.125]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999998e-9 or 0.125 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

   if -2.1999999999999998e-9 < y < 0.125

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

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

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 99.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-9} \lor \neg \left(y \leq 0.125\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ t_2 := \mathsf{fma}\left(t\_1, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+166}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t\_1, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)) (t_2 (fma t_1 b (- x (* (- y 1.0) z)))))
   (if (<= b -3.5e-24)
     t_2
     (if (<= b 8.5e-31)
       (- (fma (- 1.0 y) z x) (* (- t 1.0) a))
       (if (<= b 2.1e+166) t_2 (fma (- 1.0 t) a (fma t_1 b x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double t_2 = fma(t_1, b, (x - ((y - 1.0) * z)));
	double tmp;
	if (b <= -3.5e-24) {
		tmp = t_2;
	} else if (b <= 8.5e-31) {
		tmp = fma((1.0 - y), z, x) - ((t - 1.0) * a);
	} else if (b <= 2.1e+166) {
		tmp = t_2;
	} else {
		tmp = fma((1.0 - t), a, fma(t_1, b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	t_2 = fma(t_1, b, Float64(x - Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (b <= -3.5e-24)
		tmp = t_2;
	elseif (b <= 8.5e-31)
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a));
	elseif (b <= 2.1e+166)
		tmp = t_2;
	else
		tmp = fma(Float64(1.0 - t), a, fma(t_1, b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e-24], t$95$2, If[LessEqual[b, 8.5e-31], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+166], t$95$2, N[(N[(1.0 - t), $MachinePrecision] * a + N[(t$95$1 * b + x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4999999999999996e-24 or 8.5000000000000007e-31 < b < 2.1000000000000001e166

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   if -3.4999999999999996e-24 < b < 8.5000000000000007e-31

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 94.9%

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

   if 2.1000000000000001e166 < b

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 99.9%

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

Alternative 4: 95.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+178}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + \mathsf{fma}\left(b - z, y, x\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 8e+178)
   (- (+ (fma (- b z) y (fma (- t 2.0) b x)) z) (* (- t 1.0) a))
   (+ (+ (fma -2.0 b z) (fma (- b z) y x)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 8e+178) {
		tmp = (fma((b - z), y, fma((t - 2.0), b, x)) + z) - ((t - 1.0) * a);
	} else {
		tmp = (fma(-2.0, b, z) + fma((b - z), y, x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 8e+178)
		tmp = Float64(Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, x)) + z) - Float64(Float64(t - 1.0) * a));
	else
		tmp = Float64(Float64(fma(-2.0, b, z) + fma(Float64(b - z), y, x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 8e+178], N[(N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.0000000000000004e178

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 95.7%

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

   if 8.0000000000000004e178 < y

   1. Initial program 70.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 100.0%

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

Alternative 5: 86.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 1.15 \cdot 10^{+117}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.4e-24) (not (<= b 1.15e+117)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
   (- (fma (- 1.0 y) z x) (* (- t 1.0) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.4e-24) || !(b <= 1.15e+117)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = fma((1.0 - y), z, x) - ((t - 1.0) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.4e-24) || !(b <= 1.15e+117))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.4e-24], N[Not[LessEqual[b, 1.15e+117]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.40000000000000025e-24 or 1.14999999999999994e117 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 90.4%

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

   if -6.40000000000000025e-24 < b < 1.14999999999999994e117

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 1.15 \cdot 10^{+117}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 1.3 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.4e-24) (not (<= b 1.3e-20)))
   (fma (- (+ t y) 2.0) b (+ x z))
   (- (fma (- 1.0 y) z x) (* (- t 1.0) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.4e-24) || !(b <= 1.3e-20)) {
		tmp = fma(((t + y) - 2.0), b, (x + z));
	} else {
		tmp = fma((1.0 - y), z, x) - ((t - 1.0) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.4e-24) || !(b <= 1.3e-20))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x + z));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.4e-24], N[Not[LessEqual[b, 1.3e-20]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.40000000000000025e-24 or 1.29999999999999997e-20 < b

   1. Initial program 87.8%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 86.3

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

   5. Applied rewrites 86.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.5%

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

   if -6.40000000000000025e-24 < b < 1.29999999999999997e-20

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 95.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 1.3 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot a\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.06:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-75}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 440000000:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) a)))
   (if (<= t -2.25e+49)
     t_1
     (if (<= t -0.06)
       (* y b)
       (if (<= t 6.2e-75) (+ a x) (if (<= t 440000000.0) (* (- z) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * a;
	double tmp;
	if (t <= -2.25e+49) {
		tmp = t_1;
	} else if (t <= -0.06) {
		tmp = y * b;
	} else if (t <= 6.2e-75) {
		tmp = a + x;
	} else if (t <= 440000000.0) {
		tmp = -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 = -t * a
    if (t <= (-2.25d+49)) then
        tmp = t_1
    else if (t <= (-0.06d0)) then
        tmp = y * b
    else if (t <= 6.2d-75) then
        tmp = a + x
    else if (t <= 440000000.0d0) then
        tmp = -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 = -t * a;
	double tmp;
	if (t <= -2.25e+49) {
		tmp = t_1;
	} else if (t <= -0.06) {
		tmp = y * b;
	} else if (t <= 6.2e-75) {
		tmp = a + x;
	} else if (t <= 440000000.0) {
		tmp = -z * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * a
	tmp = 0
	if t <= -2.25e+49:
		tmp = t_1
	elif t <= -0.06:
		tmp = y * b
	elif t <= 6.2e-75:
		tmp = a + x
	elif t <= 440000000.0:
		tmp = -z * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * a)
	tmp = 0.0
	if (t <= -2.25e+49)
		tmp = t_1;
	elseif (t <= -0.06)
		tmp = Float64(y * b);
	elseif (t <= 6.2e-75)
		tmp = Float64(a + x);
	elseif (t <= 440000000.0)
		tmp = Float64(Float64(-z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * a;
	tmp = 0.0;
	if (t <= -2.25e+49)
		tmp = t_1;
	elseif (t <= -0.06)
		tmp = y * b;
	elseif (t <= 6.2e-75)
		tmp = a + x;
	elseif (t <= 440000000.0)
		tmp = -z * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * a), $MachinePrecision]}, If[LessEqual[t, -2.25e+49], t$95$1, If[LessEqual[t, -0.06], N[(y * b), $MachinePrecision], If[LessEqual[t, 6.2e-75], N[(a + x), $MachinePrecision], If[LessEqual[t, 440000000.0], N[((-z) * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.24999999999999991e49 or 4.4e8 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 37.5

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

   5. Applied rewrites 37.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 37.2%

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

   if -2.24999999999999991e49 < t < -0.059999999999999998

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.1%

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

   if -0.059999999999999998 < t < 6.20000000000000013e-75

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 67.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 38.8%

       \[\leadsto a + x \]

   if 6.20000000000000013e-75 < t < 4.4e8

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 65.8%

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

Alternative 8: 66.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -7e+61)
     t_1
     (if (<= y -1.1e-28)
       (fma (- 1.0 t) a x)
       (if (<= y 1.85e+15) (+ (fma (- t 2.0) b z) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -7e+61) {
		tmp = t_1;
	} else if (y <= -1.1e-28) {
		tmp = fma((1.0 - t), a, x);
	} else if (y <= 1.85e+15) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -7e+61)
		tmp = t_1;
	elseif (y <= -1.1e-28)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (y <= 1.85e+15)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7e+61], t$95$1, If[LessEqual[y, -1.1e-28], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[y, 1.85e+15], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000036e61 or 1.85e15 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -7.00000000000000036e61 < y < -1.09999999999999998e-28

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 66.5%

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

   if -1.09999999999999998e-28 < y < 1.85e15

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.7%

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

Alternative 9: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+116}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -6.4e-24)
     t_1
     (if (<= b 2.9e-28)
       (fma (- 1.0 t) a x)
       (if (<= b 5.8e+116) (* (- 1.0 y) z) 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 <= -6.4e-24) {
		tmp = t_1;
	} else if (b <= 2.9e-28) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 5.8e+116) {
		tmp = (1.0 - y) * z;
	} 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 <= -6.4e-24)
		tmp = t_1;
	elseif (b <= 2.9e-28)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 5.8e+116)
		tmp = Float64(Float64(1.0 - y) * z);
	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, -6.4e-24], t$95$1, If[LessEqual[b, 2.9e-28], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 5.8e+116], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.40000000000000025e-24 or 5.8000000000000003e116 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.5%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 78.3

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

   11. Applied rewrites 78.3%

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

   if -6.40000000000000025e-24 < b < 2.90000000000000013e-28

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 57.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.8%

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

   if 2.90000000000000013e-28 < b < 5.8000000000000003e116

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.9

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

   5. Applied rewrites 52.9%

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

Alternative 10: 73.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-30} \lor \neg \left(b \leq 8 \cdot 10^{+51}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.2e-30) (not (<= b 8e+51)))
   (fma (- (+ t y) 2.0) b (+ x z))
   (+ (fma (- 1.0 y) z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.2e-30) || !(b <= 8e+51)) {
		tmp = fma(((t + y) - 2.0), b, (x + z));
	} else {
		tmp = fma((1.0 - y), z, x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.2e-30) || !(b <= 8e+51))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x + z));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.2e-30], N[Not[LessEqual[b, 8e+51]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000006e-30 or 8e51 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.3%

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

   if -7.2000000000000006e-30 < b < 8e51

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 73.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-30} \lor \neg \left(b \leq 8 \cdot 10^{+51}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{elif}\;t \leq 3100000000:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.9e+29)
     t_1
     (if (<= t 4.4e-74)
       (+ (fma (- y 2.0) b x) a)
       (if (<= t 3100000000.0) (* (- b 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 <= -5.9e+29) {
		tmp = t_1;
	} else if (t <= 4.4e-74) {
		tmp = fma((y - 2.0), b, x) + a;
	} else if (t <= 3100000000.0) {
		tmp = (b - 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 <= -5.9e+29)
		tmp = t_1;
	elseif (t <= 4.4e-74)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	elseif (t <= 3100000000.0)
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.9e+29], t$95$1, If[LessEqual[t, 4.4e-74], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 3100000000.0], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8999999999999999e29 or 3.1e9 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.5

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

   5. Applied rewrites 63.5%

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

   if -5.8999999999999999e29 < t < 4.40000000000000021e-74

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 68.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 65.7%

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

   if 4.40000000000000021e-74 < t < 3.1e9

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

Alternative 12: 48.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -0.112:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-217}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3100000000:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -0.112)
     t_1
     (if (<= t -1.8e-217)
       (+ a x)
       (if (<= t 3100000000.0) (* (- 1.0 y) z) 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 <= -0.112) {
		tmp = t_1;
	} else if (t <= -1.8e-217) {
		tmp = a + x;
	} else if (t <= 3100000000.0) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-0.112d0)) then
        tmp = t_1
    else if (t <= (-1.8d-217)) then
        tmp = a + x
    else if (t <= 3100000000.0d0) then
        tmp = (1.0d0 - y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -0.112) {
		tmp = t_1;
	} else if (t <= -1.8e-217) {
		tmp = a + x;
	} else if (t <= 3100000000.0) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -0.112:
		tmp = t_1
	elif t <= -1.8e-217:
		tmp = a + x
	elif t <= 3100000000.0:
		tmp = (1.0 - y) * z
	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 <= -0.112)
		tmp = t_1;
	elseif (t <= -1.8e-217)
		tmp = Float64(a + x);
	elseif (t <= 3100000000.0)
		tmp = Float64(Float64(1.0 - y) * z);
	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 <= -0.112)
		tmp = t_1;
	elseif (t <= -1.8e-217)
		tmp = a + x;
	elseif (t <= 3100000000.0)
		tmp = (1.0 - y) * z;
	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, -0.112], t$95$1, If[LessEqual[t, -1.8e-217], N[(a + x), $MachinePrecision], If[LessEqual[t, 3100000000.0], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.112000000000000002 or 3.1e9 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.7

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

   5. Applied rewrites 60.7%

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

   if -0.112000000000000002 < t < -1.79999999999999991e-217

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.5%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

       \[\leadsto a + x \]

   if -1.79999999999999991e-217 < t < 3.1e9

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.8

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

   5. Applied rewrites 43.8%

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

Alternative 13: 37.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-159}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+97}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -3.8e+57)
     t_1
     (if (<= a -3.4e-159)
       (* (- z) y)
       (if (<= a 9.4e+97) (* (- y 2.0) b) 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 <= -3.8e+57) {
		tmp = t_1;
	} else if (a <= -3.4e-159) {
		tmp = -z * y;
	} else if (a <= 9.4e+97) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - t) * a
    if (a <= (-3.8d+57)) then
        tmp = t_1
    else if (a <= (-3.4d-159)) then
        tmp = -z * y
    else if (a <= 9.4d+97) then
        tmp = (y - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -3.8e+57) {
		tmp = t_1;
	} else if (a <= -3.4e-159) {
		tmp = -z * y;
	} else if (a <= 9.4e+97) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -3.8e+57:
		tmp = t_1
	elif a <= -3.4e-159:
		tmp = -z * y
	elif a <= 9.4e+97:
		tmp = (y - 2.0) * b
	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 <= -3.8e+57)
		tmp = t_1;
	elseif (a <= -3.4e-159)
		tmp = Float64(Float64(-z) * y);
	elseif (a <= 9.4e+97)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -3.8e+57)
		tmp = t_1;
	elseif (a <= -3.4e-159)
		tmp = -z * y;
	elseif (a <= 9.4e+97)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -3.8e+57], t$95$1, If[LessEqual[a, -3.4e-159], N[((-z) * y), $MachinePrecision], If[LessEqual[a, 9.4e+97], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7999999999999999e57 or 9.3999999999999994e97 < a

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -3.7999999999999999e57 < a < -3.39999999999999984e-159

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.1

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

   5. Applied rewrites 44.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.5%

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

   if -3.39999999999999984e-159 < a < 9.3999999999999994e97

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 69.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 44.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 27.5%

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

   12. Taylor expanded in a around 0

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

   14. Applied rewrites 26.6%

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

Alternative 14: 36.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot a\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.06:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3100000000:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) a)))
   (if (<= t -2.25e+49)
     t_1
     (if (<= t -0.06) (* y b) (if (<= t 3100000000.0) (+ a x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * a;
	double tmp;
	if (t <= -2.25e+49) {
		tmp = t_1;
	} else if (t <= -0.06) {
		tmp = y * b;
	} else if (t <= 3100000000.0) {
		tmp = a + x;
	} 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 * a
    if (t <= (-2.25d+49)) then
        tmp = t_1
    else if (t <= (-0.06d0)) then
        tmp = y * b
    else if (t <= 3100000000.0d0) then
        tmp = a + x
    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 * a;
	double tmp;
	if (t <= -2.25e+49) {
		tmp = t_1;
	} else if (t <= -0.06) {
		tmp = y * b;
	} else if (t <= 3100000000.0) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * a
	tmp = 0
	if t <= -2.25e+49:
		tmp = t_1
	elif t <= -0.06:
		tmp = y * b
	elif t <= 3100000000.0:
		tmp = a + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * a)
	tmp = 0.0
	if (t <= -2.25e+49)
		tmp = t_1;
	elseif (t <= -0.06)
		tmp = Float64(y * b);
	elseif (t <= 3100000000.0)
		tmp = Float64(a + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * a;
	tmp = 0.0;
	if (t <= -2.25e+49)
		tmp = t_1;
	elseif (t <= -0.06)
		tmp = y * b;
	elseif (t <= 3100000000.0)
		tmp = a + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * a), $MachinePrecision]}, If[LessEqual[t, -2.25e+49], t$95$1, If[LessEqual[t, -0.06], N[(y * b), $MachinePrecision], If[LessEqual[t, 3100000000.0], N[(a + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.24999999999999991e49 or 3.1e9 < t

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 37.7

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

   5. Applied rewrites 37.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 37.5%

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

   if -2.24999999999999991e49 < t < -0.059999999999999998

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.1%

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

   if -0.059999999999999998 < t < 3.1e9

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 35.9%

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

Alternative 15: 67.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.4e-24) (not (<= b 8.5e+124)))
   (* (- (+ t y) 2.0) b)
   (+ (fma (- 1.0 y) z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.4e-24) || !(b <= 8.5e+124)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - y), z, x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.4e-24) || !(b <= 8.5e+124))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.4e-24], N[Not[LessEqual[b, 8.5e+124]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.40000000000000025e-24 or 8.4999999999999997e124 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.2%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 79.0

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

   11. Applied rewrites 79.0%

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

   if -6.40000000000000025e-24 < b < 8.4999999999999997e124

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 72.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-24} \lor \neg \left(b \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+61} \lor \neg \left(y \leq 7.2 \cdot 10^{+19}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7e+61) (not (<= y 7.2e+19)))
   (* (- b z) y)
   (fma (- 1.0 t) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7e+61) || !(y <= 7.2e+19)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((1.0 - t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7e+61) || !(y <= 7.2e+19))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(1.0 - t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7e+61], N[Not[LessEqual[y, 7.2e+19]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000036e61 or 7.2e19 < y

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -7.00000000000000036e61 < y < 7.2e19

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+61} \lor \neg \left(y \leq 7.2 \cdot 10^{+19}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+63} \lor \neg \left(y \leq 6.6 \cdot 10^{+31}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e+63) (not (<= y 6.6e+31))) (* (- b z) y) (* (- b a) t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+63) || !(y <= 6.6e+31)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d+63)) .or. (.not. (y <= 6.6d+31))) then
        tmp = (b - z) * y
    else
        tmp = (b - a) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+63) || !(y <= 6.6e+31)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e+63) or not (y <= 6.6e+31):
		tmp = (b - z) * y
	else:
		tmp = (b - a) * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+63) || !(y <= 6.6e+31))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e+63) || ~((y <= 6.6e+31)))
		tmp = (b - z) * y;
	else
		tmp = (b - a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e+63], N[Not[LessEqual[y, 6.6e+31]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e63 or 6.59999999999999985e31 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -1.9000000000000001e63 < y < 6.59999999999999985e31

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.0

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

   5. Applied rewrites 44.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+63} \lor \neg \left(y \leq 6.6 \cdot 10^{+31}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-20} \lor \neg \left(z \leq 2.9 \cdot 10^{+130}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.35e-20) (not (<= z 2.9e+130)))
   (* (- 1.0 y) z)
   (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.35e-20) || !(z <= 2.9e+130)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.35d-20)) .or. (.not. (z <= 2.9d+130))) then
        tmp = (1.0d0 - y) * z
    else
        tmp = (1.0d0 - t) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.35e-20) || !(z <= 2.9e+130)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.35e-20) or not (z <= 2.9e+130):
		tmp = (1.0 - y) * z
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.35e-20) || !(z <= 2.9e+130))
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.35e-20) || ~((z <= 2.9e+130)))
		tmp = (1.0 - y) * z;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.35e-20], N[Not[LessEqual[z, 2.9e+130]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35000000000000007e-20 or 2.8999999999999999e130 < z

   1. Initial program 88.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 58.0

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

   5. Applied rewrites 58.0%

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

   if -2.35000000000000007e-20 < z < 2.8999999999999999e130

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.6

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

   5. Applied rewrites 38.6%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-20} \lor \neg \left(z \leq 2.9 \cdot 10^{+130}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 33.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+45} \lor \neg \left(b \leq 1.2 \cdot 10^{+55}\right):\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.65e+45) (not (<= b 1.2e+55))) (* (- y 2.0) b) (* (- z) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.65e+45) || !(b <= 1.2e+55)) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.65d+45)) .or. (.not. (b <= 1.2d+55))) then
        tmp = (y - 2.0d0) * b
    else
        tmp = -z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.65e+45) || !(b <= 1.2e+55)) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.65e+45) or not (b <= 1.2e+55):
		tmp = (y - 2.0) * b
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.65e+45) || !(b <= 1.2e+55))
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.65e+45) || ~((b <= 1.2e+55)))
		tmp = (y - 2.0) * b;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.65e+45], N[Not[LessEqual[b, 1.2e+55]], $MachinePrecision]], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-z) * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.65e45 or 1.2e55 < b

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 87.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 52.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 49.2%

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

   12. Taylor expanded in a around 0

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

   14. Applied rewrites 45.0%

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

   if -1.65e45 < b < 1.2e55

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.9

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

   5. Applied rewrites 33.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 31.8%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+45} \lor \neg \left(b \leq 1.2 \cdot 10^{+55}\right):\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+48} \lor \neg \left(b \leq 4.8 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.1e+48) (not (<= b 4.8e+57))) (* y b) (+ a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+48) || !(b <= 4.8e+57)) {
		tmp = y * b;
	} else {
		tmp = a + 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 ((b <= (-2.1d+48)) .or. (.not. (b <= 4.8d+57))) then
        tmp = y * b
    else
        tmp = a + 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 ((b <= -2.1e+48) || !(b <= 4.8e+57)) {
		tmp = y * b;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.1e+48) or not (b <= 4.8e+57):
		tmp = y * b
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.1e+48) || !(b <= 4.8e+57))
		tmp = Float64(y * b);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.1e+48) || ~((b <= 4.8e+57)))
		tmp = y * b;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.1e+48], N[Not[LessEqual[b, 4.8e+57]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0999999999999998e48 or 4.80000000000000009e57 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.3%

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

   if -2.0999999999999998e48 < b < 4.80000000000000009e57

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

   5. Applied rewrites 58.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 31.5%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 28.4%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+48} \lor \neg \left(b \leq 4.8 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.5% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in z around 0

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

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

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

   2. +-commutative N/A

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

   3. mul-1-neg N/A

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

   4. associate-*r* N/A

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

5. Applied rewrites 70.5%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 40.5%

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

9. Taylor expanded in b around 0

   \[\leadsto a + x \]
10. Step-by-step derivation

11. Applied rewrites 20.7%

    \[\leadsto a + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025016 
(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)))