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

Percentage Accurate: 95.3% → 98.4%

Time: 15.0s

Alternatives: 23

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   4. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 81.8

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

   8. Applied rewrites 81.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 81.8%

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

       1. lift-+.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-fma.f64 N/A

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

       4. associate-+l+ N/A

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

       5. lower-fma.f64 N/A

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

       6. lift--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. lower-fma.f64 81.8

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

   13. Applied rewrites 81.8%

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

Alternative 2: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -880000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, a\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-37}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -880000000.0)
     t_1
     (if (<= t 1.8e-240)
       (fma y b x)
       (if (<= t 2.6e-190)
         (fma (- t 2.0) b a)
         (if (<= t 2.7e-37)
           (* (- b z) y)
           (if (<= t 1.55e+84) (- x (- z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -880000000.0) {
		tmp = t_1;
	} else if (t <= 1.8e-240) {
		tmp = fma(y, b, x);
	} else if (t <= 2.6e-190) {
		tmp = fma((t - 2.0), b, a);
	} else if (t <= 2.7e-37) {
		tmp = (b - z) * y;
	} else if (t <= 1.55e+84) {
		tmp = x - -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -880000000.0)
		tmp = t_1;
	elseif (t <= 1.8e-240)
		tmp = fma(y, b, x);
	elseif (t <= 2.6e-190)
		tmp = fma(Float64(t - 2.0), b, a);
	elseif (t <= 2.7e-37)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1.55e+84)
		tmp = Float64(x - Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -880000000.0], t$95$1, If[LessEqual[t, 1.8e-240], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 2.6e-190], N[(N[(t - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 2.7e-37], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.55e+84], N[(x - (-z)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.8e8 or 1.55000000000000001e84 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -8.8e8 < t < 1.7999999999999999e-240

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 64.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 50.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 50.6

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

      5. +-commutative 50.6

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

   10. Applied rewrites 50.6%

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

   if 1.7999999999999999e-240 < t < 2.5999999999999998e-190

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.3

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

   5. Applied rewrites 65.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 65.3

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

   7. Applied rewrites 65.3%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 65.3%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 64.7%

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

   if 2.5999999999999998e-190 < t < 2.70000000000000016e-37

   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 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 58.3

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

   5. Applied rewrites 58.3%

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

   if 2.70000000000000016e-37 < t < 1.55000000000000001e84

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 86.7

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 86.7%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 60.9%

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

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0038:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+163}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-a, t, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -0.0038)
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))
   (if (<= a 1.8e+163)
     (- (+ (fma (- b z) y (* (- t 2.0) b)) x) (- z))
     (fma (- (+ t y) 2.0) b (fma (- a) t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -0.0038) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (a <= 1.8e+163) {
		tmp = (fma((b - z), y, ((t - 2.0) * b)) + x) - -z;
	} else {
		tmp = fma(((t + y) - 2.0), b, fma(-a, t, a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -0.0038)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (a <= 1.8e+163)
		tmp = Float64(Float64(fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b)) + x) - Float64(-z));
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-a), t, a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -0.0038], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+163], N[(N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - (-z)), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-a) * t + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.00379999999999999999

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 84.6

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

   5. Applied rewrites 84.6%

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

   if -0.00379999999999999999 < a < 1.79999999999999989e163

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.1

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 92.8

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

   8. Applied rewrites 92.8%

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

   if 1.79999999999999989e163 < a

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 92.9

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

   5. Applied rewrites 92.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 93.0

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

   7. Applied rewrites 93.0%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 93.0

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

   10. Applied rewrites 93.0%

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

Alternative 4: 84.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+80} \lor \neg \left(b \leq 5.7 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-a, t, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.6e+80) (not (<= b 5.7e+38)))
   (fma (- (+ t y) 2.0) b (fma (- a) t a))
   (- (fma (- y) z x) (fma (- t 1.0) a (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.6e+80) || !(b <= 5.7e+38)) {
		tmp = fma(((t + y) - 2.0), b, fma(-a, t, a));
	} else {
		tmp = fma(-y, z, x) - fma((t - 1.0), a, -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.6e+80) || !(b <= 5.7e+38))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-a), t, a));
	else
		tmp = Float64(fma(Float64(-y), z, x) - fma(Float64(t - 1.0), a, Float64(-z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.6e+80], N[Not[LessEqual[b, 5.7e+38]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-a) * t + a), $MachinePrecision]), $MachinePrecision], N[(N[((-y) * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.60000000000000008e80 or 5.6999999999999997e38 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 85.5

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

   7. Applied rewrites 85.5%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 85.5

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

   10. Applied rewrites 85.5%

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

   if -4.60000000000000008e80 < b < 5.6999999999999997e38

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 92.3

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

   8. Applied rewrites 92.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+80} \lor \neg \left(b \leq 5.7 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-a, t, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right) - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -880000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-37}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -880000000.0)
     t_1
     (if (<= t -8e-303)
       (fma y b x)
       (if (<= t 2.7e-37)
         (* (- b z) y)
         (if (<= t 1.55e+84) (- x (- z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -880000000.0) {
		tmp = t_1;
	} else if (t <= -8e-303) {
		tmp = fma(y, b, x);
	} else if (t <= 2.7e-37) {
		tmp = (b - z) * y;
	} else if (t <= 1.55e+84) {
		tmp = x - -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -880000000.0)
		tmp = t_1;
	elseif (t <= -8e-303)
		tmp = fma(y, b, x);
	elseif (t <= 2.7e-37)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1.55e+84)
		tmp = Float64(x - Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -880000000.0], t$95$1, If[LessEqual[t, -8e-303], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 2.7e-37], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1.55e+84], N[(x - (-z)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.8e8 or 1.55000000000000001e84 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -8.8e8 < t < -7.99999999999999944e-303

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 66.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 53.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 53.4

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

      5. +-commutative 53.4

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

   10. Applied rewrites 53.4%

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

   if -7.99999999999999944e-303 < t < 2.70000000000000016e-37

   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 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 47.4

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

   5. Applied rewrites 47.4%

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

   if 2.70000000000000016e-37 < t < 1.55000000000000001e84

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 86.7

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 86.7%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 60.9%

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

Alternative 6: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+80} \lor \neg \left(b \leq 5.7 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-a, t, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.6e+80) (not (<= b 5.7e+38)))
   (fma (- (+ t y) 2.0) b (fma (- a) t a))
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.6e+80) || !(b <= 5.7e+38)) {
		tmp = fma(((t + y) - 2.0), b, fma(-a, t, a));
	} else {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.6e+80) || !(b <= 5.7e+38))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-a), t, a));
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.6e+80], N[Not[LessEqual[b, 5.7e+38]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-a) * t + a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.60000000000000008e80 or 5.6999999999999997e38 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 85.5

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

   7. Applied rewrites 85.5%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 85.5

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

   10. Applied rewrites 85.5%

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

   if -4.60000000000000008e80 < b < 5.6999999999999997e38

   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 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 92.3

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

   5. Applied rewrites 92.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+80} \lor \neg \left(b \leq 5.7 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-a, t, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.8e+80)
   (fma (- (+ t y) 2.0) b a)
   (if (<= b 5.6e+28)
     (- x (fma (- t 1.0) a (* (- y 1.0) z)))
     (+ x (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e+80) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else if (b <= 5.6e+28) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.8e+80)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	elseif (b <= 5.6e+28)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.8e+80], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[b, 5.6e+28], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.80000000000000011e80

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 86.4

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

   5. Applied rewrites 86.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 88.4

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

   7. Applied rewrites 88.4%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 86.6%

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

   if -8.80000000000000011e80 < b < 5.6000000000000003e28

   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 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 92.8

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

   5. Applied rewrites 92.8%

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

   if 5.6000000000000003e28 < b

   1. Initial program 89.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 77.7%

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

Alternative 8: 56.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-115}:\\ \;\;\;\;x - \mathsf{fma}\left(-1, a, -z\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b a)))
   (if (<= b -7.4e+71)
     t_1
     (if (<= b 4.4e-115)
       (- x (fma -1.0 a (- z)))
       (if (<= b 3.8e+28) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, a);
	double tmp;
	if (b <= -7.4e+71) {
		tmp = t_1;
	} else if (b <= 4.4e-115) {
		tmp = x - fma(-1.0, a, -z);
	} else if (b <= 3.8e+28) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, a)
	tmp = 0.0
	if (b <= -7.4e+71)
		tmp = t_1;
	elseif (b <= 4.4e-115)
		tmp = Float64(x - fma(-1.0, a, Float64(-z)));
	elseif (b <= 3.8e+28)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision]}, If[LessEqual[b, -7.4e+71], t$95$1, If[LessEqual[b, 4.4e-115], N[(x - N[(-1.0 * a + (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+28], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4e71 or 3.7999999999999999e28 < 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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 83.5

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

   7. Applied rewrites 83.5%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 80.8%

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

   if -7.4e71 < b < 4.3999999999999999e-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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 75.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.4%

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

   if 4.3999999999999999e-115 < b < 3.7999999999999999e28

   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 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 52.7

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

   5. Applied rewrites 52.7%

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

Alternative 9: 54.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-115}:\\ \;\;\;\;x - \mathsf{fma}\left(-1, a, -z\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -7.4e+71)
     t_1
     (if (<= b 4.4e-115)
       (- x (fma -1.0 a (- z)))
       (if (<= b 3.8e+28) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -7.4e+71) {
		tmp = t_1;
	} else if (b <= 4.4e-115) {
		tmp = x - fma(-1.0, a, -z);
	} else if (b <= 3.8e+28) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.4e+71)
		tmp = t_1;
	elseif (b <= 4.4e-115)
		tmp = Float64(x - fma(-1.0, a, Float64(-z)));
	elseif (b <= 3.8e+28)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.4e+71], t$95$1, If[LessEqual[b, 4.4e-115], N[(x - N[(-1.0 * a + (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+28], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4e71 or 3.7999999999999999e28 < 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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 74.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 74.9

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

   5. Applied rewrites 74.9%

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

   if -7.4e71 < b < 4.3999999999999999e-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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 75.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.4%

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

   if 4.3999999999999999e-115 < b < 3.7999999999999999e28

   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 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 52.7

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

   5. Applied rewrites 52.7%

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

Alternative 10: 70.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+76} \lor \neg \left(b \leq 520000\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.5e+76) (not (<= b 520000.0)))
   (fma (- (+ t y) 2.0) b a)
   (- x (fma (- t 1.0) a (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+76) || !(b <= 520000.0)) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else {
		tmp = x - fma((t - 1.0), a, -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e+76) || !(b <= 520000.0))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.5e+76], N[Not[LessEqual[b, 520000.0]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.49999999999999996e76 or 5.2e5 < b

   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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.2

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

   5. Applied rewrites 81.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 82.2

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

   7. Applied rewrites 82.2%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 79.6%

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

   if -2.49999999999999996e76 < b < 5.2e5

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 72.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+76} \lor \neg \left(b \leq 520000\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -7800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -7800.0)
     t_1
     (if (<= t 1.2e-36)
       (fma (- y 2.0) b a)
       (if (<= t 1.55e+84) (- x (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -7800.0) {
		tmp = t_1;
	} else if (t <= 1.2e-36) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 1.55e+84) {
		tmp = x - -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -7800.0)
		tmp = t_1;
	elseif (t <= 1.2e-36)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 1.55e+84)
		tmp = Float64(x - Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7800.0], t$95$1, If[LessEqual[t, 1.2e-36], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 1.55e+84], N[(x - (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7800 or 1.55000000000000001e84 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in 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 66.8

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

   5. Applied rewrites 66.8%

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

   if -7800 < t < 1.2e-36

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.6

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

   5. Applied rewrites 56.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 56.7

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

   7. Applied rewrites 56.7%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.1%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 55.9%

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

   if 1.2e-36 < t < 1.55000000000000001e84

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 86.7

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 86.7%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 60.9%

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

Alternative 12: 52.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -880000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+81}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -880000000.0)
     t_1
     (if (<= t 4.6e-20) (fma y b x) (if (<= t 5e+81) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -880000000.0) {
		tmp = t_1;
	} else if (t <= 4.6e-20) {
		tmp = fma(y, b, x);
	} else if (t <= 5e+81) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -880000000.0)
		tmp = t_1;
	elseif (t <= 4.6e-20)
		tmp = fma(y, b, x);
	elseif (t <= 5e+81)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -880000000.0], t$95$1, If[LessEqual[t, 4.6e-20], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 5e+81], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8e8 or 4.9999999999999998e81 < t

   1. Initial program 92.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 66.8

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

   5. Applied rewrites 66.8%

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

   if -8.8e8 < t < 4.5999999999999998e-20

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 59.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 46.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 46.5

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

      5. +-commutative 46.5

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

   10. Applied rewrites 46.5%

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

   if 4.5999999999999998e-20 < t < 4.9999999999999998e81

   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 78.5

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

   5. Applied rewrites 78.5%

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

Alternative 13: 45.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, a\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-45}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- a) t a)))
   (if (<= a -1.4e+81)
     t_1
     (if (<= a -2.4e-45) (* (- 1.0 y) z) (if (<= a 2e+48) (fma y b x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-a, t, a);
	double tmp;
	if (a <= -1.4e+81) {
		tmp = t_1;
	} else if (a <= -2.4e-45) {
		tmp = (1.0 - y) * z;
	} else if (a <= 2e+48) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-a), t, a)
	tmp = 0.0
	if (a <= -1.4e+81)
		tmp = t_1;
	elseif (a <= -2.4e-45)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (a <= 2e+48)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t + a), $MachinePrecision]}, If[LessEqual[a, -1.4e+81], t$95$1, If[LessEqual[a, -2.4e-45], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 2e+48], N[(y * b + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999997e81 or 2.00000000000000009e48 < a

   1. Initial program 92.9%

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

   3. Taylor expanded in 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 63.3

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

   5. Applied rewrites 63.3%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 63.3

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

   8. Applied rewrites 63.3%

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

   if -1.39999999999999997e81 < a < -2.3999999999999999e-45

   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 46.9

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

   5. Applied rewrites 46.9%

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

   if -2.3999999999999999e-45 < a < 2.00000000000000009e48

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 45.7

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

      5. +-commutative 45.7

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

   10. Applied rewrites 45.7%

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

Alternative 14: 70.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-y\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+76)
   (fma (- (+ t y) 2.0) b (* (- y) z))
   (if (<= b 1.15e-21)
     (- x (fma (- t 1.0) a (- z)))
     (+ x (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+76) {
		tmp = fma(((t + y) - 2.0), b, (-y * z));
	} else if (b <= 1.15e-21) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+76)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-y) * z));
	elseif (b <= 1.15e-21)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+76], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-y) * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-21], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.65e76

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.9

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

   5. Applied rewrites 83.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 85.8

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 85.1

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

   10. Applied rewrites 85.1%

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

   if -1.65e76 < b < 1.15e-21

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 73.3%

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

   if 1.15e-21 < b

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 73.6%

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

Alternative 15: 71.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+76)
   (fma (- (+ t y) 2.0) b a)
   (if (<= b 1.15e-21)
     (- x (fma (- t 1.0) a (- z)))
     (+ x (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+76) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else if (b <= 1.15e-21) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+76)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	elseif (b <= 1.15e-21)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+76], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[b, 1.15e-21], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.49999999999999996e76

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.9

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

   5. Applied rewrites 83.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 85.8

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 84.1%

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

   if -2.49999999999999996e76 < b < 1.15e-21

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 73.3%

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

   if 1.15e-21 < b

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 73.6%

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

Alternative 16: 63.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+68} \lor \neg \left(b \leq 2.6 \cdot 10^{+33}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right) - \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.8e+68) (not (<= b 2.6e+33)))
   (fma (- (+ t y) 2.0) b a)
   (- (fma (- y) z x) (- z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.8e+68) || !(b <= 2.6e+33)) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else {
		tmp = fma(-y, z, x) - -z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.8e+68) || !(b <= 2.6e+33))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	else
		tmp = Float64(fma(Float64(-y), z, x) - Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.8e+68], N[Not[LessEqual[b, 2.6e+33]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], N[(N[((-y) * z + x), $MachinePrecision] - (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.80000000000000037e68 or 2.5999999999999997e33 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 84.3

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

   7. Applied rewrites 84.3%

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

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 81.6%

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

   if -7.80000000000000037e68 < b < 2.5999999999999997e33

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 67.2

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

   8. Applied rewrites 67.2%

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

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. associate-*r* N/A

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

       3. lower-fma.f64 N/A

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

       4. mul-1-neg N/A

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

       5. lower-neg.f64 59.6

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

   11. Applied rewrites 59.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+68} \lor \neg \left(b \leq 2.6 \cdot 10^{+33}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right) - \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+29} \lor \neg \left(a \leq 2 \cdot 10^{+48}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.8e+29) (not (<= a 2e+48))) (fma (- a) t a) (fma y b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.8e+29) || !(a <= 2e+48)) {
		tmp = fma(-a, t, a);
	} else {
		tmp = fma(y, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.8e+29) || !(a <= 2e+48))
		tmp = fma(Float64(-a), t, a);
	else
		tmp = fma(y, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.8e+29], N[Not[LessEqual[a, 2e+48]], $MachinePrecision]], N[((-a) * t + a), $MachinePrecision], N[(y * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.79999999999999971e29 or 2.00000000000000009e48 < a

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 60.1

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 60.1

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

   8. Applied rewrites 60.1%

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

   if -3.79999999999999971e29 < a < 2.00000000000000009e48

   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 x around inf

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 43.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 43.4

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

      5. +-commutative 43.4

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

   10. Applied rewrites 43.4%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+29} \lor \neg \left(a \leq 2 \cdot 10^{+48}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+135} \lor \neg \left(t \leq 6.5 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.2e+135) (not (<= t 6.5e+87))) (* b t) (fma y b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.2e+135) || !(t <= 6.5e+87)) {
		tmp = b * t;
	} else {
		tmp = fma(y, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.2e+135) || !(t <= 6.5e+87))
		tmp = Float64(b * t);
	else
		tmp = fma(y, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.2e+135], N[Not[LessEqual[t, 6.5e+87]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(y * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000019e135 or 6.5000000000000002e87 < 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 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 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 42.2%

      \[\leadsto b \cdot t \]

   if -4.20000000000000019e135 < t < 6.5000000000000002e87

   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 x around inf

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 41.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 41.9

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

      5. +-commutative 41.9

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

   10. Applied rewrites 41.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+135} \lor \neg \left(t \leq 6.5 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+50}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.6e+50) (* (- a) t) (if (<= t 6.5e+87) (fma y b x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e+50) {
		tmp = -a * t;
	} else if (t <= 6.5e+87) {
		tmp = fma(y, b, x);
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.6e+50)
		tmp = Float64(Float64(-a) * t);
	elseif (t <= 6.5e+87)
		tmp = fma(y, b, x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.6e+50], N[((-a) * t), $MachinePrecision], If[LessEqual[t, 6.5e+87], N[(y * b + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999991e50

   1. Initial program 96.1%

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

   3. Taylor expanded in 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 68.3

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

   5. Applied rewrites 68.3%

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

   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 43.7

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

   8. Applied rewrites 43.7%

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

   if -1.59999999999999991e50 < t < 6.5000000000000002e87

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 44.4

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

      5. +-commutative 44.4

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

   10. Applied rewrites 44.4%

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

   if 6.5000000000000002e87 < t

   1. Initial program 89.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 69.5

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

   5. Applied rewrites 69.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 43.9%

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

Alternative 20: 26.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+135} \lor \neg \left(t \leq 5 \cdot 10^{+28}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.25e+135) (not (<= t 5e+28))) (* b t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e+135) || !(t <= 5e+28)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.25d+135)) .or. (.not. (t <= 5d+28))) then
        tmp = b * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.25e+135) || !(t <= 5e+28)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.25e+135) or not (t <= 5e+28):
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.25e+135) || !(t <= 5e+28))
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.25e+135) || ~((t <= 5e+28)))
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.25e+135], N[Not[LessEqual[t, 5e+28]], $MachinePrecision]], N[(b * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000007e135 or 4.99999999999999957e28 < t

   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 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 69.5

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

   5. Applied rewrites 69.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 40.1%

      \[\leadsto b \cdot t \]

   if -1.25000000000000007e135 < t < 4.99999999999999957e28

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 26.2%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+135} \lor \neg \left(t \leq 5 \cdot 10^{+28}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+173} \lor \neg \left(a \leq 2.8 \cdot 10^{+44}\right):\\ \;\;\;\;1 \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.55e+173) (not (<= a 2.8e+44))) (* 1.0 a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.55e+173) || !(a <= 2.8e+44)) {
		tmp = 1.0 * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.55d+173)) .or. (.not. (a <= 2.8d+44))) then
        tmp = 1.0d0 * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.55e+173) || !(a <= 2.8e+44)) {
		tmp = 1.0 * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.55e+173) or not (a <= 2.8e+44):
		tmp = 1.0 * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.55e+173) || !(a <= 2.8e+44))
		tmp = Float64(1.0 * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.55e+173) || ~((a <= 2.8e+44)))
		tmp = 1.0 * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.55e+173], N[Not[LessEqual[a, 2.8e+44]], $MachinePrecision]], N[(1.0 * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e173 or 2.8000000000000001e44 < a

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 67.2

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto 1 \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 28.1%

      \[\leadsto 1 \cdot a \]

   if -1.55e173 < a < 2.8000000000000001e44

   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 x around inf

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

   5. Applied rewrites 25.7%

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

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+173} \lor \neg \left(a \leq 2.8 \cdot 10^{+44}\right):\\ \;\;\;\;1 \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 33.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+78}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+89}:\\ \;\;\;\;x - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+78) (* b t) (if (<= b 4.8e+89) (- x (- z)) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+78) {
		tmp = b * t;
	} else if (b <= 4.8e+89) {
		tmp = x - -z;
	} 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 <= (-1.75d+78)) then
        tmp = b * t
    else if (b <= 4.8d+89) then
        tmp = x - -z
    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 <= -1.75e+78) {
		tmp = b * t;
	} else if (b <= 4.8e+89) {
		tmp = x - -z;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+78:
		tmp = b * t
	elif b <= 4.8e+89:
		tmp = x - -z
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+78)
		tmp = Float64(b * t);
	elseif (b <= 4.8e+89)
		tmp = Float64(x - Float64(-z));
	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 <= -1.75e+78)
		tmp = b * t;
	elseif (b <= 4.8e+89)
		tmp = x - -z;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+78], N[(b * t), $MachinePrecision], If[LessEqual[b, 4.8e+89], N[(x - (-z)), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7500000000000001e78

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 44.4

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

   5. Applied rewrites 44.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 38.8%

      \[\leadsto b \cdot t \]

   if -1.7500000000000001e78 < b < 4.80000000000000009e89

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 68.2

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

   8. Applied rewrites 68.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 66.5%

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

   12. Taylor expanded in x around inf

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

   14. Applied rewrites 36.0%

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

   if 4.80000000000000009e89 < 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 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 44.8

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

   5. Applied rewrites 44.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 41.9%

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

Alternative 23: 16.0% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 19.0%

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

Reproduce

herbie shell --seed 2025043 
(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)))