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

Percentage Accurate: 95.4% → 97.9%

Time: 6.6s

Alternatives: 26

Speedup: 0.5×

• 37.0% 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: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 30.8%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 76.9

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

   8. Applied rewrites 76.9%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in a around 0

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

       1. associate-+r+ N/A

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

       2. *-commutative N/A

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

       3. *-commutative N/A

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

       4. +-commutative N/A

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

       5. lower-+.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. lower--.f64 N/A

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

       10. +-commutative N/A

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

       11. *-commutative N/A

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

       12. lower-fma.f64 N/A

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

       13. lift--.f64 N/A

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

       14. lift-+.f64 N/A

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

       15. *-commutative N/A

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

       16. lower-*.f64 N/A

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

       17. lift--.f64 100.0

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

   11. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 30.8%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 76.9

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

   8. Applied rewrites 76.9%

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

Alternative 3: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z + a\\ t_2 := \left(t + y\right) - 2\\ t_3 := x - \mathsf{fma}\left(a, t, -a\right)\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, x\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-165}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (- 1.0 y) z) a))
        (t_2 (- (+ t y) 2.0))
        (t_3 (- x (fma a t (- a)))))
   (if (<= b -2.9e+21)
     (fma t_2 b x)
     (if (<= b -2.5e-49)
       t_1
       (if (<= b -2.9e-165)
         t_3
         (if (<= b 5e-112) t_1 (if (<= b 1.1e+91) t_3 (fma t_2 b z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((1.0 - y) * z) + a;
	double t_2 = (t + y) - 2.0;
	double t_3 = x - fma(a, t, -a);
	double tmp;
	if (b <= -2.9e+21) {
		tmp = fma(t_2, b, x);
	} else if (b <= -2.5e-49) {
		tmp = t_1;
	} else if (b <= -2.9e-165) {
		tmp = t_3;
	} else if (b <= 5e-112) {
		tmp = t_1;
	} else if (b <= 1.1e+91) {
		tmp = t_3;
	} else {
		tmp = fma(t_2, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(1.0 - y) * z) + a)
	t_2 = Float64(Float64(t + y) - 2.0)
	t_3 = Float64(x - fma(a, t, Float64(-a)))
	tmp = 0.0
	if (b <= -2.9e+21)
		tmp = fma(t_2, b, x);
	elseif (b <= -2.5e-49)
		tmp = t_1;
	elseif (b <= -2.9e-165)
		tmp = t_3;
	elseif (b <= 5e-112)
		tmp = t_1;
	elseif (b <= 1.1e+91)
		tmp = t_3;
	else
		tmp = fma(t_2, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(a * t + (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.9e+21], N[(t$95$2 * b + x), $MachinePrecision], If[LessEqual[b, -2.5e-49], t$95$1, If[LessEqual[b, -2.9e-165], t$95$3, If[LessEqual[b, 5e-112], t$95$1, If[LessEqual[b, 1.1e+91], t$95$3, N[(t$95$2 * b + z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.9e21

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 74.2

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

   7. Applied rewrites 74.2%

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

   if -2.9e21 < b < -2.4999999999999999e-49 or -2.9e-165 < b < 5.00000000000000044e-112

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 97.4

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 97.4%

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

   12. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 63.0

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

   14. Applied rewrites 63.0%

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

   if -2.4999999999999999e-49 < b < -2.9e-165 or 5.00000000000000044e-112 < b < 1.1e91

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 68.8%

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

   if 1.1e91 < b

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 87.6

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

   10. Applied rewrites 87.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-49}:\\ \;\;\;\;\left(1 - y\right) \cdot z + a\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-165}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t, -a\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-112}:\\ \;\;\;\;\left(1 - y\right) \cdot z + a\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ t_2 := \mathsf{fma}\left(t\_1, b, x\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t, -a\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-178}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, z\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-79}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)) (t_2 (fma t_1 b x)))
   (if (<= a -1.2e+62)
     (- x (fma a t (- a)))
     (if (<= a -1.65e-178)
       (fma t_1 b z)
       (if (<= a 7.6e-117)
         t_2
         (if (<= a 2e-79)
           (* (- 1.0 y) z)
           (if (<= a 2.65e+97) t_2 (* (- 1.0 t) a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double t_2 = fma(t_1, b, x);
	double tmp;
	if (a <= -1.2e+62) {
		tmp = x - fma(a, t, -a);
	} else if (a <= -1.65e-178) {
		tmp = fma(t_1, b, z);
	} else if (a <= 7.6e-117) {
		tmp = t_2;
	} else if (a <= 2e-79) {
		tmp = (1.0 - y) * z;
	} else if (a <= 2.65e+97) {
		tmp = t_2;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	t_2 = fma(t_1, b, x)
	tmp = 0.0
	if (a <= -1.2e+62)
		tmp = Float64(x - fma(a, t, Float64(-a)));
	elseif (a <= -1.65e-178)
		tmp = fma(t_1, b, z);
	elseif (a <= 7.6e-117)
		tmp = t_2;
	elseif (a <= 2e-79)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (a <= 2.65e+97)
		tmp = t_2;
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * b + x), $MachinePrecision]}, If[LessEqual[a, -1.2e+62], N[(x - N[(a * t + (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-178], N[(t$95$1 * b + z), $MachinePrecision], If[LessEqual[a, 7.6e-117], t$95$2, If[LessEqual[a, 2e-79], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2.65e+97], t$95$2, N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e62

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 92.4

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

   8. Applied rewrites 92.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 75.0%

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

   if -1.2e62 < a < -1.6500000000000001e-178

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 68.2

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

   10. Applied rewrites 68.2%

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

   if -1.6500000000000001e-178 < a < 7.59999999999999945e-117 or 2e-79 < a < 2.6500000000000001e97

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 67.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 67.9

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

   7. Applied rewrites 67.9%

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

   if 7.59999999999999945e-117 < a < 2e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 91.0

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

   5. Applied rewrites 91.0%

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

   if 2.6500000000000001e97 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.5

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

   5. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 94.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+83} \lor \neg \left(b \leq 9.5 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.5e+83) (not (<= b 9.5e+93)))
   (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))
   (+ (+ (fma y b (fma (- 1.0 y) z (* (- b a) t))) x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.5e+83) || !(b <= 9.5e+93)) {
		tmp = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = (fma(y, b, fma((1.0 - y), z, ((b - a) * t))) + x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.5e+83) || !(b <= 9.5e+93))
		tmp = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = Float64(Float64(fma(y, b, fma(Float64(1.0 - y), z, Float64(Float64(b - a) * t))) + x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.5e+83], N[Not[LessEqual[b, 9.5e+93]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * b + N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5000000000000002e83 or 9.4999999999999991e93 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 93.5%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 92.2

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

   8. Applied rewrites 92.2%

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

   if -9.5000000000000002e83 < b < 9.4999999999999991e93

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 98.1

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

   8. Applied rewrites 98.1%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 98.8%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 97.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+83} \lor \neg \left(b \leq 9.5 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(a, t, -a\right)\\ t_2 := \left(b - z\right) \cdot y\\ t_3 := \mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-250}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma a t (- a))))
        (t_2 (* (- b z) y))
        (t_3 (fma (- t 2.0) b z)))
   (if (<= y -3.6e+17)
     t_2
     (if (<= y -9.5e-74)
       t_1
       (if (<= y -7.2e-250)
         t_3
         (if (<= y 2.5e-203) t_1 (if (<= y 2.6e+27) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma(a, t, -a);
	double t_2 = (b - z) * y;
	double t_3 = fma((t - 2.0), b, z);
	double tmp;
	if (y <= -3.6e+17) {
		tmp = t_2;
	} else if (y <= -9.5e-74) {
		tmp = t_1;
	} else if (y <= -7.2e-250) {
		tmp = t_3;
	} else if (y <= 2.5e-203) {
		tmp = t_1;
	} else if (y <= 2.6e+27) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(a, t, Float64(-a)))
	t_2 = Float64(Float64(b - z) * y)
	t_3 = fma(Float64(t - 2.0), b, z)
	tmp = 0.0
	if (y <= -3.6e+17)
		tmp = t_2;
	elseif (y <= -9.5e-74)
		tmp = t_1;
	elseif (y <= -7.2e-250)
		tmp = t_3;
	elseif (y <= 2.5e-203)
		tmp = t_1;
	elseif (y <= 2.6e+27)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(a * t + (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]}, If[LessEqual[y, -3.6e+17], t$95$2, If[LessEqual[y, -9.5e-74], t$95$1, If[LessEqual[y, -7.2e-250], t$95$3, If[LessEqual[y, 2.5e-203], t$95$1, If[LessEqual[y, 2.6e+27], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e17 or 2.60000000000000009e27 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -3.6e17 < y < -9.5000000000000007e-74 or -7.19999999999999964e-250 < y < 2.5000000000000001e-203

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 72.0%

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

   if -9.5000000000000007e-74 < y < -7.19999999999999964e-250 or 2.5000000000000001e-203 < y < 2.60000000000000009e27

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 61.8

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

   10. Applied rewrites 61.8%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 61.5%

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

Alternative 7: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+61}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t, -a\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-79}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= a -6.5e+61)
     (- x (fma a t (- a)))
     (if (<= a 7.6e-117)
       t_1
       (if (<= a 2e-79)
         (* (- 1.0 y) z)
         (if (<= a 2.65e+97) t_1 (* (- 1.0 t) a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (a <= -6.5e+61) {
		tmp = x - fma(a, t, -a);
	} else if (a <= 7.6e-117) {
		tmp = t_1;
	} else if (a <= 2e-79) {
		tmp = (1.0 - y) * z;
	} else if (a <= 2.65e+97) {
		tmp = t_1;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (a <= -6.5e+61)
		tmp = Float64(x - fma(a, t, Float64(-a)));
	elseif (a <= 7.6e-117)
		tmp = t_1;
	elseif (a <= 2e-79)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (a <= 2.65e+97)
		tmp = t_1;
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[a, -6.5e+61], N[(x - N[(a * t + (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-117], t$95$1, If[LessEqual[a, 2e-79], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2.65e+97], t$95$1, N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.4999999999999996e61

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 92.4

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

   8. Applied rewrites 92.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 75.0%

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

   if -6.4999999999999996e61 < a < 7.59999999999999945e-117 or 2e-79 < a < 2.6500000000000001e97

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 64.4

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

   7. Applied rewrites 64.4%

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

   if 7.59999999999999945e-117 < a < 2e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 91.0

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

   5. Applied rewrites 91.0%

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

   if 2.6500000000000001e97 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.5

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

   5. Applied rewrites 75.5%

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

Alternative 8: 86.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t\_1 - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, z, b\right) \cdot y - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= a -9.5e+61)
     (- t_1 (* a (- t 1.0)))
     (if (<= a 3.3e+97)
       (fma (- 1.0 y) z t_1)
       (- (* (fma -1.0 z b) y) (* (- t 1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (a <= -9.5e+61) {
		tmp = t_1 - (a * (t - 1.0));
	} else if (a <= 3.3e+97) {
		tmp = fma((1.0 - y), z, t_1);
	} else {
		tmp = (fma(-1.0, z, b) * y) - ((t - 1.0) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (a <= -9.5e+61)
		tmp = Float64(t_1 - Float64(a * Float64(t - 1.0)));
	elseif (a <= 3.3e+97)
		tmp = fma(Float64(1.0 - y), z, t_1);
	else
		tmp = Float64(Float64(fma(-1.0, z, b) * y) - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[a, -9.5e+61], N[(t$95$1 - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+97], N[(N[(1.0 - y), $MachinePrecision] * z + t$95$1), $MachinePrecision], N[(N[(N[(-1.0 * z + b), $MachinePrecision] * y), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999959e61

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 87.2

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

   8. Applied rewrites 87.2%

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

   if -9.49999999999999959e61 < a < 3.3000000000000001e97

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 96.2

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

   8. Applied rewrites 96.2%

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

   if 3.3000000000000001e97 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 89.6

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

   8. Applied rewrites 89.6%

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

Alternative 9: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+61}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, z, b\right) \cdot y - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.5e+61)
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))
   (if (<= a 3.3e+97)
     (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))
     (- (* (fma -1.0 z b) y) (* (- t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+61) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (a <= 3.3e+97) {
		tmp = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = (fma(-1.0, z, b) * y) - ((t - 1.0) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.5e+61)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (a <= 3.3e+97)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = Float64(Float64(fma(-1.0, z, b) * y) - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.5e+61], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+97], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 * z + b), $MachinePrecision] * y), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.4999999999999996e61

   1. Initial program 90.5%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -6.4999999999999996e61 < a < 3.3000000000000001e97

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 96.2

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

   8. Applied rewrites 96.2%

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

   if 3.3000000000000001e97 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 89.6

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

   8. Applied rewrites 89.6%

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

Alternative 10: 86.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+61} \lor \neg \left(a \leq 4.2 \cdot 10^{+145}\right):\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.5e+61) (not (<= a 4.2e+145)))
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))
   (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.5e+61) || !(a <= 4.2e+145)) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.5e+61) || !(a <= 4.2e+145))
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.5e+61], N[Not[LessEqual[a, 4.2e+145]], $MachinePrecision]], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4999999999999996e61 or 4.19999999999999979e145 < a

   1. Initial program 90.3%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -6.4999999999999996e61 < a < 4.19999999999999979e145

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift-+.f64 94.7

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

   8. Applied rewrites 94.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+61} \lor \neg \left(a \leq 4.2 \cdot 10^{+145}\right):\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-272}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.6e+17)
     t_1
     (if (<= y -9e-272)
       (* (- b a) t)
       (if (<= y 2.5e-203) (+ x a) (if (<= y 2.6e+27) (fma t b z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.6e+17) {
		tmp = t_1;
	} else if (y <= -9e-272) {
		tmp = (b - a) * t;
	} else if (y <= 2.5e-203) {
		tmp = x + a;
	} else if (y <= 2.6e+27) {
		tmp = fma(t, b, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.6e+17)
		tmp = t_1;
	elseif (y <= -9e-272)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 2.5e-203)
		tmp = Float64(x + a);
	elseif (y <= 2.6e+27)
		tmp = fma(t, b, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.6e+17], t$95$1, If[LessEqual[y, -9e-272], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.5e-203], N[(x + a), $MachinePrecision], If[LessEqual[y, 2.6e+27], N[(t * b + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e17 or 2.60000000000000009e27 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -3.6e17 < y < -8.9999999999999995e-272

   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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 48.9

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

   5. Applied rewrites 48.9%

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

   if -8.9999999999999995e-272 < y < 2.5000000000000001e-203

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 99.9%

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

   12. Taylor expanded in x around inf

       \[\leadsto x - \left(-a\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 54.2%

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

   if 2.5000000000000001e-203 < y < 2.60000000000000009e27

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.7

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

   5. Applied rewrites 56.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 56.6

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

   10. Applied rewrites 56.6%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 46.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+17}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-272}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -2.16 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+93}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -2.16e+80)
     (fma t_1 b x)
     (if (<= b 3.9e+93)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (fma t_1 b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -2.16e+80) {
		tmp = fma(t_1, b, x);
	} else if (b <= 3.9e+93) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma(t_1, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -2.16e+80)
		tmp = fma(t_1, b, x);
	elseif (b <= 3.9e+93)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(t_1, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -2.16e+80], N[(t$95$1 * b + x), $MachinePrecision], If[LessEqual[b, 3.9e+93], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.16e80

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 84.7

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

   7. Applied rewrites 84.7%

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

   if -2.16e80 < b < 3.9000000000000002e93

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if 3.9000000000000002e93 < b

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 87.6

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

   10. Applied rewrites 87.6%

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

Alternative 13: 35.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -9 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -9e+165)
     (fma t b z)
     (if (<= t -1.95e+80)
       t_1
       (if (<= t 1.56e+47) (fma y b z) (if (<= t 4e+122) t_1 (fma t b z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -9e+165) {
		tmp = fma(t, b, z);
	} else if (t <= -1.95e+80) {
		tmp = t_1;
	} else if (t <= 1.56e+47) {
		tmp = fma(y, b, z);
	} else if (t <= 4e+122) {
		tmp = t_1;
	} else {
		tmp = fma(t, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -9e+165)
		tmp = fma(t, b, z);
	elseif (t <= -1.95e+80)
		tmp = t_1;
	elseif (t <= 1.56e+47)
		tmp = fma(y, b, z);
	elseif (t <= 4e+122)
		tmp = t_1;
	else
		tmp = fma(t, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -9e+165], N[(t * b + z), $MachinePrecision], If[LessEqual[t, -1.95e+80], t$95$1, If[LessEqual[t, 1.56e+47], N[(y * b + z), $MachinePrecision], If[LessEqual[t, 4e+122], t$95$1, N[(t * b + z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999993e165 or 4.00000000000000006e122 < t

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.7

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

   5. Applied rewrites 65.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 56.7

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

   10. Applied rewrites 56.7%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 52.9%

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

   if -8.9999999999999993e165 < t < -1.94999999999999999e80 or 1.55999999999999998e47 < t < 4.00000000000000006e122

   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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.3

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

   5. Applied rewrites 65.3%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 61.9

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

   8. Applied rewrites 61.9%

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

   if -1.94999999999999999e80 < t < 1.55999999999999998e47

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 50.3

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

   10. Applied rewrites 50.3%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 40.4%

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

Alternative 14: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+93}:\\ \;\;\;\;\left(1 - y\right) \cdot z - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -6e+79)
     (fma t_1 b x)
     (if (<= b 2.35e+93) (- (* (- 1.0 y) z) (* (- t 1.0) a)) (fma t_1 b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -6e+79) {
		tmp = fma(t_1, b, x);
	} else if (b <= 2.35e+93) {
		tmp = ((1.0 - y) * z) - ((t - 1.0) * a);
	} else {
		tmp = fma(t_1, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -6e+79)
		tmp = fma(t_1, b, x);
	elseif (b <= 2.35e+93)
		tmp = Float64(Float64(Float64(1.0 - y) * z) - Float64(Float64(t - 1.0) * a));
	else
		tmp = fma(t_1, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -6e+79], N[(t$95$1 * b + x), $MachinePrecision], If[LessEqual[b, 2.35e+93], N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999948e79

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 84.7

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

   7. Applied rewrites 84.7%

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

   if -5.99999999999999948e79 < b < 2.3499999999999999e93

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 70.8

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

   8. Applied rewrites 70.8%

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

   if 2.3499999999999999e93 < b

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 87.6

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

   10. Applied rewrites 87.6%

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

Alternative 15: 42.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -8 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-247}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -8e+61)
     t_1
     (if (<= a 5.3e-247) (fma t b z) (if (<= a 3.4e+95) (fma y b z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -8e+61) {
		tmp = t_1;
	} else if (a <= 5.3e-247) {
		tmp = fma(t, b, z);
	} else if (a <= 3.4e+95) {
		tmp = fma(y, b, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -8e+61)
		tmp = t_1;
	elseif (a <= 5.3e-247)
		tmp = fma(t, b, z);
	elseif (a <= 3.4e+95)
		tmp = fma(y, b, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -8e+61], t$95$1, If[LessEqual[a, 5.3e-247], N[(t * b + z), $MachinePrecision], If[LessEqual[a, 3.4e+95], N[(y * b + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999996e61 or 3.40000000000000022e95 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.7

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

   5. Applied rewrites 68.7%

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

   if -7.9999999999999996e61 < a < 5.2999999999999998e-247

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 61.7

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

   10. Applied rewrites 61.7%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 41.0%

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

   if 5.2999999999999998e-247 < a < 3.40000000000000022e95

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 59.2

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

   10. Applied rewrites 59.2%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 40.0%

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

Alternative 16: 70.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;\left(\left(1 - y\right) \cdot z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -6e+79)
     (fma t_1 b x)
     (if (<= b 4.5e+75) (+ (+ (* (- 1.0 y) z) x) a) (fma t_1 b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -6e+79) {
		tmp = fma(t_1, b, x);
	} else if (b <= 4.5e+75) {
		tmp = (((1.0 - y) * z) + x) + a;
	} else {
		tmp = fma(t_1, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -6e+79)
		tmp = fma(t_1, b, x);
	elseif (b <= 4.5e+75)
		tmp = Float64(Float64(Float64(Float64(1.0 - y) * z) + x) + a);
	else
		tmp = fma(t_1, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -6e+79], N[(t$95$1 * b + x), $MachinePrecision], If[LessEqual[b, 4.5e+75], N[(N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], N[(t$95$1 * b + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999948e79

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 84.7

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

   7. Applied rewrites 84.7%

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

   if -5.99999999999999948e79 < b < 4.5000000000000004e75

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 98.1

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

   8. Applied rewrites 98.1%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 98.7%

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

   12. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 70.0

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

   14. Applied rewrites 70.0%

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

   if 4.5000000000000004e75 < b

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 84.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 84.8

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

   10. Applied rewrites 84.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+75}:\\ \;\;\;\;\left(\left(1 - y\right) \cdot z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-115}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e-6)
   (fma t b z)
   (if (<= t -4.5e-115) (+ x a) (if (<= t 1.95e+88) (fma y b z) (fma t b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e-6) {
		tmp = fma(t, b, z);
	} else if (t <= -4.5e-115) {
		tmp = x + a;
	} else if (t <= 1.95e+88) {
		tmp = fma(y, b, z);
	} else {
		tmp = fma(t, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e-6)
		tmp = fma(t, b, z);
	elseif (t <= -4.5e-115)
		tmp = Float64(x + a);
	elseif (t <= 1.95e+88)
		tmp = fma(y, b, z);
	else
		tmp = fma(t, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e-6], N[(t * b + z), $MachinePrecision], If[LessEqual[t, -4.5e-115], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.95e+88], N[(y * b + z), $MachinePrecision], N[(t * b + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999989e-6 or 1.9500000000000001e88 < t

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.6

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 50.5

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

   10. Applied rewrites 50.5%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 44.5%

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

   if -6.99999999999999989e-6 < t < -4.50000000000000023e-115

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 100.0%

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

   12. Taylor expanded in x around inf

       \[\leadsto x - \left(-a\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 46.7%

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

   if -4.50000000000000023e-115 < t < 1.9500000000000001e88

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.7

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

   5. Applied rewrites 63.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 51.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 51.7

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

   10. Applied rewrites 51.7%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 42.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-115}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 2.6 \cdot 10^{+27}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -90.0) (not (<= y 2.6e+27))) (* (- b z) y) (fma (- t 2.0) b z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -90.0) || !(y <= 2.6e+27)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((t - 2.0), b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -90.0) || !(y <= 2.6e+27))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(t - 2.0), b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -90.0], N[Not[LessEqual[y, 2.6e+27]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -90 or 2.60000000000000009e27 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -90 < y < 2.60000000000000009e27

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.1

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

   5. Applied rewrites 52.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 51.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 51.8

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

   10. Applied rewrites 51.8%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 51.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 2.6 \cdot 10^{+27}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+79} \lor \neg \left(t \leq 1.08 \cdot 10^{+46}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.4e+79) (not (<= t 1.08e+46))) (* (- b a) t) (fma y b z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.4e+79) || !(t <= 1.08e+46)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(y, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.4e+79) || !(t <= 1.08e+46))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(y, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.4e+79], N[Not[LessEqual[t, 1.08e+46]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(y * b + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999998e79 or 1.07999999999999994e46 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -4.3999999999999998e79 < t < 1.07999999999999994e46

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-+.f64 50.3

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

   10. Applied rewrites 50.3%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 40.4%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+79} \lor \neg \left(t \leq 1.08 \cdot 10^{+46}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+58} \lor \neg \left(a \leq 3.1 \cdot 10^{+95}\right):\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.06e+58) (not (<= a 3.1e+95)))
   (* (- 1.0 t) a)
   (* (- 1.0 y) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.06e+58) || !(a <= 3.1e+95)) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (1.0 - y) * 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 ((a <= (-1.06d+58)) .or. (.not. (a <= 3.1d+95))) then
        tmp = (1.0d0 - t) * a
    else
        tmp = (1.0d0 - y) * 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 ((a <= -1.06e+58) || !(a <= 3.1e+95)) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.06e+58) or not (a <= 3.1e+95):
		tmp = (1.0 - t) * a
	else:
		tmp = (1.0 - y) * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.06e+58) || !(a <= 3.1e+95))
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = Float64(Float64(1.0 - y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.06e+58) || ~((a <= 3.1e+95)))
		tmp = (1.0 - t) * a;
	else
		tmp = (1.0 - y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.06e+58], N[Not[LessEqual[a, 3.1e+95]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05999999999999997e58 or 3.1000000000000003e95 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      3. lower--.f64 68.7

         \[\leadsto \left(1 - t\right) \cdot a \]

   5. Applied rewrites 68.7%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   if -1.05999999999999997e58 < a < 3.1000000000000003e95

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      3. lower--.f64 40.8

         \[\leadsto \left(1 - y\right) \cdot z \]

   5. Applied rewrites 40.8%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+58} \lor \neg \left(a \leq 3.1 \cdot 10^{+95}\right):\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+51} \lor \neg \left(y \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+51) (not (<= y 2.6e+38))) (* b y) (fma t b z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+51) || !(y <= 2.6e+38)) {
		tmp = b * y;
	} else {
		tmp = fma(t, b, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+51) || !(y <= 2.6e+38))
		tmp = Float64(b * y);
	else
		tmp = fma(t, b, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+51], N[Not[LessEqual[y, 2.6e+38]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(t * b + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000005e51 or 2.5999999999999999e38 < y

   1. Initial program 90.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 73.0

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 39.6%

      \[\leadsto b \cdot y \]

   if -2.30000000000000005e51 < y < 2.5999999999999999e38

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lower--.f64 54.1

         \[\leadsto \left(1 - y\right) \cdot z + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 50.7%

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{z + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto z + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      3. lift-+.f64 N/A

         \[\leadsto z + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto z + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + z} \]

      6. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b + z \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, z\right)} \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, z\right) \]

      9. lift-+.f64 50.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, z\right) \]

   10. Applied rewrites 50.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, z\right)} \]

   11. Taylor expanded in t around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, z\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 40.4%

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+51} \lor \neg \left(y \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+82} \lor \neg \left(t \leq 2.55 \cdot 10^{+46}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.32e+82) (not (<= t 2.55e+46))) (* b t) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.32e+82) || !(t <= 2.55e+46)) {
		tmp = b * t;
	} else {
		tmp = x + 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 ((t <= (-1.32d+82)) .or. (.not. (t <= 2.55d+46))) then
        tmp = b * t
    else
        tmp = x + 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 ((t <= -1.32e+82) || !(t <= 2.55e+46)) {
		tmp = b * t;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.32e+82) or not (t <= 2.55e+46):
		tmp = b * t
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.32e+82) || !(t <= 2.55e+46))
		tmp = Float64(b * t);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.32e+82) || ~((t <= 2.55e+46)))
		tmp = b * t;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.32e+82], N[Not[LessEqual[t, 2.55e+46]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e82 or 2.5499999999999999e46 < t

   1. Initial program 91.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 72.3

         \[\leadsto \left(b - a\right) \cdot t \]

   5. Applied rewrites 72.3%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 39.2%

      \[\leadsto b \cdot t \]

   if -1.32e82 < t < 2.5499999999999999e46

   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. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot a + \color{blue}{a \cdot t}\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(a \cdot t + -1 \cdot \color{blue}{a}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -1 \cdot a\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, \mathsf{neg}\left(a\right)\right) \]

      4. lower-neg.f64 99.3

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -a\right) \]

   8. Applied rewrites 99.3%

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, \color{blue}{t}, -a\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   10. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - -1 \cdot \color{blue}{a} \]

   11. Applied rewrites 97.4%

       \[\leadsto \left(\mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) - \color{blue}{\left(-a\right)} \]

   12. Taylor expanded in x around inf

       \[\leadsto x - \left(-a\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 31.2%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+82} \lor \neg \left(t \leq 2.55 \cdot 10^{+46}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+138} \lor \neg \left(z \leq 2.6 \cdot 10^{+114}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+138) (not (<= z 2.6e+114))) (* 1.0 z) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+138) || !(z <= 2.6e+114)) {
		tmp = 1.0 * z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.9d+138)) .or. (.not. (z <= 2.6d+114))) then
        tmp = 1.0d0 * z
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+138) || !(z <= 2.6e+114)) {
		tmp = 1.0 * z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e+138) or not (z <= 2.6e+114):
		tmp = 1.0 * z
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e+138) || !(z <= 2.6e+114))
		tmp = Float64(1.0 * z);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.9e+138) || ~((z <= 2.6e+114)))
		tmp = 1.0 * z;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+138], N[Not[LessEqual[z, 2.6e+114]], $MachinePrecision]], N[(1.0 * z), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e138 or 2.6e114 < z

   1. Initial program 88.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - y\right) \cdot \color{blue}{z} \]

      3. lower--.f64 71.2

         \[\leadsto \left(1 - y\right) \cdot z \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 30.6%

      \[\leadsto 1 \cdot z \]

   if -2.9000000000000001e138 < z < 2.6e114

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot a + \color{blue}{a \cdot t}\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(a \cdot t + -1 \cdot \color{blue}{a}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -1 \cdot a\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, \mathsf{neg}\left(a\right)\right) \]

      4. lower-neg.f64 97.8

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -a\right) \]

   8. Applied rewrites 97.8%

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, \color{blue}{t}, -a\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   10. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - -1 \cdot \color{blue}{a} \]

   11. Applied rewrites 98.9%

       \[\leadsto \left(\mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) - \color{blue}{\left(-a\right)} \]

   12. Taylor expanded in x around inf

       \[\leadsto x - \left(-a\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 28.5%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+138} \lor \neg \left(z \leq 2.6 \cdot 10^{+114}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 32.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+94}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.8e+84) (* b t) (if (<= b 1.45e+94) (+ x a) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e+84) {
		tmp = b * t;
	} else if (b <= 1.45e+94) {
		tmp = x + a;
	} 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 (b <= (-3.8d+84)) then
        tmp = b * t
    else if (b <= 1.45d+94) then
        tmp = x + a
    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 (b <= -3.8e+84) {
		tmp = b * t;
	} else if (b <= 1.45e+94) {
		tmp = x + a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.8e+84:
		tmp = b * t
	elif b <= 1.45e+94:
		tmp = x + a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.8e+84)
		tmp = Float64(b * t);
	elseif (b <= 1.45e+94)
		tmp = Float64(x + a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.8e+84)
		tmp = b * t;
	elseif (b <= 1.45e+94)
		tmp = x + a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.8e+84], N[(b * t), $MachinePrecision], If[LessEqual[b, 1.45e+94], N[(x + a), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.8000000000000001e84

   1. Initial program 90.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 49.6

         \[\leadsto \left(b - a\right) \cdot t \]

   5. Applied rewrites 49.6%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

      \[\leadsto b \cdot t \]

   if -3.8000000000000001e84 < b < 1.4499999999999999e94

   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. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot a + \color{blue}{a \cdot t}\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(a \cdot t + -1 \cdot \color{blue}{a}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -1 \cdot a\right) \]

      3. mul-1-neg N/A

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, \mathsf{neg}\left(a\right)\right) \]

      4. lower-neg.f64 98.2

         \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -a\right) \]

   8. Applied rewrites 98.2%

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, \color{blue}{t}, -a\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   10. Step-by-step derivation

       1. lower--.f64 N/A

          \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - -1 \cdot \color{blue}{a} \]

   11. Applied rewrites 98.8%

       \[\leadsto \left(\mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) - \color{blue}{\left(-a\right)} \]

   12. Taylor expanded in x around inf

       \[\leadsto x - \left(-a\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 30.4%

       \[\leadsto x - \left(-a\right) \]

   if 1.4499999999999999e94 < b

   1. Initial program 87.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 56.4

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 52.3%

      \[\leadsto b \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+94}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 24.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ x + a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + a;
}

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 + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + a;
}

Python

def code(x, y, z, t, a, b):
	return x + a

Julia

function code(x, y, z, t, a, b)
	return Float64(x + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + a), $MachinePrecision]

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - a \cdot \left(t - 1\right)} \]
4. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \left(x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

5. Applied rewrites 96.5%

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(t - 1\right) \cdot a} \]

6. Taylor expanded in t around 0

   \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot a + \color{blue}{a \cdot t}\right) \]
7. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \left(a \cdot t + -1 \cdot \color{blue}{a}\right) \]

   2. lower-fma.f64 N/A

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -1 \cdot a\right) \]

   3. mul-1-neg N/A

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, \mathsf{neg}\left(a\right)\right) \]

   4. lower-neg.f64 96.5

      \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, t, -a\right) \]

8. Applied rewrites 96.5%

   \[\leadsto \left(\mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(a, \color{blue}{t}, -a\right) \]

9. Taylor expanded in t around 0

   \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - \color{blue}{-1 \cdot a} \]
10. Step-by-step derivation

    1. lower--.f64 N/A

       \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + \left(t \cdot \left(b - a\right) + z \cdot \left(1 - y\right)\right)\right)\right) - -1 \cdot \color{blue}{a} \]

11. Applied rewrites 96.1%

    \[\leadsto \left(\mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, \left(b - a\right) \cdot t\right)\right) + x\right) - \color{blue}{\left(-a\right)} \]

12. Taylor expanded in x around inf

    \[\leadsto x - \left(-a\right) \]
13. Step-by-step derivation

14. Applied rewrites 22.1%

    \[\leadsto x - \left(-a\right) \]

15. Final simplification 22.1%

    \[\leadsto x + a \]
16. Add Preprocessing

Alternative 26: 15.5% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 14.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025085 
(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)))