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

Percentage Accurate: 95.4% → 97.5%

Time: 5.2s

Alternatives: 21

Speedup: 1.0×

• 36.7% 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: 95.4% 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: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 49.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 49.9

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

   4. Applied rewrites 49.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate--l+ N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 46.4

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

   6. Applied rewrites 46.4%

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

Alternative 2: 96.9% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1e+92)
   (+ x (- (fma (- b a) t (* (- y 2.0) b)) (fma (- y 1.0) z (- a))))
   (+ x (- (fma (- b z) y (* (- t 2.0) b)) (fma (- t 1.0) a (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1e+92) {
		tmp = x + (fma((b - a), t, ((y - 2.0) * b)) - fma((y - 1.0), z, -a));
	} else {
		tmp = x + (fma((b - z), y, ((t - 2.0) * b)) - fma((t - 1.0), a, -z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1e+92)
		tmp = Float64(x + Float64(fma(Float64(b - a), t, Float64(Float64(y - 2.0) * b)) - fma(Float64(y - 1.0), z, Float64(-a))));
	else
		tmp = Float64(x + Float64(fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b)) - fma(Float64(t - 1.0), a, Float64(-z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1e+92], N[(x + N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1e92

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.5

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

   4. Applied rewrites 97.5%

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

   if 1e92 < y

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 93.9

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

   4. Applied rewrites 93.9%

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

Alternative 3: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

2. Taylor expanded in t around 0

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

   1. associate--l+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower--.f64 N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift--.f64 N/A

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

   15. mul-1-neg N/A

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

   16. lower-neg.f64 96.2

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

4. Applied rewrites 96.2%

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

Alternative 4: 83.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+126}:\\ \;\;\;\;x + \mathsf{fma}\left(t - 2, b, b \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-y, z, z\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.1e+126)
   (+ x (fma (- t 2.0) b (* b y)))
   (if (<= b 1.9e+83)
     (+ x (- (fma (- y) z z) (* a (- t 1.0))))
     (+ 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 <= -5.1e+126) {
		tmp = x + fma((t - 2.0), b, (b * y));
	} else if (b <= 1.9e+83) {
		tmp = x + (fma(-y, z, z) - (a * (t - 1.0)));
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.1e+126)
		tmp = Float64(x + fma(Float64(t - 2.0), b, Float64(b * y)));
	elseif (b <= 1.9e+83)
		tmp = Float64(x + Float64(fma(Float64(-y), z, z) - Float64(a * Float64(t - 1.0))));
	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, -5.1e+126], N[(x + N[(N[(t - 2.0), $MachinePrecision] * b + N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+83], N[(x + N[(N[((-y) * z + z), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $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 < -5.1000000000000001e126

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 85.8%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   5. 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. associate--l+ N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 82.6

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

   6. Applied rewrites 82.6%

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

   if -5.1000000000000001e126 < b < 1.9000000000000001e83

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 84.0

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

   7. Applied rewrites 84.0%

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

   if 1.9000000000000001e83 < b

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 80.7%

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

Alternative 5: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+126}:\\ \;\;\;\;x + \mathsf{fma}\left(t - 2, b, b \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.1e+126)
   (+ x (fma (- t 2.0) b (* b y)))
   (if (<= b 1.9e+83)
     (- (fma (- 1.0 y) z x) (* (- t 1.0) a))
     (+ 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 <= -5.1e+126) {
		tmp = x + fma((t - 2.0), b, (b * y));
	} else if (b <= 1.9e+83) {
		tmp = fma((1.0 - y), z, x) - ((t - 1.0) * a);
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.1e+126)
		tmp = Float64(x + fma(Float64(t - 2.0), b, Float64(b * y)));
	elseif (b <= 1.9e+83)
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a));
	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, -5.1e+126], N[(x + N[(N[(t - 2.0), $MachinePrecision] * b + N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+83], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $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 < -5.1000000000000001e126

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 85.8%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   5. 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. associate--l+ N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 82.6

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

   6. Applied rewrites 82.6%

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

   if -5.1000000000000001e126 < b < 1.9000000000000001e83

   1. Initial program 98.2%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

      5. *-commutative N/A

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

      6. lower--.f64 N/A

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

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

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. sub-negate-rev N/A

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

      12. +-commutative N/A

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

      13. sub-negate-rev N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-negate-rev N/A

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

      19. lower--.f64 N/A

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

   4. Applied rewrites 84.0%

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

   if 1.9000000000000001e83 < b

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 80.7%

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

Alternative 6: 71.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3400000000:\\ \;\;\;\;x + \left(z - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -4.8e+93)
     t_1
     (if (<= b 3400000000.0) (+ x (- z (* a (- t 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -4.8e+93) {
		tmp = t_1;
	} else if (b <= 3400000000.0) {
		tmp = x + (z - (a * (t - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-4.8d+93)) then
        tmp = t_1
    else if (b <= 3400000000.0d0) then
        tmp = x + (z - (a * (t - 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -4.8e+93) {
		tmp = t_1;
	} else if (b <= 3400000000.0) {
		tmp = x + (z - (a * (t - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -4.8e+93:
		tmp = t_1
	elif b <= 3400000000.0:
		tmp = x + (z - (a * (t - 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -4.8e+93)
		tmp = t_1;
	elseif (b <= 3400000000.0)
		tmp = Float64(x + Float64(z - Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -4.8e+93)
		tmp = t_1;
	elseif (b <= 3400000000.0)
		tmp = x + (z - (a * (t - 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+93], t$95$1, If[LessEqual[b, 3400000000.0], N[(x + N[(z - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.80000000000000021e93 or 3.4e9 < b

   1. Initial program 90.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 77.3%

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

   if -4.80000000000000021e93 < b < 3.4e9

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 87.9

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

   7. Applied rewrites 87.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 67.9%

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

Alternative 7: 68.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+95}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 106000000000:\\ \;\;\;\;x + \left(z - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, b \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e+95)
   (* (- (+ t y) 2.0) b)
   (if (<= b 106000000000.0)
     (+ x (- z (* a (- t 1.0))))
     (fma (- t 2.0) b (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+95) {
		tmp = ((t + y) - 2.0) * b;
	} else if (b <= 106000000000.0) {
		tmp = x + (z - (a * (t - 1.0)));
	} else {
		tmp = fma((t - 2.0), b, (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e+95)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	elseif (b <= 106000000000.0)
		tmp = Float64(x + Float64(z - Float64(a * Float64(t - 1.0))));
	else
		tmp = fma(Float64(t - 2.0), b, Float64(b * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e+95], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 106000000000.0], N[(x + N[(z - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(b * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2999999999999998e95

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 77.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 77.7

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

   4. Applied rewrites 77.7%

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

   if -3.2999999999999998e95 < b < 1.06e11

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 87.8

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

   7. Applied rewrites 87.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 67.9%

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

   if 1.06e11 < b

   1. Initial program 90.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 66.5

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 66.5

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

   4. Applied rewrites 66.5%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lift-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 64.4

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

   6. Applied rewrites 64.4%

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

Alternative 8: 62.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.82:\\ \;\;\;\;x + \left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.6e+88) t_1 (if (<= b 0.82) (+ x (* (- 1.0 t) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.6e+88) {
		tmp = t_1;
	} else if (b <= 0.82) {
		tmp = x + ((1.0 - t) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-2.6d+88)) then
        tmp = t_1
    else if (b <= 0.82d0) then
        tmp = x + ((1.0d0 - t) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.6e+88) {
		tmp = t_1;
	} else if (b <= 0.82) {
		tmp = x + ((1.0 - t) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -2.6e+88:
		tmp = t_1
	elif b <= 0.82:
		tmp = x + ((1.0 - t) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.6e+88)
		tmp = t_1;
	elseif (b <= 0.82)
		tmp = Float64(x + Float64(Float64(1.0 - t) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.6e+88)
		tmp = t_1;
	elseif (b <= 0.82)
		tmp = x + ((1.0 - t) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.6e+88], t$95$1, If[LessEqual[b, 0.82], N[(x + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6000000000000001e88 or 0.819999999999999951 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 70.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 70.2

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

   4. Applied rewrites 70.2%

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

   if -2.6000000000000001e88 < b < 0.819999999999999951

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto x + \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      3. sub-flip N/A

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

      4. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      8. sub-negate-rev N/A

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

      9. lower--.f64 56.3

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

   7. Applied rewrites 56.3%

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

Alternative 9: 61.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 0.82:\\ \;\;\;\;x + \left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, b \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.6e+88)
   (* (- (+ t y) 2.0) b)
   (if (<= b 0.82) (+ x (* (- 1.0 t) a)) (fma (- t 2.0) b (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+88) {
		tmp = ((t + y) - 2.0) * b;
	} else if (b <= 0.82) {
		tmp = x + ((1.0 - t) * a);
	} else {
		tmp = fma((t - 2.0), b, (b * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.6e+88)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	elseif (b <= 0.82)
		tmp = Float64(x + Float64(Float64(1.0 - t) * a));
	else
		tmp = fma(Float64(t - 2.0), b, Float64(b * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.6e+88], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 0.82], N[(x + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(b * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000001e88

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 76.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 76.9

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

   4. Applied rewrites 76.9%

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

   if -2.6000000000000001e88 < b < 0.819999999999999951

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.0

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

   4. Applied rewrites 99.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto x + \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      3. sub-flip N/A

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

      4. sub-negate-rev N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      8. sub-negate-rev N/A

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

      9. lower--.f64 56.3

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

   7. Applied rewrites 56.3%

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

   if 0.819999999999999951 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 65.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 65.6

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

   4. Applied rewrites 65.6%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lift-fma.f64 N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 63.6

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

   6. Applied rewrites 63.6%

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

Alternative 10: 57.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -680000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+137}:\\ \;\;\;\;x + \left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -680000000.0)
     t_1
     (if (<= t 3.45e+19)
       (fma (- y 2.0) b x)
       (if (<= t 4.5e+137) (+ x (* (- a) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -680000000.0) {
		tmp = t_1;
	} else if (t <= 3.45e+19) {
		tmp = fma((y - 2.0), b, x);
	} else if (t <= 4.5e+137) {
		tmp = x + (-a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -680000000.0)
		tmp = t_1;
	elseif (t <= 3.45e+19)
		tmp = fma(Float64(y - 2.0), b, x);
	elseif (t <= 4.5e+137)
		tmp = Float64(x + Float64(Float64(-a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -680000000.0], t$95$1, If[LessEqual[t, 3.45e+19], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[t, 4.5e+137], N[(x + N[((-a) * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8e8 or 4.5000000000000001e137 < t

   1. Initial program 92.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.7

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

   4. Applied rewrites 69.7%

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

   if -6.8e8 < t < 3.45e19

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 51.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 51.2

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

   9. Applied rewrites 51.2%

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

   if 3.45e19 < t < 4.5000000000000001e137

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 95.3

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

   4. Applied rewrites 95.3%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 65.6

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 40.5

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

   10. Applied rewrites 40.5%

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

Alternative 11: 51.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -265000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+137}:\\ \;\;\;\;x + \left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -265000000.0)
     t_1
     (if (<= t 1.7e+25)
       (fma y b x)
       (if (<= t 4.5e+137) (+ x (* (- a) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -265000000.0) {
		tmp = t_1;
	} else if (t <= 1.7e+25) {
		tmp = fma(y, b, x);
	} else if (t <= 4.5e+137) {
		tmp = x + (-a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -265000000.0)
		tmp = t_1;
	elseif (t <= 1.7e+25)
		tmp = fma(y, b, x);
	elseif (t <= 4.5e+137)
		tmp = Float64(x + Float64(Float64(-a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -265000000.0], t$95$1, If[LessEqual[t, 1.7e+25], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 4.5e+137], N[(x + N[((-a) * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.65e8 or 4.5000000000000001e137 < t

   1. Initial program 92.1%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.7

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

   4. Applied rewrites 69.7%

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

   if -2.65e8 < t < 1.69999999999999992e25

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 39.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 39.3

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

   9. Applied rewrites 39.3%

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

   if 1.69999999999999992e25 < t < 4.5000000000000001e137

   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. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 95.0

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

   4. Applied rewrites 95.0%

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

   5. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 65.2

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

   7. Applied rewrites 65.2%

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

   8. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 40.4

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

   10. Applied rewrites 40.4%

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

Alternative 12: 51.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -265000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -265000000.0) t_1 (if (<= t 2.35e+70) (fma y b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -265000000.0) {
		tmp = t_1;
	} else if (t <= 2.35e+70) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -265000000.0)
		tmp = t_1;
	elseif (t <= 2.35e+70)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -265000000.0], t$95$1, If[LessEqual[t, 2.35e+70], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.65e8 or 2.3499999999999999e70 < t

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.5

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

   4. Applied rewrites 67.5%

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

   if -2.65e8 < t < 2.3499999999999999e70

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 39.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 39.0

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

   9. Applied rewrites 39.0%

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

Alternative 13: 45.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+181}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -1.15e+150)
     t_1
     (if (<= z 1.5e-59)
       (fma y b x)
       (if (<= z 5.3e+181) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.15e+150) {
		tmp = t_1;
	} else if (z <= 1.5e-59) {
		tmp = fma(y, b, x);
	} else if (z <= 5.3e+181) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1.15e+150)
		tmp = t_1;
	elseif (z <= 1.5e-59)
		tmp = fma(y, b, x);
	elseif (z <= 5.3e+181)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.15e+150], t$95$1, If[LessEqual[z, 1.5e-59], N[(y * b + x), $MachinePrecision], If[LessEqual[z, 5.3e+181], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000001e150 or 5.2999999999999996e181 < z

   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. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 69.4

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

   4. Applied rewrites 69.4%

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

   if -1.15000000000000001e150 < z < 1.5e-59

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 61.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 38.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.9

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

   9. Applied rewrites 38.9%

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

   if 1.5e-59 < z < 5.2999999999999996e181

   1. Initial program 94.6%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 28.4

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

   4. Applied rewrites 28.4%

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

Alternative 14: 44.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -5.1e+14) t_1 (if (<= a 3.2e+71) (fma y b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -5.1e+14) {
		tmp = t_1;
	} else if (a <= 3.2e+71) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -5.1e+14)
		tmp = t_1;
	elseif (a <= 3.2e+71)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -5.1e+14], t$95$1, If[LessEqual[a, 3.2e+71], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1e14 or 3.20000000000000023e71 < a

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 54.4

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

   4. Applied rewrites 54.4%

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

   if -5.1e14 < a < 3.20000000000000023e71

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 38.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.1

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

   9. Applied rewrites 38.1%

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

Alternative 15: 39.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+70}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+70) (* (- a) t) (if (<= t 8.2e+137) (fma y b x) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+70) {
		tmp = -a * t;
	} else if (t <= 8.2e+137) {
		tmp = fma(y, b, x);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+70)
		tmp = Float64(Float64(-a) * t);
	elseif (t <= 8.2e+137)
		tmp = fma(y, b, x);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+70], N[((-a) * t), $MachinePrecision], If[LessEqual[t, 8.2e+137], N[(y * b + x), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000002e70

   1. Initial program 92.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.8

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

   4. Applied rewrites 71.8%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 41.2

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

   7. Applied rewrites 41.2%

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

   if -3.2000000000000002e70 < t < 8.19999999999999994e137

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 37.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 37.8

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

   9. Applied rewrites 37.8%

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

   if 8.19999999999999994e137 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 44.7

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 44.7

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

   4. Applied rewrites 44.7%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 41.2%

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

Alternative 16: 27.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-222}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-12}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+75)
   (* (- a) t)
   (if (<= t 6.6e-222)
     (* b y)
     (if (<= t 6.4e-12) a (if (<= t 7.6e+107) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+75) {
		tmp = -a * t;
	} else if (t <= 6.6e-222) {
		tmp = b * y;
	} else if (t <= 6.4e-12) {
		tmp = a;
	} else if (t <= 7.6e+107) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+75)) then
        tmp = -a * t
    else if (t <= 6.6d-222) then
        tmp = b * y
    else if (t <= 6.4d-12) then
        tmp = a
    else if (t <= 7.6d+107) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+75) {
		tmp = -a * t;
	} else if (t <= 6.6e-222) {
		tmp = b * y;
	} else if (t <= 6.4e-12) {
		tmp = a;
	} else if (t <= 7.6e+107) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+75:
		tmp = -a * t
	elif t <= 6.6e-222:
		tmp = b * y
	elif t <= 6.4e-12:
		tmp = a
	elif t <= 7.6e+107:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+75)
		tmp = Float64(Float64(-a) * t);
	elseif (t <= 6.6e-222)
		tmp = Float64(b * y);
	elseif (t <= 6.4e-12)
		tmp = a;
	elseif (t <= 7.6e+107)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+75)
		tmp = -a * t;
	elseif (t <= 6.6e-222)
		tmp = b * y;
	elseif (t <= 6.4e-12)
		tmp = a;
	elseif (t <= 7.6e+107)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+75], N[((-a) * t), $MachinePrecision], If[LessEqual[t, 6.6e-222], N[(b * y), $MachinePrecision], If[LessEqual[t, 6.4e-12], a, If[LessEqual[t, 7.6e+107], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7499999999999999e75

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 41.6

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

   7. Applied rewrites 41.6%

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

   if -1.7499999999999999e75 < t < 6.60000000000000004e-222

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.7

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

   4. Applied rewrites 39.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 22.0%

      \[\leadsto b \cdot y \]

   if 6.60000000000000004e-222 < t < 6.4000000000000002e-12

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 19.9

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

   4. Applied rewrites 19.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 19.8%

      \[\leadsto a \]

   if 6.4000000000000002e-12 < t < 7.5999999999999996e107

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 16.0%

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

   if 7.5999999999999996e107 < t

   1. Initial program 89.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 44.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 44.1

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

   4. Applied rewrites 44.1%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 39.4%

      \[\leadsto t \cdot b \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 26.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-32}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-222}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-12}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.3e-32)
   (* t b)
   (if (<= t 6.6e-222)
     (* b y)
     (if (<= t 6.4e-12) a (if (<= t 7.6e+107) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.3e-32) {
		tmp = t * b;
	} else if (t <= 6.6e-222) {
		tmp = b * y;
	} else if (t <= 6.4e-12) {
		tmp = a;
	} else if (t <= 7.6e+107) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.3d-32)) then
        tmp = t * b
    else if (t <= 6.6d-222) then
        tmp = b * y
    else if (t <= 6.4d-12) then
        tmp = a
    else if (t <= 7.6d+107) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.3e-32) {
		tmp = t * b;
	} else if (t <= 6.6e-222) {
		tmp = b * y;
	} else if (t <= 6.4e-12) {
		tmp = a;
	} else if (t <= 7.6e+107) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.3e-32:
		tmp = t * b
	elif t <= 6.6e-222:
		tmp = b * y
	elif t <= 6.4e-12:
		tmp = a
	elif t <= 7.6e+107:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.3e-32)
		tmp = Float64(t * b);
	elseif (t <= 6.6e-222)
		tmp = Float64(b * y);
	elseif (t <= 6.4e-12)
		tmp = a;
	elseif (t <= 7.6e+107)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.3e-32)
		tmp = t * b;
	elseif (t <= 6.6e-222)
		tmp = b * y;
	elseif (t <= 6.4e-12)
		tmp = a;
	elseif (t <= 7.6e+107)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.3e-32], N[(t * b), $MachinePrecision], If[LessEqual[t, 6.6e-222], N[(b * y), $MachinePrecision], If[LessEqual[t, 6.4e-12], a, If[LessEqual[t, 7.6e+107], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3000000000000001e-32 or 7.5999999999999996e107 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 41.3

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 41.3

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

   4. Applied rewrites 41.3%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 33.5%

      \[\leadsto t \cdot b \]

   if -2.3000000000000001e-32 < t < 6.60000000000000004e-222

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.9

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

   4. Applied rewrites 39.9%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 22.5%

      \[\leadsto b \cdot y \]

   if 6.60000000000000004e-222 < t < 6.4000000000000002e-12

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 19.9

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

   4. Applied rewrites 19.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 19.8%

      \[\leadsto a \]

   if 6.4000000000000002e-12 < t < 7.5999999999999996e107

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 16.0%

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

Alternative 18: 26.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-218}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e+48)
   (* b y)
   (if (<= y -9.2e-218) z (if (<= y 3e+39) x (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e+48) {
		tmp = b * y;
	} else if (y <= -9.2e-218) {
		tmp = z;
	} else if (y <= 3e+39) {
		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 <= (-1.35d+48)) then
        tmp = b * y
    else if (y <= (-9.2d-218)) then
        tmp = z
    else if (y <= 3d+39) 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 <= -1.35e+48) {
		tmp = b * y;
	} else if (y <= -9.2e-218) {
		tmp = z;
	} else if (y <= 3e+39) {
		tmp = x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e+48:
		tmp = b * y
	elif y <= -9.2e-218:
		tmp = z
	elif y <= 3e+39:
		tmp = x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e+48)
		tmp = Float64(b * y);
	elseif (y <= -9.2e-218)
		tmp = z;
	elseif (y <= 3e+39)
		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 <= -1.35e+48)
		tmp = b * y;
	elseif (y <= -9.2e-218)
		tmp = z;
	elseif (y <= 3e+39)
		tmp = x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e+48], N[(b * y), $MachinePrecision], If[LessEqual[y, -9.2e-218], z, If[LessEqual[y, 3e+39], x, N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35000000000000002e48 or 3e39 < y

   1. Initial program 92.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.1

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

   4. Applied rewrites 68.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 36.8%

      \[\leadsto b \cdot y \]

   if -1.35000000000000002e48 < y < -9.19999999999999979e-218

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 20.5

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

   4. Applied rewrites 20.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 17.0%

      \[\leadsto z \]

   if -9.19999999999999979e-218 < y < 3e39

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 18.9%

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

Alternative 19: 20.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+150}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.4e+150) z (if (<= z 6e-60) x (if (<= z 4.5e+96) a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.4e+150) {
		tmp = z;
	} else if (z <= 6e-60) {
		tmp = x;
	} else if (z <= 4.5e+96) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.4d+150)) then
        tmp = z
    else if (z <= 6d-60) then
        tmp = x
    else if (z <= 4.5d+96) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.4e+150) {
		tmp = z;
	} else if (z <= 6e-60) {
		tmp = x;
	} else if (z <= 4.5e+96) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.4e+150:
		tmp = z
	elif z <= 6e-60:
		tmp = x
	elif z <= 4.5e+96:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.4e+150)
		tmp = z;
	elseif (z <= 6e-60)
		tmp = x;
	elseif (z <= 4.5e+96)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.4e+150)
		tmp = z;
	elseif (z <= 6e-60)
		tmp = x;
	elseif (z <= 4.5e+96)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.4e+150], z, If[LessEqual[z, 6e-60], x, If[LessEqual[z, 4.5e+96], a, z]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000005e150 or 4.49999999999999957e96 < z

   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. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 63.6

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

   4. Applied rewrites 63.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 24.9%

      \[\leadsto z \]

   if -1.40000000000000005e150 < z < 6.00000000000000038e-60

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 19.7%

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

   if 6.00000000000000038e-60 < z < 4.49999999999999957e96

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 31.7

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

   4. Applied rewrites 31.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 12.0%

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

Alternative 20: 19.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+245}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.05e+245) a (if (<= a 1.8e+111) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.05e+245) {
		tmp = a;
	} else if (a <= 1.8e+111) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.05d+245)) then
        tmp = a
    else if (a <= 1.8d+111) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.05e+245) {
		tmp = a;
	} else if (a <= 1.8e+111) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.05e+245:
		tmp = a
	elif a <= 1.8e+111:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.05e+245)
		tmp = a;
	elseif (a <= 1.8e+111)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.05e+245)
		tmp = a;
	elseif (a <= 1.8e+111)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.05e+245], a, If[LessEqual[a, 1.8e+111], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05000000000000002e245 or 1.8000000000000001e111 < a

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

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

      7. lower--.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto a \]

   if -2.05000000000000002e245 < a < 1.8000000000000001e111

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 17.8%

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

Alternative 21: 15.5% accurate, 28.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 15.5%

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

Reproduce

herbie shell --seed 2025128 
(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)))