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

Percentage Accurate: 95.3% → 97.4%

Time: 4.5s

Alternatives: 18

Speedup: 1.1×

• 36.3% 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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. associate--l- N/A

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

   17. *-commutative N/A

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

   18. *-commutative N/A

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

3. Applied rewrites 97.4%

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

Alternative 2: 44.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-247}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+94}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -2.9e+33)
     t_1
     (if (<= a -4.5e-247)
       (fma y b x)
       (if (<= a 2.7e-119)
         (fma t b x)
         (if (<= a 9.2e+94) (* (- 1.0 y) z) 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 <= -2.9e+33) {
		tmp = t_1;
	} else if (a <= -4.5e-247) {
		tmp = fma(y, b, x);
	} else if (a <= 2.7e-119) {
		tmp = fma(t, b, x);
	} else if (a <= 9.2e+94) {
		tmp = (1.0 - y) * z;
	} 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 <= -2.9e+33)
		tmp = t_1;
	elseif (a <= -4.5e-247)
		tmp = fma(y, b, x);
	elseif (a <= 2.7e-119)
		tmp = fma(t, b, x);
	elseif (a <= 9.2e+94)
		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[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -2.9e+33], t$95$1, If[LessEqual[a, -4.5e-247], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 2.7e-119], N[(t * b + x), $MachinePrecision], If[LessEqual[a, 9.2e+94], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.90000000000000025e33 or 9.1999999999999999e94 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.4

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

   4. Applied rewrites 55.4%

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

   if -2.90000000000000025e33 < a < -4.5000000000000002e-247

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 63.7

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

   6. Applied rewrites 63.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 38.0%

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

   if -4.5000000000000002e-247 < a < 2.70000000000000027e-119

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 64.0

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

   6. Applied rewrites 64.0%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 42.2%

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

   if 2.70000000000000027e-119 < a < 9.1999999999999999e94

   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. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 28.9

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

   4. Applied rewrites 28.9%

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

Alternative 3: 45.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-247}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-119}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -2.9e+33)
     t_1
     (if (<= a -4.5e-247)
       (fma y b x)
       (if (<= a 3e-119) (fma t b x) (if (<= a 3.5e+111) (fma y b x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -2.9e+33) {
		tmp = t_1;
	} else if (a <= -4.5e-247) {
		tmp = fma(y, b, x);
	} else if (a <= 3e-119) {
		tmp = fma(t, b, x);
	} else if (a <= 3.5e+111) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -2.9e+33)
		tmp = t_1;
	elseif (a <= -4.5e-247)
		tmp = fma(y, b, x);
	elseif (a <= 3e-119)
		tmp = fma(t, b, x);
	elseif (a <= 3.5e+111)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -2.9e+33], t$95$1, If[LessEqual[a, -4.5e-247], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 3e-119], N[(t * b + x), $MachinePrecision], If[LessEqual[a, 3.5e+111], N[(y * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.90000000000000025e33 or 3.5000000000000002e111 < a

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.1

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

   4. Applied rewrites 56.1%

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

   if -2.90000000000000025e33 < a < -4.5000000000000002e-247 or 3.0000000000000002e-119 < a < 3.5000000000000002e111

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 61.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 61.2

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

   6. Applied rewrites 61.2%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 37.2%

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

   if -4.5000000000000002e-247 < a < 3.0000000000000002e-119

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 64.0

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

   6. Applied rewrites 64.0%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 42.2%

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

Alternative 4: 80.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;a + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+144}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(1 - y\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e-23)
   (+ a (* (- (+ y t) 2.0) b))
   (if (<= b 7.8e+144)
     (- x (fma (- t 1.0) a (* (- y 1.0) z)))
     (fma (- (+ t y) 2.0) b (* (- 1.0 y) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e-23) {
		tmp = a + (((y + t) - 2.0) * b);
	} else if (b <= 7.8e+144) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma(((t + y) - 2.0), b, ((1.0 - y) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e-23)
		tmp = Float64(a + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 7.8e+144)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(1.0 - y) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e-23], N[(a + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+144], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1999999999999999e-23

   1. Initial program 92.3%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.9

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

   4. Applied rewrites 71.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   if -2.1999999999999999e-23 < b < 7.80000000000000036e144

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 85.9

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

   4. Applied rewrites 85.9%

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

   if 7.80000000000000036e144 < b

   1. Initial program 88.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   3. Applied rewrites 92.4%

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

   4. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l- N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 84.1

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

   6. Applied rewrites 84.1%

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

Alternative 5: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) - 2\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;a + t\_1 \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+145}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ y t) 2.0)))
   (if (<= b -2.2e-23)
     (+ a (* t_1 b))
     (if (<= b 1.85e+145)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (fma t_1 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) - 2.0;
	double tmp;
	if (b <= -2.2e-23) {
		tmp = a + (t_1 * b);
	} else if (b <= 1.85e+145) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma(t_1, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) - 2.0)
	tmp = 0.0
	if (b <= -2.2e-23)
		tmp = Float64(a + Float64(t_1 * b));
	elseif (b <= 1.85e+145)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(t_1, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -2.2e-23], N[(a + N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+145], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1999999999999999e-23

   1. Initial program 92.3%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.9

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

   4. Applied rewrites 71.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   if -2.1999999999999999e-23 < b < 1.84999999999999997e145

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 85.9

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

   4. Applied rewrites 85.9%

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

   if 1.84999999999999997e145 < b

   1. Initial program 88.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 85.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 85.9

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

   6. Applied rewrites 85.9%

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

Alternative 6: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-133}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;y \leq 23500000:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.8e+50)
     t_1
     (if (<= y -1.5e-133)
       (fma t b x)
       (if (<= y 23500000.0) (* (- b a) t) 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 <= -4.8e+50) {
		tmp = t_1;
	} else if (y <= -1.5e-133) {
		tmp = fma(t, b, x);
	} else if (y <= 23500000.0) {
		tmp = (b - a) * t;
	} 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 <= -4.8e+50)
		tmp = t_1;
	elseif (y <= -1.5e-133)
		tmp = fma(t, b, x);
	elseif (y <= 23500000.0)
		tmp = Float64(Float64(b - a) * t);
	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, -4.8e+50], t$95$1, If[LessEqual[y, -1.5e-133], N[(t * b + x), $MachinePrecision], If[LessEqual[y, 23500000.0], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000004e50 or 2.35e7 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.2

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

   4. Applied rewrites 67.2%

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

   if -4.8000000000000004e50 < y < -1.5000000000000001e-133

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 50.9

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

   6. Applied rewrites 50.9%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 37.5%

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

   if -1.5000000000000001e-133 < y < 2.35e7

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.1

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

   4. Applied rewrites 39.1%

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

Alternative 7: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-102}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+35}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.65e+59)
     t_1
     (if (<= t 2.1e-102)
       (fma y b x)
       (if (<= t 1.25e+35) (* (- 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 <= -1.65e+59) {
		tmp = t_1;
	} else if (t <= 2.1e-102) {
		tmp = fma(y, b, x);
	} else if (t <= 1.25e+35) {
		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 <= -1.65e+59)
		tmp = t_1;
	elseif (t <= 2.1e-102)
		tmp = fma(y, b, x);
	elseif (t <= 1.25e+35)
		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[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.65e+59], t$95$1, If[LessEqual[t, 2.1e-102], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 1.25e+35], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.65e59 or 1.25000000000000005e35 < t

   1. Initial program 91.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.2

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

   4. Applied rewrites 69.2%

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

   if -1.65e59 < t < 2.1e-102

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.5

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

   6. Applied rewrites 51.5%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 39.4%

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

   if 2.1e-102 < t < 1.25000000000000005e35

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 35.5

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

   4. Applied rewrites 35.5%

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

Alternative 8: 69.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) - 2\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;a + t\_1 \cdot b\\ \mathbf{elif}\;b \leq 0.17:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ y t) 2.0)))
   (if (<= b -2.2e-23)
     (+ a (* t_1 b))
     (if (<= b 0.17) (- x (fma (- t 1.0) a (- z))) (fma t_1 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) - 2.0;
	double tmp;
	if (b <= -2.2e-23) {
		tmp = a + (t_1 * b);
	} else if (b <= 0.17) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = fma(t_1, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) - 2.0)
	tmp = 0.0
	if (b <= -2.2e-23)
		tmp = Float64(a + Float64(t_1 * b));
	elseif (b <= 0.17)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = fma(t_1, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -2.2e-23], N[(a + N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.17], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1999999999999999e-23

   1. Initial program 92.3%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.9

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

   4. Applied rewrites 71.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   if -2.1999999999999999e-23 < b < 0.170000000000000012

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 69.6%

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

   if 0.170000000000000012 < b

   1. Initial program 91.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 72.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 72.3

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

   6. Applied rewrites 72.3%

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

Alternative 9: 70.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.17:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ y t) 2.0) b x)))
   (if (<= b -2.2e-23)
     t_1
     (if (<= b 0.17) (- x (fma (- t 1.0) a (- z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((y + t) - 2.0), b, x);
	double tmp;
	if (b <= -2.2e-23) {
		tmp = t_1;
	} else if (b <= 0.17) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(y + t) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.2e-23)
		tmp = t_1;
	elseif (b <= 0.17)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.2e-23], t$95$1, If[LessEqual[b, 0.17], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1999999999999999e-23 or 0.170000000000000012 < b

   1. Initial program 91.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 71.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 71.0

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

   6. Applied rewrites 71.0%

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

   if -2.1999999999999999e-23 < b < 0.170000000000000012

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 69.6%

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

Alternative 10: 64.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-19}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ y t) 2.0) b x)))
   (if (<= b -2.1e-23) t_1 (if (<= b 9e-19) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((y + t) - 2.0), b, x);
	double tmp;
	if (b <= -2.1e-23) {
		tmp = t_1;
	} else if (b <= 9e-19) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(y + t) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.1e-23)
		tmp = t_1;
	elseif (b <= 9e-19)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.1e-23], t$95$1, If[LessEqual[b, 9e-19], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1000000000000001e-23 or 9.00000000000000026e-19 < b

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 70.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 70.4

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

   6. Applied rewrites 70.4%

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

   if -2.1000000000000001e-23 < b < 9.00000000000000026e-19

   1. Initial program 99.1%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.5

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

   4. Applied rewrites 92.5%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 58.0

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

   7. Applied rewrites 58.0%

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

Alternative 11: 60.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-13}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.2e-23) t_1 (if (<= b 1e-13) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.2e-23) {
		tmp = t_1;
	} else if (b <= 1e-13) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-2.2d-23)) then
        tmp = t_1
    else if (b <= 1d-13) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.2e-23) {
		tmp = t_1;
	} else if (b <= 1e-13) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -2.2e-23:
		tmp = t_1
	elif b <= 1e-13:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.2e-23)
		tmp = t_1;
	elseif (b <= 1e-13)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.2e-23)
		tmp = t_1;
	elseif (b <= 1e-13)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.2e-23], t$95$1, If[LessEqual[b, 1e-13], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1999999999999999e-23 or 1e-13 < b

   1. Initial program 92.1%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 62.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 62.2

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

   4. Applied rewrites 62.2%

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

   if -2.1999999999999999e-23 < b < 1e-13

   1. Initial program 99.1%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.4

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

   4. Applied rewrites 92.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 57.9

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

   7. Applied rewrites 57.9%

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

Alternative 12: 57.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.8e+50) t_1 (if (<= y 6.8e+38) (fma (- t 2.0) b 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 <= -4.8e+50) {
		tmp = t_1;
	} else if (y <= 6.8e+38) {
		tmp = fma((t - 2.0), b, 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 <= -4.8e+50)
		tmp = t_1;
	elseif (y <= 6.8e+38)
		tmp = fma(Float64(t - 2.0), b, 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, -4.8e+50], t$95$1, If[LessEqual[y, 6.8e+38], N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000004e50 or 6.79999999999999992e38 < y

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.0

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

   4. Applied rewrites 69.0%

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

   if -4.8000000000000004e50 < y < 6.79999999999999992e38

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.0

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

   6. Applied rewrites 51.0%

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

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{t} - 2, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 49.1%

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

Alternative 13: 39.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e-12) (fma y b x) (if (<= y 4.8e+45) (fma t b x) (* (- z) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e-12) {
		tmp = fma(y, b, x);
	} else if (y <= 4.8e+45) {
		tmp = fma(t, b, x);
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e-12)
		tmp = fma(y, b, x);
	elseif (y <= 4.8e+45)
		tmp = fma(t, b, x);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e-12], N[(y * b + x), $MachinePrecision], If[LessEqual[y, 4.8e+45], N[(t * b + x), $MachinePrecision], N[((-z) * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000002e-12

   1. Initial program 92.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 50.7

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

   6. Applied rewrites 50.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 41.0%

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

   if -2.9000000000000002e-12 < y < 4.79999999999999979e45

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.1

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

   6. Applied rewrites 51.1%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 39.4%

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

   if 4.79999999999999979e45 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y \]

      2. lift-neg.f64 39.6

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

   7. Applied rewrites 39.6%

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

Alternative 14: 40.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e-12) (fma y b x) (if (<= y 6e+23) (fma t b x) (fma y b x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e-12) {
		tmp = fma(y, b, x);
	} else if (y <= 6e+23) {
		tmp = fma(t, b, x);
	} else {
		tmp = fma(y, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e-12)
		tmp = fma(y, b, x);
	elseif (y <= 6e+23)
		tmp = fma(t, b, x);
	else
		tmp = fma(y, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e-12], N[(y * b + x), $MachinePrecision], If[LessEqual[y, 6e+23], N[(t * b + x), $MachinePrecision], N[(y * b + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-12 or 6.0000000000000002e23 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 50.7

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

   6. Applied rewrites 50.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 42.3%

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

   if -2.9000000000000002e-12 < y < 6.0000000000000002e23

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.1

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

   6. Applied rewrites 51.1%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 39.5%

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

Alternative 15: 37.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+51}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3e+51) (* b y) (if (<= y 2.1e+44) (fma t b x) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3e+51) {
		tmp = b * y;
	} else if (y <= 2.1e+44) {
		tmp = fma(t, b, x);
	} else {
		tmp = b * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3e+51)
		tmp = Float64(b * y);
	elseif (y <= 2.1e+44)
		tmp = fma(t, b, x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3e+51], N[(b * y), $MachinePrecision], If[LessEqual[y, 2.1e+44], N[(t * b + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e51 or 2.09999999999999987e44 < y

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 36.3%

      \[\leadsto b \cdot y \]

   if -3e51 < y < 2.09999999999999987e44

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lift--.f64 N/A

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

      10. lift-+.f64 51.1

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

   6. Applied rewrites 51.1%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 38.9%

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

Alternative 16: 27.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-12}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e-12) (* b y) (if (<= y 6e+23) (* b t) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e-12) {
		tmp = b * y;
	} else if (y <= 6e+23) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.9d-12)) then
        tmp = b * y
    else if (y <= 6d+23) then
        tmp = b * t
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e-12) {
		tmp = b * y;
	} else if (y <= 6e+23) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.9e-12:
		tmp = b * y
	elif y <= 6e+23:
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e-12)
		tmp = Float64(b * y);
	elseif (y <= 6e+23)
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.9e-12)
		tmp = b * y;
	elseif (y <= 6e+23)
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e-12], N[(b * y), $MachinePrecision], If[LessEqual[y, 6e+23], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e-12 or 6.0000000000000002e23 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.5

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

   4. Applied rewrites 64.5%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 33.5%

      \[\leadsto b \cdot y \]

   if -2.9000000000000002e-12 < y < 6.0000000000000002e23

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.6

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

   4. Applied rewrites 38.6%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 21.4%

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

Alternative 17: 27.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+59}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.66e+59) (* b t) (if (<= t 1.7e+33) x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.66e+59) {
		tmp = b * t;
	} else if (t <= 1.7e+33) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.66d+59)) then
        tmp = b * t
    else if (t <= 1.7d+33) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.66e+59) {
		tmp = b * t;
	} else if (t <= 1.7e+33) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.66e+59:
		tmp = b * t
	elif t <= 1.7e+33:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.66e+59)
		tmp = Float64(b * t);
	elseif (t <= 1.7e+33)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.66e+59)
		tmp = b * t;
	elseif (t <= 1.7e+33)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.66e+59], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.7e+33], x, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6599999999999999e59 or 1.7e33 < t

   1. Initial program 91.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.2

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

   4. Applied rewrites 69.2%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 37.0%

      \[\leadsto b \cdot t \]

   if -1.6599999999999999e59 < t < 1.7e33

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 15.6% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.3%

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

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 15.6%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025095 
(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)))