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

Percentage Accurate: 95.0% → 97.0%

Time: 13.3s

Alternatives: 18

Speedup: 0.9×

• 36.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{+190}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \mathsf{fma}\left(t - 1, a, \mathsf{fma}\left(z, y, -z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(y - 2, b, b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.8e+190)
   (fma (- (+ t y) 2.0) b (- x (fma (- t 1.0) a (fma z y (- z)))))
   (+ x (fma (- y 2.0) b (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.8e+190) {
		tmp = fma(((t + y) - 2.0), b, (x - fma((t - 1.0), a, fma(z, y, -z))));
	} else {
		tmp = x + fma((y - 2.0), b, (b * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.8e+190)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - fma(Float64(t - 1.0), a, fma(z, y, Float64(-z)))));
	else
		tmp = Float64(x + fma(Float64(y - 2.0), b, Float64(b * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.8e+190], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(z * y + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - 2.0), $MachinePrecision] * b + N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.79999999999999964e190

   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. Add Preprocessing
   3. 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

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 99.1

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

   7. Applied rewrites 99.1%

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

   if 3.79999999999999964e190 < b

   1. Initial program 76.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.2%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 100.0

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

   7. Applied rewrites 100.0%

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

Alternative 2: 47.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, z\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-116}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-86}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z z)) (t_2 (* (- b a) t)))
   (if (<= t -5e+19)
     t_2
     (if (<= t 1.15e-265)
       t_1
       (if (<= t 1.3e-116)
         (* (- y 2.0) b)
         (if (<= t 1.35e-86) (* (- 1.0 t) a) (if (<= t 1.2e+61) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, z);
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5e+19) {
		tmp = t_2;
	} else if (t <= 1.15e-265) {
		tmp = t_1;
	} else if (t <= 1.3e-116) {
		tmp = (y - 2.0) * b;
	} else if (t <= 1.35e-86) {
		tmp = (1.0 - t) * a;
	} else if (t <= 1.2e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, z)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5e+19)
		tmp = t_2;
	elseif (t <= 1.15e-265)
		tmp = t_1;
	elseif (t <= 1.3e-116)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 1.35e-86)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (t <= 1.2e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5e+19], t$95$2, If[LessEqual[t, 1.15e-265], t$95$1, If[LessEqual[t, 1.3e-116], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 1.35e-86], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, 1.2e+61], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5e19 or 1.1999999999999999e61 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if -5e19 < t < 1.1499999999999999e-265 or 1.34999999999999996e-86 < t < 1.1999999999999999e61

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.0

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

   5. Applied rewrites 38.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 38.0

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

   8. Applied rewrites 38.0%

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

   if 1.1499999999999999e-265 < t < 1.3e-116

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 61.8

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

   7. Applied rewrites 61.8%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 61.8

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

   10. Applied rewrites 61.8%

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

   if 1.3e-116 < t < 1.34999999999999996e-86

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.2

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

   5. Applied rewrites 53.2%

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

Alternative 3: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t b (- x (* (- y 1.0) z)))))
   (if (<= z -2.1e+152)
     t_1
     (if (<= z 3.3e-99)
       (fma (- (+ t y) 2.0) b (- x (- z)))
       (if (<= z 1.12e+42) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, b, (x - ((y - 1.0) * z)));
	double tmp;
	if (z <= -2.1e+152) {
		tmp = t_1;
	} else if (z <= 3.3e-99) {
		tmp = fma(((t + y) - 2.0), b, (x - -z));
	} else if (z <= 1.12e+42) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, b, Float64(x - Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (z <= -2.1e+152)
		tmp = t_1;
	elseif (z <= 3.3e-99)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-z)));
	elseif (z <= 1.12e+42)
		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[(t * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+152], t$95$1, If[LessEqual[z, 3.3e-99], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+42], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000002e152 or 1.12e42 < z

   1. Initial program 93.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 87.0

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

   7. Applied rewrites 87.0%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 82.9%

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

   if -2.1000000000000002e152 < z < 3.29999999999999986e-99

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 66.6

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

   10. Applied rewrites 66.6%

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

   if 3.29999999999999986e-99 < z < 1.12e42

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 75.7

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

   5. Applied rewrites 75.7%

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

Alternative 4: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t b (- x (* (- y 1.0) z)))))
   (if (<= z -2.1e+152)
     t_1
     (if (<= z 3.3e-99)
       (+ x (* (- (+ y t) 2.0) b))
       (if (<= z 1.12e+42) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, b, (x - ((y - 1.0) * z)));
	double tmp;
	if (z <= -2.1e+152) {
		tmp = t_1;
	} else if (z <= 3.3e-99) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 1.12e+42) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, b, Float64(x - Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (z <= -2.1e+152)
		tmp = t_1;
	elseif (z <= 3.3e-99)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (z <= 1.12e+42)
		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[(t * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+152], t$95$1, If[LessEqual[z, 3.3e-99], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+42], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000002e152 or 1.12e42 < z

   1. Initial program 93.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 87.0

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

   7. Applied rewrites 87.0%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 82.9%

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

   if -2.1000000000000002e152 < z < 3.29999999999999986e-99

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.1%

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

   if 3.29999999999999986e-99 < z < 1.12e42

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 75.7

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

   5. Applied rewrites 75.7%

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

Alternative 5: 83.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+171}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9e+113)
   (fma (- (+ t y) 2.0) b (- x (- z)))
   (if (<= b 2.7e+171)
     (- x (fma (- t 1.0) a (* (- y 1.0) z)))
     (+ x (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e+113) {
		tmp = fma(((t + y) - 2.0), b, (x - -z));
	} else if (b <= 2.7e+171) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9e+113)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-z)));
	elseif (b <= 2.7e+171)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9e+113], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+171], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.0000000000000001e113

   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. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 86.9

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

   7. Applied rewrites 86.9%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 91.6

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

   10. Applied rewrites 91.6%

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

   if -9.0000000000000001e113 < b < 2.6999999999999998e171

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if 2.6999999999999998e171 < b

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.9%

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

Alternative 6: 26.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 10^{-267}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-84}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 82000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.2e+74)
   (* b y)
   (if (<= y 1e-267)
     x
     (if (<= y 1.4e-84) z (if (<= y 82000000.0) x (* b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e+74) {
		tmp = b * y;
	} else if (y <= 1e-267) {
		tmp = x;
	} else if (y <= 1.4e-84) {
		tmp = z;
	} else if (y <= 82000000.0) {
		tmp = x;
	} 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 <= (-4.2d+74)) then
        tmp = b * y
    else if (y <= 1d-267) then
        tmp = x
    else if (y <= 1.4d-84) then
        tmp = z
    else if (y <= 82000000.0d0) then
        tmp = x
    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 <= -4.2e+74) {
		tmp = b * y;
	} else if (y <= 1e-267) {
		tmp = x;
	} else if (y <= 1.4e-84) {
		tmp = z;
	} else if (y <= 82000000.0) {
		tmp = x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.2e+74:
		tmp = b * y
	elif y <= 1e-267:
		tmp = x
	elif y <= 1.4e-84:
		tmp = z
	elif y <= 82000000.0:
		tmp = x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.2e+74)
		tmp = Float64(b * y);
	elseif (y <= 1e-267)
		tmp = x;
	elseif (y <= 1.4e-84)
		tmp = z;
	elseif (y <= 82000000.0)
		tmp = x;
	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 <= -4.2e+74)
		tmp = b * y;
	elseif (y <= 1e-267)
		tmp = x;
	elseif (y <= 1.4e-84)
		tmp = z;
	elseif (y <= 82000000.0)
		tmp = x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.2e+74], N[(b * y), $MachinePrecision], If[LessEqual[y, 1e-267], x, If[LessEqual[y, 1.4e-84], z, If[LessEqual[y, 82000000.0], x, N[(b * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999998e74 or 8.2e7 < y

   1. Initial program 91.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 94.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 48.4

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

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 41.3

         \[\leadsto b \cdot y \]

   10. Applied rewrites 41.3%

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

   if -4.1999999999999998e74 < y < 9.9999999999999998e-268 or 1.39999999999999991e-84 < y < 8.2e7

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 30.9%

      \[\leadsto \color{blue}{x} \]

   if 9.9999999999999998e-268 < y < 1.39999999999999991e-84

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. 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 29.5

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

   5. Applied rewrites 29.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 29.5%

      \[\leadsto z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 58.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, z\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+45}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z z)))
   (if (<= z -3.3e+172)
     t_1
     (if (<= z 3.3e-99)
       (+ x (* (- (+ y t) 2.0) b))
       (if (<= z 2.2e+45) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, z);
	double tmp;
	if (z <= -3.3e+172) {
		tmp = t_1;
	} else if (z <= 3.3e-99) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 2.2e+45) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, z)
	tmp = 0.0
	if (z <= -3.3e+172)
		tmp = t_1;
	elseif (z <= 3.3e-99)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (z <= 2.2e+45)
		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[((-y) * z + z), $MachinePrecision]}, If[LessEqual[z, -3.3e+172], t$95$1, If[LessEqual[z, 3.3e-99], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+45], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999983e172 or 2.2e45 < z

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. 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 61.0

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 61.0

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

   8. Applied rewrites 61.0%

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

   if -3.29999999999999983e172 < z < 3.29999999999999986e-99

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.7%

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

   if 3.29999999999999986e-99 < z < 2.2e45

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 75.7

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

   5. Applied rewrites 75.7%

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

Alternative 8: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-285}:\\ \;\;\;\;x + b \cdot t\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.3e+30)
     t_1
     (if (<= y -1.9e-285)
       (+ x (* b t))
       (if (<= y 1.16e+51) (* (- 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 <= -1.3e+30) {
		tmp = t_1;
	} else if (y <= -1.9e-285) {
		tmp = x + (b * t);
	} else if (y <= 1.16e+51) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-1.3d+30)) then
        tmp = t_1
    else if (y <= (-1.9d-285)) then
        tmp = x + (b * t)
    else if (y <= 1.16d+51) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.3e+30) {
		tmp = t_1;
	} else if (y <= -1.9e-285) {
		tmp = x + (b * t);
	} else if (y <= 1.16e+51) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -1.3e+30:
		tmp = t_1
	elif y <= -1.9e-285:
		tmp = x + (b * t)
	elif y <= 1.16e+51:
		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 <= -1.3e+30)
		tmp = t_1;
	elseif (y <= -1.9e-285)
		tmp = Float64(x + Float64(b * t));
	elseif (y <= 1.16e+51)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -1.3e+30)
		tmp = t_1;
	elseif (y <= -1.9e-285)
		tmp = x + (b * t);
	elseif (y <= 1.16e+51)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.3e+30], t$95$1, If[LessEqual[y, -1.9e-285], N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+51], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.29999999999999994e30 or 1.16e51 < y

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.4

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

   5. Applied rewrites 67.4%

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

   if -1.29999999999999994e30 < y < -1.9000000000000001e-285

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.3%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 51.5

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

   8. Applied rewrites 51.5%

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

   if -1.9000000000000001e-285 < y < 1.16e51

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 46.1

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

   5. Applied rewrites 46.1%

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

Alternative 9: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-87}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -2.7e+61)
     t_1
     (if (<= a -1.55e-87)
       (* (- y 2.0) b)
       (if (<= a 7.5e+32) (fma (- y) z 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 <= -2.7e+61) {
		tmp = t_1;
	} else if (a <= -1.55e-87) {
		tmp = (y - 2.0) * b;
	} else if (a <= 7.5e+32) {
		tmp = fma(-y, z, 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 <= -2.7e+61)
		tmp = t_1;
	elseif (a <= -1.55e-87)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (a <= 7.5e+32)
		tmp = fma(Float64(-y), z, 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, -2.7e+61], t$95$1, If[LessEqual[a, -1.55e-87], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 7.5e+32], N[((-y) * z + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7000000000000002e61 or 7.49999999999999959e32 < a

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9

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

   5. Applied rewrites 56.9%

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

   if -2.7000000000000002e61 < a < -1.54999999999999999e-87

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 53.8

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

   7. Applied rewrites 53.8%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 36.3

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

   10. Applied rewrites 36.3%

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

   if -1.54999999999999999e-87 < a < 7.49999999999999959e32

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.5

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

   5. Applied rewrites 39.5%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 39.5

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

   8. Applied rewrites 39.5%

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

Alternative 10: 26.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+109)
   (* b y)
   (if (<= b 4.8e-128) x (if (<= b 4.2e+42) (* (- a) t) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 4.8e-128) {
		tmp = x;
	} else if (b <= 4.2e+42) {
		tmp = -a * t;
	} 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 (b <= (-9.5d+109)) then
        tmp = b * y
    else if (b <= 4.8d-128) then
        tmp = x
    else if (b <= 4.2d+42) then
        tmp = -a * t
    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 (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 4.8e-128) {
		tmp = x;
	} else if (b <= 4.2e+42) {
		tmp = -a * t;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+109:
		tmp = b * y
	elif b <= 4.8e-128:
		tmp = x
	elif b <= 4.2e+42:
		tmp = -a * t
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+109)
		tmp = Float64(b * y);
	elseif (b <= 4.8e-128)
		tmp = x;
	elseif (b <= 4.2e+42)
		tmp = Float64(Float64(-a) * t);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+109)
		tmp = b * y;
	elseif (b <= 4.8e-128)
		tmp = x;
	elseif (b <= 4.2e+42)
		tmp = -a * t;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+109], N[(b * y), $MachinePrecision], If[LessEqual[b, 4.8e-128], x, If[LessEqual[b, 4.2e+42], N[((-a) * t), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999972e109

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 44.7

         \[\leadsto b \cdot y \]

   10. Applied rewrites 44.7%

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

   if -9.49999999999999972e109 < b < 4.7999999999999996e-128

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 28.0%

      \[\leadsto \color{blue}{x} \]

   if 4.7999999999999996e-128 < b < 4.19999999999999991e42

   1. Initial program 95.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 42.2

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

   5. Applied rewrites 42.2%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot t \]

      2. lower-neg.f64 33.6

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

   8. Applied rewrites 33.6%

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

   if 4.19999999999999991e42 < b

   1. Initial program 87.7%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 51.6

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

   5. Applied rewrites 51.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 44.8%

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

Alternative 11: 26.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+59}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+109)
   (* b y)
   (if (<= b 8.2e-66) x (if (<= b 1.8e+59) (* (- y) z) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 8.2e-66) {
		tmp = x;
	} else if (b <= 1.8e+59) {
		tmp = -y * z;
	} 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 (b <= (-9.5d+109)) then
        tmp = b * y
    else if (b <= 8.2d-66) then
        tmp = x
    else if (b <= 1.8d+59) then
        tmp = -y * z
    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 (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 8.2e-66) {
		tmp = x;
	} else if (b <= 1.8e+59) {
		tmp = -y * z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+109:
		tmp = b * y
	elif b <= 8.2e-66:
		tmp = x
	elif b <= 1.8e+59:
		tmp = -y * z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+109)
		tmp = Float64(b * y);
	elseif (b <= 8.2e-66)
		tmp = x;
	elseif (b <= 1.8e+59)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+109)
		tmp = b * y;
	elseif (b <= 8.2e-66)
		tmp = x;
	elseif (b <= 1.8e+59)
		tmp = -y * z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+109], N[(b * y), $MachinePrecision], If[LessEqual[b, 8.2e-66], x, If[LessEqual[b, 1.8e+59], N[((-y) * z), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999972e109

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 44.7

         \[\leadsto b \cdot y \]

   10. Applied rewrites 44.7%

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

   if -9.49999999999999972e109 < b < 8.19999999999999996e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 27.3%

      \[\leadsto \color{blue}{x} \]

   if 8.19999999999999996e-66 < b < 1.7999999999999999e59

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. 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 39.5

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

   5. Applied rewrites 39.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 30.2

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

   8. Applied rewrites 30.2%

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

   if 1.7999999999999999e59 < b

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 52.5

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

   5. Applied rewrites 52.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 45.4%

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

Alternative 12: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+19} \lor \neg \left(t \leq 1.2 \cdot 10^{+61}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e+19) (not (<= t 1.2e+61))) (* (- b a) t) (* (- b z) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+19) || !(t <= 1.2e+61)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.2d+19)) .or. (.not. (t <= 1.2d+61))) then
        tmp = (b - a) * t
    else
        tmp = (b - z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+19) || !(t <= 1.2e+61)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e+19) or not (t <= 1.2e+61):
		tmp = (b - a) * t
	else:
		tmp = (b - z) * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e+19) || !(t <= 1.2e+61))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(b - z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.2e+19) || ~((t <= 1.2e+61)))
		tmp = (b - a) * t;
	else
		tmp = (b - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e+19], N[Not[LessEqual[t, 1.2e+61]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e19 or 1.1999999999999999e61 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if -5.2e19 < t < 1.1999999999999999e61

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.5

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

   5. Applied rewrites 39.5%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+19} \lor \neg \left(t \leq 1.2 \cdot 10^{+61}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+151} \lor \neg \left(b \leq 5.3 \cdot 10^{+149}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.2e+151) (not (<= b 5.3e+149)))
   (* (- t 2.0) b)
   (fma (- y) z z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+151) || !(b <= 5.3e+149)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = fma(-y, z, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.2e+151) || !(b <= 5.3e+149))
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = fma(Float64(-y), z, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.2e+151], N[Not[LessEqual[b, 5.3e+149]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-y) * z + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.1999999999999996e151 or 5.30000000000000032e149 < b

   1. Initial program 88.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 90.1%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 86.0

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

   7. Applied rewrites 86.0%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.7

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

   10. Applied rewrites 60.7%

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

   if -8.1999999999999996e151 < b < 5.30000000000000032e149

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. 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 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 35.3

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

   8. Applied rewrites 35.3%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+151} \lor \neg \left(b \leq 5.3 \cdot 10^{+149}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+110}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+110)
   (* (- y 2.0) b)
   (if (<= b 5.3e+149) (fma (- y) z z) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+110) {
		tmp = (y - 2.0) * b;
	} else if (b <= 5.3e+149) {
		tmp = fma(-y, z, z);
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+110)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 5.3e+149)
		tmp = fma(Float64(-y), z, z);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+110], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 5.3e+149], N[((-y) * z + z), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e110

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 53.9

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

   10. Applied rewrites 53.9%

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

   if -1.15e110 < b < 5.30000000000000032e149

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

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

   5. Applied rewrites 35.5%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 35.5

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

   8. Applied rewrites 35.5%

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

   if 5.30000000000000032e149 < b

   1. Initial program 82.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 85.3%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 88.6

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

   7. Applied rewrites 88.6%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.8

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

   10. Applied rewrites 67.8%

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

Alternative 15: 34.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+110) (* b y) (if (<= b 5.3e+149) (fma (- y) z z) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+110) {
		tmp = b * y;
	} else if (b <= 5.3e+149) {
		tmp = fma(-y, z, z);
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+110)
		tmp = Float64(b * y);
	elseif (b <= 5.3e+149)
		tmp = fma(Float64(-y), z, z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+110], N[(b * y), $MachinePrecision], If[LessEqual[b, 5.3e+149], N[((-y) * z + z), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.24999999999999995e110

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 44.7

         \[\leadsto b \cdot y \]

   10. Applied rewrites 44.7%

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

   if -1.24999999999999995e110 < b < 5.30000000000000032e149

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

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

   5. Applied rewrites 35.5%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 35.5

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

   8. Applied rewrites 35.5%

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

   if 5.30000000000000032e149 < b

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 56.6%

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

Alternative 16: 25.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 1750000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+109) (* b y) (if (<= b 1750000000000.0) x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 1750000000000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+109)) then
        tmp = b * y
    else if (b <= 1750000000000.0d0) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+109) {
		tmp = b * y;
	} else if (b <= 1750000000000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+109:
		tmp = b * y
	elif b <= 1750000000000.0:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+109)
		tmp = Float64(b * y);
	elseif (b <= 1750000000000.0)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+109)
		tmp = b * y;
	elseif (b <= 1750000000000.0)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+109], N[(b * y), $MachinePrecision], If[LessEqual[b, 1750000000000.0], x, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.49999999999999972e109

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. 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

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in b around inf

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate--l- N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lift--.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 79.5

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 44.7

         \[\leadsto b \cdot y \]

   10. Applied rewrites 44.7%

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

   if -9.49999999999999972e109 < b < 1.75e12

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 25.6%

      \[\leadsto \color{blue}{x} \]

   if 1.75e12 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 48.6

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

   5. Applied rewrites 48.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 39.5%

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

Alternative 17: 21.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+89}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.6e+79) x (if (<= x 9.8e+89) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.6e+79) {
		tmp = x;
	} else if (x <= 9.8e+89) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5.6d+79)) then
        tmp = x
    else if (x <= 9.8d+89) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.6e+79) {
		tmp = x;
	} else if (x <= 9.8e+89) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.6e+79:
		tmp = x
	elif x <= 9.8e+89:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.6e+79)
		tmp = x;
	elseif (x <= 9.8e+89)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.6e+79)
		tmp = x;
	elseif (x <= 9.8e+89)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.6e+79], x, If[LessEqual[x, 9.8e+89], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6000000000000002e79 or 9.79999999999999992e89 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{x} \]

   if -5.6000000000000002e79 < x < 9.79999999999999992e89

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. 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 29.6

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

   5. Applied rewrites 29.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 16.0%

      \[\leadsto z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 16.0% 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 95.7%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 18.1%

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

Reproduce

herbie shell --seed 2025045 
(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)))