Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 90.9% → 93.8%

Time: 4.4s

Alternatives: 7

Speedup: N/A×

• 29.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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)
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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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)
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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 4e+299)
     (/ t_1 (* a 2.0))
     (* (fma (/ (* 0.5 x) z) (/ y a) (* (/ t a) -4.5)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= 4e+299) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = fma(((0.5 * x) / z), (y / a), ((t / a) * -4.5)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= 4e+299)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(fma(Float64(Float64(0.5 * x) / z), Float64(y / a), Float64(Float64(t / a) * -4.5)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+299], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.5 * x), $MachinePrecision] / z), $MachinePrecision] * N[(y / a), $MachinePrecision] + N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e299

   1. Initial program 95.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   if 4.0000000000000002e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 45.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 68.3

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      3. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      4. associate-/l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{y \cdot x}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      7. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. lower-fma.f64 N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. associate-*r/ N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot \left(x \cdot y\right)}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      12. associate-*r* N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      13. *-commutative N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{z \cdot a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      14. times-frac N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot x}{z} \cdot \frac{y}{a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      16. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      18. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      20. lift-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      21. lift-*.f64 87.5

          \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   7. Applied rewrites 87.5%

      \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.8% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) 4e+299)
   (/ (fma (* -9.0 z) t (* y x)) (* a 2.0))
   (* (fma (/ (* 0.5 x) z) (/ y a) (* (/ t a) -4.5)) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 4e+299) {
		tmp = fma((-9.0 * z), t, (y * x)) / (a * 2.0);
	} else {
		tmp = fma(((0.5 * x) / z), (y / a), ((t / a) * -4.5)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 4e+299)
		tmp = Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / Float64(a * 2.0));
	else
		tmp = Float64(fma(Float64(Float64(0.5 * x) / z), Float64(y / a), Float64(Float64(t / a) * -4.5)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 4e+299], N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.5 * x), $MachinePrecision] / z), $MachinePrecision] * N[(y / a), $MachinePrecision] + N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e299

   1. Initial program 95.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

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

         \[\leadsto \frac{x \cdot y + \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot z\right)}}{a \cdot 2} \]

      2. metadata-eval N/A

         \[\leadsto \frac{x \cdot y + -9 \cdot \left(\color{blue}{t} \cdot z\right)}{a \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{-9 \cdot \left(t \cdot z\right) + \color{blue}{x \cdot y}}{a \cdot 2} \]

      4. *-commutative N/A

         \[\leadsto \frac{-9 \cdot \left(z \cdot t\right) + x \cdot y}{a \cdot 2} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(-9 \cdot z\right) \cdot t + \color{blue}{x} \cdot y}{a \cdot 2} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot z, \color{blue}{t}, x \cdot y\right)}{a \cdot 2} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot z, t, x \cdot y\right)}{a \cdot 2} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a \cdot 2} \]

      9. lower-*.f64 95.6

         \[\leadsto \frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{a \cdot 2} \]

   5. Applied rewrites 95.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}}{a \cdot 2} \]

   if 4.0000000000000002e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 45.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 68.3

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      3. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      4. associate-/l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{y \cdot x}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      7. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. lower-fma.f64 N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. associate-*r/ N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot \left(x \cdot y\right)}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      12. associate-*r* N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      13. *-commutative N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{z \cdot a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      14. times-frac N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot x}{z} \cdot \frac{y}{a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      16. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      18. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      20. lift-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      21. lift-*.f64 87.5

          \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   7. Applied rewrites 87.5%

      \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 92.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{t \cdot z}{y}, -9, x\right) \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -1e+98)
     (* (/ (fma (/ (* y x) z) 0.5 (* -4.5 t)) a) z)
     (if (<= t_1 5e+58)
       (/ (* (fma (/ (* t z) y) -9.0 x) y) (* a 2.0))
       (* (fma (/ (* 0.5 x) z) (/ y a) (* (/ t a) -4.5)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -1e+98) {
		tmp = (fma(((y * x) / z), 0.5, (-4.5 * t)) / a) * z;
	} else if (t_1 <= 5e+58) {
		tmp = (fma(((t * z) / y), -9.0, x) * y) / (a * 2.0);
	} else {
		tmp = fma(((0.5 * x) / z), (y / a), ((t / a) * -4.5)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -1e+98)
		tmp = Float64(Float64(fma(Float64(Float64(y * x) / z), 0.5, Float64(-4.5 * t)) / a) * z);
	elseif (t_1 <= 5e+58)
		tmp = Float64(Float64(fma(Float64(Float64(t * z) / y), -9.0, x) * y) / Float64(a * 2.0));
	else
		tmp = Float64(fma(Float64(Float64(0.5 * x) / z), Float64(y / a), Float64(Float64(t / a) * -4.5)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+98], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 0.5 + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+58], N[(N[(N[(N[(N[(t * z), $MachinePrecision] / y), $MachinePrecision] * -9.0 + x), $MachinePrecision] * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(0.5 * x), $MachinePrecision] / z), $MachinePrecision] * N[(y / a), $MachinePrecision] + N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -9.99999999999999998e97

   1. Initial program 68.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 88.1

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]

   6. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]

      2. +-commutative N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot y}{z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      8. lower-*.f64 90.5

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   8. Applied rewrites 90.5%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   if -9.99999999999999998e97 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.99999999999999986e58

   1. Initial program 94.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(x + -9 \cdot \frac{t \cdot z}{y}\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(x + -9 \cdot \frac{t \cdot z}{y}\right) \cdot \color{blue}{y}}{a \cdot 2} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(x + -9 \cdot \frac{t \cdot z}{y}\right) \cdot \color{blue}{y}}{a \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{\left(-9 \cdot \frac{t \cdot z}{y} + x\right) \cdot y}{a \cdot 2} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\frac{t \cdot z}{y} \cdot -9 + x\right) \cdot y}{a \cdot 2} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{t \cdot z}{y}, -9, x\right) \cdot y}{a \cdot 2} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{t \cdot z}{y}, -9, x\right) \cdot y}{a \cdot 2} \]

      7. lower-*.f64 93.2

         \[\leadsto \frac{\mathsf{fma}\left(\frac{t \cdot z}{y}, -9, x\right) \cdot y}{a \cdot 2} \]

   5. Applied rewrites 93.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{t \cdot z}{y}, -9, x\right) \cdot y}}{a \cdot 2} \]

   if 4.99999999999999986e58 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 81.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 68.3

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      3. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      4. associate-/l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{y \cdot x}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      7. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. lower-fma.f64 N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. associate-*r/ N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot \left(x \cdot y\right)}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      12. associate-*r* N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      13. *-commutative N/A

          \[\leadsto \left(\frac{\left(\frac{1}{2} \cdot x\right) \cdot y}{z \cdot a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      14. times-frac N/A

          \[\leadsto \left(\frac{\frac{1}{2} \cdot x}{z} \cdot \frac{y}{a} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      16. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      18. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      20. lift-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{1}{2} \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      21. lift-*.f64 82.8

          \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   7. Applied rewrites 82.8%

      \[\leadsto \mathsf{fma}\left(\frac{0.5 \cdot x}{z}, \frac{y}{a}, \frac{t}{a} \cdot -4.5\right) \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\frac{\frac{y \cdot x}{a}}{2} - \frac{9 \cdot z}{a} \cdot \frac{t}{2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (fma (/ x a) 0.5 (* (/ (* t (/ z a)) y) -4.5)) y)))
   (if (<= (* x y) -2e+266)
     t_1
     (if (<= (* x y) 5e+75)
       (- (/ (/ (* y x) a) 2.0) (* (/ (* 9.0 z) a) (/ t 2.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / a), 0.5, (((t * (z / a)) / y) * -4.5)) * y;
	double tmp;
	if ((x * y) <= -2e+266) {
		tmp = t_1;
	} else if ((x * y) <= 5e+75) {
		tmp = (((y * x) / a) / 2.0) - (((9.0 * z) / a) * (t / 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(fma(Float64(x / a), 0.5, Float64(Float64(Float64(t * Float64(z / a)) / y) * -4.5)) * y)
	tmp = 0.0
	if (Float64(x * y) <= -2e+266)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+75)
		tmp = Float64(Float64(Float64(Float64(y * x) / a) / 2.0) - Float64(Float64(Float64(9.0 * z) / a) * Float64(t / 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x / a), $MachinePrecision] * 0.5 + N[(N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+266], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+75], N[(N[(N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision] / 2.0), $MachinePrecision] - N[(N[(N[(9.0 * z), $MachinePrecision] / a), $MachinePrecision] * N[(t / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.0000000000000001e266 or 5.0000000000000002e75 < (*.f64 x y)

   1. Initial program 75.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{a} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x}{a} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      12. lower-*.f64 82.8

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y \]

   5. Applied rewrites 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      2. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      5. lower-/.f64 88.1

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]

   7. Applied rewrites 88.1%

      \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]

   if -2.0000000000000001e266 < (*.f64 x y) < 5.0000000000000002e75

   1. Initial program 92.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{\color{blue}{a \cdot 2}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot y - \left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      5. div-sub N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{a}}{2}} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{a}}{2}} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      9. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{x \cdot y}{a}}}{2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\color{blue}{y \cdot x}}{a}}{2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\color{blue}{y \cdot x}}{a}}{2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2} \]

      14. *-commutative N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \frac{\color{blue}{\left(9 \cdot z\right)} \cdot t}{a \cdot 2} \]

      15. times-frac N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \color{blue}{\frac{9 \cdot z}{a} \cdot \frac{t}{2}} \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \color{blue}{\frac{9 \cdot z}{a} \cdot \frac{t}{2}} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \color{blue}{\frac{9 \cdot z}{a}} \cdot \frac{t}{2} \]

      18. lower-*.f64 N/A

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \frac{\color{blue}{9 \cdot z}}{a} \cdot \frac{t}{2} \]

      19. lower-/.f64 95.9

          \[\leadsto \frac{\frac{y \cdot x}{a}}{2} - \frac{9 \cdot z}{a} \cdot \color{blue}{\frac{t}{2}} \]

   4. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot x}{a}}{2} - \frac{9 \cdot z}{a} \cdot \frac{t}{2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 88.0% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8.5e-66)
   (* (fma (/ x a) 0.5 (* (/ (* t (/ z a)) y) -4.5)) y)
   (if (<= y 2.1e-92)
     (* (/ (fma (/ (* y x) z) 0.5 (* -4.5 t)) a) z)
     (* (fma (/ x a) 0.5 (* (/ (/ (* t z) a) y) -4.5)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8.5e-66) {
		tmp = fma((x / a), 0.5, (((t * (z / a)) / y) * -4.5)) * y;
	} else if (y <= 2.1e-92) {
		tmp = (fma(((y * x) / z), 0.5, (-4.5 * t)) / a) * z;
	} else {
		tmp = fma((x / a), 0.5, ((((t * z) / a) / y) * -4.5)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8.5e-66)
		tmp = Float64(fma(Float64(x / a), 0.5, Float64(Float64(Float64(t * Float64(z / a)) / y) * -4.5)) * y);
	elseif (y <= 2.1e-92)
		tmp = Float64(Float64(fma(Float64(Float64(y * x) / z), 0.5, Float64(-4.5 * t)) / a) * z);
	else
		tmp = Float64(fma(Float64(x / a), 0.5, Float64(Float64(Float64(Float64(t * z) / a) / y) * -4.5)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8.5e-66], N[(N[(N[(x / a), $MachinePrecision] * 0.5 + N[(N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 2.1e-92], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 0.5 + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * 0.5 + N[(N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999966e-66

   1. Initial program 85.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{a} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x}{a} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      12. lower-*.f64 84.0

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y \]

   5. Applied rewrites 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      2. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      5. lower-/.f64 89.7

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]

   7. Applied rewrites 89.7%

      \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]

   if -8.49999999999999966e-66 < y < 2.1e-92

   1. Initial program 89.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 88.5

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]

   6. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]

      2. +-commutative N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot y}{z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      8. lower-*.f64 88.6

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   8. Applied rewrites 88.6%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   if 2.1e-92 < y

   1. Initial program 88.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{a} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x}{a} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      12. lower-*.f64 88.9

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y \]

   5. Applied rewrites 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 4e+25)
   (* (/ (fma (/ (* y x) z) 0.5 (* -4.5 t)) a) z)
   (* (fma (/ x a) 0.5 (* (/ (* t (/ z a)) y) -4.5)) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4e+25) {
		tmp = (fma(((y * x) / z), 0.5, (-4.5 * t)) / a) * z;
	} else {
		tmp = fma((x / a), 0.5, (((t * (z / a)) / y) * -4.5)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4e+25)
		tmp = Float64(Float64(fma(Float64(Float64(y * x) / z), 0.5, Float64(-4.5 * t)) / a) * z);
	else
		tmp = Float64(fma(Float64(x / a), 0.5, Float64(Float64(Float64(t * Float64(z / a)) / y) * -4.5)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 4e+25], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 0.5 + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * 0.5 + N[(N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.00000000000000036e25

   1. Initial program 90.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

      13. lower-/.f64 80.0

          \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

   5. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]

   6. Taylor expanded in a around 0

      \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]

      2. +-commutative N/A

         \[\leadsto \frac{\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      3. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot y}{z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot t}{a} \cdot z \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

      8. lower-*.f64 83.7

         \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   8. Applied rewrites 83.7%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

   if 4.00000000000000036e25 < a

   1. Initial program 79.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y} + \frac{1}{2} \cdot \frac{x}{a}\right) \cdot \color{blue}{y} \]

      3. +-commutative N/A

         \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{a} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(\frac{x}{a} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot y}\right) \cdot y \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot z}{a \cdot y} \cdot \frac{-9}{2}\right) \cdot y \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      12. lower-*.f64 80.9

          \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y \]

   5. Applied rewrites 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{\frac{t \cdot z}{a}}{y} \cdot -4.5\right) \cdot y} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      2. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{\frac{t \cdot z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, \frac{1}{2}, \frac{t \cdot \frac{z}{a}}{y} \cdot \frac{-9}{2}\right) \cdot y \]

      5. lower-/.f64 84.2

         \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]

   7. Applied rewrites 84.2%

      \[\leadsto \mathsf{fma}\left(\frac{x}{a}, 0.5, \frac{t \cdot \frac{z}{a}}{y} \cdot -4.5\right) \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.6% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (* (/ (fma (/ (* y x) z) 0.5 (* -4.5 t)) a) z))

C

double code(double x, double y, double z, double t, double a) {
	return (fma(((y * x) / z), 0.5, (-4.5 * t)) / a) * z;
}

Julia

function code(x, y, z, t, a)
	return Float64(Float64(fma(Float64(Float64(y * x) / z), 0.5, Float64(-4.5 * t)) / a) * z)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 0.5 + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 87.7%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z \cdot \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\frac{-9}{2} \cdot \frac{t}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z}\right) \cdot \color{blue}{z} \]

   3. +-commutative N/A

      \[\leadsto \left(\frac{1}{2} \cdot \frac{x \cdot y}{a \cdot z} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   4. *-commutative N/A

      \[\leadsto \left(\frac{x \cdot y}{a \cdot z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{a \cdot z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   6. associate-/r* N/A

      \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   7. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   8. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{\frac{x \cdot y}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   10. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{-9}{2} \cdot \frac{t}{a}\right) \cdot z \]

   11. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

   12. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, \frac{1}{2}, \frac{t}{a} \cdot \frac{-9}{2}\right) \cdot z \]

   13. lower-/.f64 79.0

       \[\leadsto \mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z \]

5. Applied rewrites 79.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{y \cdot x}{a}}{z}, 0.5, \frac{t}{a} \cdot -4.5\right) \cdot z} \]

6. Taylor expanded in a around 0

   \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]
7. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{\frac{-9}{2} \cdot t + \frac{1}{2} \cdot \frac{x \cdot y}{z}}{a} \cdot z \]

   2. +-commutative N/A

      \[\leadsto \frac{\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{-9}{2} \cdot t}{a} \cdot z \]

   3. *-commutative N/A

      \[\leadsto \frac{\frac{x \cdot y}{z} \cdot \frac{1}{2} + \frac{-9}{2} \cdot t}{a} \cdot z \]

   4. lower-fma.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

   5. lower-/.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{x \cdot y}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

   6. *-commutative N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, \frac{1}{2}, \frac{-9}{2} \cdot t\right)}{a} \cdot z \]

   8. lower-*.f64 79.9

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]

8. Applied rewrites 79.9%

   \[\leadsto \frac{\mathsf{fma}\left(\frac{y \cdot x}{z}, 0.5, -4.5 \cdot t\right)}{a} \cdot z \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))