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

Percentage Accurate: 79.2% → 89.6%

Time: 5.8s

Alternatives: 15

Speedup: 0.7×

• 37.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, c)
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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, c)
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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \left(a \cdot t\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* t a) -4.0 (* (fma (/ y z) 9.0 (/ b (* z x))) x)) c)))
   (if (<= z -1.4e+82)
     t_1
     (if (<= z 5.2e+44)
       (/ (+ (- (* (* x 9.0) y) (* (* 4.0 z) (* a t))) b) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t * a), -4.0, (fma((y / z), 9.0, (b / (z * x))) * x)) / c;
	double tmp;
	if (z <= -1.4e+82) {
		tmp = t_1;
	} else if (z <= 5.2e+44) {
		tmp = ((((x * 9.0) * y) - ((4.0 * z) * (a * t))) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(y / z), 9.0, Float64(b / Float64(z * x))) * x)) / c)
	tmp = 0.0
	if (z <= -1.4e+82)
		tmp = t_1;
	elseif (z <= 5.2e+44)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(4.0 * z) * Float64(a * t))) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(b / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.4e+82], t$95$1, If[LessEqual[z, 5.2e+44], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e82 or 5.1999999999999998e44 < z

   1. Initial program 58.0%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 87.0

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 87.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9 + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

      8. lower-*.f64 87.8

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   9. Applied rewrites 87.8%

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   if -1.4e82 < z < 5.1999999999999998e44

   1. Initial program 93.2%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 90.8

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 90.8%

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

Alternative 2: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;\frac{\left(t\_1 - \left(4 \cdot z\right) \cdot \left(a \cdot t\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, \frac{a}{c} \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_2 -1e-117)
     (/ (+ (- t_1 (* (* 4.0 z) (* a t))) b) (* z c))
     (if (<= t_2 INFINITY)
       (/ (fma (* t a) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
       (* (fma (* x (/ y (* (* t z) c))) 9.0 (* (/ a c) -4.0)) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -1e-117) {
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + b) / (z * c);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma((t * a), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = fma((x * (y / ((t * z) * c))), 9.0, ((a / c) * -4.0)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -1e-117)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(4.0 * z) * Float64(a * t))) + b) / Float64(z * c));
	elseif (t_2 <= Inf)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(fma(Float64(x * Float64(y / Float64(Float64(t * z) * c))), 9.0, Float64(Float64(a / c) * -4.0)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-117], N[(N[(N[(t$95$1 - N[(N[(4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * N[(y / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 9.0 + N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-117

   1. Initial program 89.0%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 89.4

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 89.4%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   if -1.00000000000000003e-117 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 83.8%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 89.9

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 89.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + -4 \cdot \frac{a}{c}\right) \cdot t \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{c \cdot \left(t \cdot z\right)} \cdot 9 + -4 \cdot \frac{a}{c}\right) \cdot t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x \cdot y}{c \cdot \left(t \cdot z\right)}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot \left(t \cdot z\right)}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot \left(t \cdot z\right)}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{c \cdot \left(t \cdot z\right)}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, -4 \cdot \frac{a}{c}\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, \frac{a}{c} \cdot -4\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, \frac{a}{c} \cdot -4\right) \cdot t \]

      12. lift-/.f64 66.5

          \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, \frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 66.5%

      \[\leadsto \mathsf{fma}\left(x \cdot \frac{y}{\left(t \cdot z\right) \cdot c}, 9, \frac{a}{c} \cdot -4\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;\frac{\left(t\_1 - \left(4 \cdot z\right) \cdot \left(a \cdot t\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_2 -1e-117)
     (/ (+ (- t_1 (* (* 4.0 z) (* a t))) b) (* z c))
     (if (<= t_2 INFINITY)
       (/ (fma (* t a) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
       (* (* (/ a c) -4.0) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -1e-117) {
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + b) / (z * c);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma((t * a), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = ((a / c) * -4.0) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -1e-117)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(4.0 * z) * Float64(a * t))) + b) / Float64(z * c));
	elseif (t_2 <= Inf)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-117], N[(N[(N[(t$95$1 - N[(N[(4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000003e-117

   1. Initial program 89.0%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 89.4

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 89.4%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   if -1.00000000000000003e-117 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 83.8%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 89.9

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 89.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 51.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 62.1

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 62.1%

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

Alternative 4: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+272}:\\ \;\;\;\;\frac{\left(y \cdot \frac{x}{c}\right) \cdot 9}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -5e+272)
     (/ (* (* y (/ x c)) 9.0) z)
     (if (<= t_1 1e+303)
       (/ (fma (* t a) -4.0 (/ (fma (* y x) 9.0 b) z)) c)
       (/ (fma (* t a) -4.0 (* (* (/ y z) 9.0) x)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -5e+272) {
		tmp = ((y * (x / c)) * 9.0) / z;
	} else if (t_1 <= 1e+303) {
		tmp = fma((t * a), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = fma((t * a), -4.0, (((y / z) * 9.0) * x)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -5e+272)
		tmp = Float64(Float64(Float64(y * Float64(x / c)) * 9.0) / z);
	elseif (t_1 <= 1e+303)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	else
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(Float64(Float64(y / z) * 9.0) * x)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+272], N[(N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y / z), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999973e272

   1. Initial program 64.1%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 64.1

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 64.1%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 55.8

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{9 \cdot \frac{x \cdot y}{c}}{z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      4. lower-*.f64 64.9

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

   9. Applied rewrites 64.9%

      \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

       3. *-commutative N/A

          \[\leadsto \frac{\frac{y \cdot x}{c} \cdot 9}{z} \]

       4. associate-/l* N/A

          \[\leadsto \frac{\left(y \cdot \frac{x}{c}\right) \cdot 9}{z} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{\left(y \cdot \frac{x}{c}\right) \cdot 9}{z} \]

       6. lower-/.f64 81.8

          \[\leadsto \frac{\left(y \cdot \frac{x}{c}\right) \cdot 9}{z} \]

   11. Applied rewrites 81.8%

       \[\leadsto \frac{\left(y \cdot \frac{x}{c}\right) \cdot 9}{z} \]

   if -4.99999999999999973e272 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e303

   1. Initial program 82.0%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 81.4%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 89.9

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 89.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   if 1e303 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 59.5%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 60.3%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 60.5

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 60.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9 + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

      8. lower-*.f64 80.5

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   9. Applied rewrites 80.5%

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z}\right) \cdot x\right)}{c} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

       3. lift-/.f64 81.8

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

   12. Applied rewrites 81.8%

       \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c}\\ \mathbf{if}\;z \leq -0.0135:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* t a) -4.0 (* (* (/ y z) 9.0) x)) c)))
   (if (<= z -0.0135)
     t_1
     (if (<= z 1.12e+43) (/ (/ (fma (* x y) 9.0 b) c) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t * a), -4.0, (((y / z) * 9.0) * x)) / c;
	double tmp;
	if (z <= -0.0135) {
		tmp = t_1;
	} else if (z <= 1.12e+43) {
		tmp = (fma((x * y), 9.0, b) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(t * a), -4.0, Float64(Float64(Float64(y / z) * 9.0) * x)) / c)
	tmp = 0.0
	if (z <= -0.0135)
		tmp = t_1;
	elseif (z <= 1.12e+43)
		tmp = Float64(Float64(fma(Float64(x * y), 9.0, b) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(N[(y / z), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -0.0135], t$95$1, If[LessEqual[z, 1.12e+43], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0134999999999999998 or 1.12e43 < z

   1. Initial program 62.1%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 70.2%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 88.0

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 88.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9 + \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{x \cdot z}\right) \cdot x\right)}{c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

      8. lower-*.f64 87.9

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   9. Applied rewrites 87.9%

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c} \]

   10. Taylor expanded in x around inf

       \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(9 \cdot \frac{y}{z}\right) \cdot x\right)}{c} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

       3. lift-/.f64 75.5

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

   12. Applied rewrites 75.5%

       \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \left(\frac{y}{z} \cdot 9\right) \cdot x\right)}{c} \]

   if -0.0134999999999999998 < z < 1.12e43

   1. Initial program 94.3%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 91.3

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 91.3%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 90.0

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{b}{c} + \frac{9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      3. div-add N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      5. +-commutative N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + b}{c}}{z} \]

      6. *-commutative N/A

         \[\leadsto \frac{\frac{\left(x \cdot y\right) \cdot 9 + b}{c}}{z} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

      8. lower-*.f64 77.1

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

   9. Applied rewrites 77.1%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -2.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* t a) -4.0 (/ b z)) c)))
   (if (<= z -2.1)
     t_1
     (if (<= z 4.2e+99) (/ (/ (fma (* x y) 9.0 b) c) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t * a), -4.0, (b / z)) / c;
	double tmp;
	if (z <= -2.1) {
		tmp = t_1;
	} else if (z <= 4.2e+99) {
		tmp = (fma((x * y), 9.0, b) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.1)
		tmp = t_1;
	elseif (z <= 4.2e+99)
		tmp = Float64(Float64(fma(Float64(x * y), 9.0, b) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.1], t$95$1, If[LessEqual[z, 4.2e+99], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000009 or 4.2000000000000002e99 < z

   1. Initial program 60.6%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      4. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right)} \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(x \cdot 9\right) \cdot y} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      10. associate-/r* N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

      11. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied rewrites 69.1%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   4. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}}{c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)}{c} \]

      3. +-commutative N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(a \cdot t\right) \cdot -4 + \left(\color{blue}{9 \cdot \frac{x \cdot y}{z}} + \frac{b}{z}\right)}{c} \]

      5. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, \color{blue}{-4}, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      9. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. div-add N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      12. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      13. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      14. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      15. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      16. lift-*.f64 87.8

          \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 87.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t \cdot a, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c} \]
   8. Step-by-step derivation

   9. Applied rewrites 72.6%

      \[\leadsto \frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c} \]

   if -2.10000000000000009 < z < 4.2000000000000002e99

   1. Initial program 92.9%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 90.5

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 90.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 88.3

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{b}{c} + \frac{9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      3. div-add N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      5. +-commutative N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + b}{c}}{z} \]

      6. *-commutative N/A

         \[\leadsto \frac{\frac{\left(x \cdot y\right) \cdot 9 + b}{c}}{z} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

      8. lower-*.f64 74.9

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

   9. Applied rewrites 74.9%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ t c) -4.0) a)))
   (if (<= a -7.8e-69)
     t_1
     (if (<= a 5.2e+185) (/ (/ (fma (* x y) 9.0 b) c) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t / c) * -4.0) * a;
	double tmp;
	if (a <= -7.8e-69) {
		tmp = t_1;
	} else if (a <= 5.2e+185) {
		tmp = (fma((x * y), 9.0, b) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t / c) * -4.0) * a)
	tmp = 0.0
	if (a <= -7.8e-69)
		tmp = t_1;
	elseif (a <= 5.2e+185)
		tmp = Float64(Float64(fma(Float64(x * y), 9.0, b) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -7.8e-69], t$95$1, If[LessEqual[a, 5.2e+185], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.79999999999999961e-69 or 5.20000000000000001e185 < a

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(c \cdot z\right) \cdot a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      3. lift-/.f64 55.0

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   7. Applied rewrites 55.0%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   if -7.79999999999999961e-69 < a < 5.20000000000000001e185

   1. Initial program 79.4%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 82.3

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 82.3%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 76.5

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{b}{c} + \frac{9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      3. div-add N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{c}}{z} \]

      5. +-commutative N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + b}{c}}{z} \]

      6. *-commutative N/A

         \[\leadsto \frac{\frac{\left(x \cdot y\right) \cdot 9 + b}{c}}{z} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

      8. lower-*.f64 68.0

         \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]

   9. Applied rewrites 68.0%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 62.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+67}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.25e+67)
   (* (* (/ t c) -4.0) a)
   (if (<= z 4.2e+99) (/ (fma (* 9.0 x) y b) (* z c)) (* (* (/ a c) -4.0) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.25e+67) {
		tmp = ((t / c) * -4.0) * a;
	} else if (z <= 4.2e+99) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else {
		tmp = ((a / c) * -4.0) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.25e+67)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	elseif (z <= 4.2e+99)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.25e+67], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 4.2e+99], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999994e67

   1. Initial program 57.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(c \cdot z\right) \cdot a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      3. lift-/.f64 56.8

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   7. Applied rewrites 56.8%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   if -1.24999999999999994e67 < z < 4.2000000000000002e99

   1. Initial program 92.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + \color{blue}{b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(x \cdot y\right) \cdot 9 + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(x \cdot y, \color{blue}{9}, b\right)}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 73.9

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c} \]

   4. Applied rewrites 73.9%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c} \]

      2. lift-fma.f64 N/A

         \[\leadsto \frac{\left(y \cdot x\right) \cdot 9 + \color{blue}{b}}{z \cdot c} \]

      3. *-commutative N/A

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right) + b}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\left(9 \cdot x\right) \cdot y + b}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, \color{blue}{y}, b\right)}{z \cdot c} \]

      7. lower-*.f64 73.9

         \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c} \]

   6. Applied rewrites 73.9%

      \[\leadsto \frac{\mathsf{fma}\left(9 \cdot x, \color{blue}{y}, b\right)}{z \cdot c} \]

   if 4.2000000000000002e99 < z

   1. Initial program 55.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 74.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 59.4

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 59.4%

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

Alternative 9: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{\left(x \cdot \frac{y}{c}\right) \cdot 9}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -3.5e-137)
   (* (* (/ a c) -4.0) t)
   (if (<= a 3.7e-168)
     (/ (/ b z) c)
     (if (<= a 2.7e+142) (/ (* (* x (/ y c)) 9.0) z) (* (* (/ t c) -4.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 3.7e-168) {
		tmp = (b / z) / c;
	} else if (a <= 2.7e+142) {
		tmp = ((x * (y / c)) * 9.0) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
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), intent (in) :: c
    real(8) :: tmp
    if (a <= (-3.5d-137)) then
        tmp = ((a / c) * (-4.0d0)) * t
    else if (a <= 3.7d-168) then
        tmp = (b / z) / c
    else if (a <= 2.7d+142) then
        tmp = ((x * (y / c)) * 9.0d0) / z
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 3.7e-168) {
		tmp = (b / z) / c;
	} else if (a <= 2.7e+142) {
		tmp = ((x * (y / c)) * 9.0) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.5e-137:
		tmp = ((a / c) * -4.0) * t
	elif a <= 3.7e-168:
		tmp = (b / z) / c
	elif a <= 2.7e+142:
		tmp = ((x * (y / c)) * 9.0) / z
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.5e-137)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (a <= 3.7e-168)
		tmp = Float64(Float64(b / z) / c);
	elseif (a <= 2.7e+142)
		tmp = Float64(Float64(Float64(x * Float64(y / c)) * 9.0) / z);
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -3.5e-137)
		tmp = ((a / c) * -4.0) * t;
	elseif (a <= 3.7e-168)
		tmp = (b / z) / c;
	elseif (a <= 2.7e+142)
		tmp = ((x * (y / c)) * 9.0) / z;
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -3.5e-137], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 3.7e-168], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 2.7e+142], N[(N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5000000000000001e-137

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 48.9

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 48.9%

      \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   if -3.5000000000000001e-137 < a < 3.69999999999999997e-168

   1. Initial program 78.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 46.7%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

      5. lower-/.f64 45.7

         \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

      6. associate-+l- 45.7

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      7. associate-*l* 45.7

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      8. *-commutative 45.7

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      9. *-commutative 45.7

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      10. associate-+l- 45.7

          \[\leadsto \frac{\frac{b}{z}}{c} \]

   6. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if 3.69999999999999997e-168 < a < 2.69999999999999983e142

   1. Initial program 80.3%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 80.4

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 80.4%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 76.3

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 76.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{9 \cdot \frac{x \cdot y}{c}}{z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

      4. lower-*.f64 35.3

         \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

   9. Applied rewrites 35.3%

      \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

       2. lift-/.f64 N/A

          \[\leadsto \frac{\frac{x \cdot y}{c} \cdot 9}{z} \]

       3. associate-/l* N/A

          \[\leadsto \frac{\left(x \cdot \frac{y}{c}\right) \cdot 9}{z} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(x \cdot \frac{y}{c}\right) \cdot 9}{z} \]

       5. lower-/.f64 37.0

          \[\leadsto \frac{\left(x \cdot \frac{y}{c}\right) \cdot 9}{z} \]

   11. Applied rewrites 37.0%

       \[\leadsto \frac{\left(x \cdot \frac{y}{c}\right) \cdot 9}{z} \]

   if 2.69999999999999983e142 < a

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 81.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(c \cdot z\right) \cdot a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      3. lift-/.f64 63.4

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   7. Applied rewrites 63.4%

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

Alternative 10: 48.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 18000000000000:\\ \;\;\;\;\frac{\left(y \cdot 9\right) \cdot x}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -3.5e-137)
   (* (* (/ a c) -4.0) t)
   (if (<= a 7.4e-269)
     (/ (/ b z) c)
     (if (<= a 18000000000000.0)
       (/ (* (* y 9.0) x) (* z c))
       (* (* (/ t c) -4.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 7.4e-269) {
		tmp = (b / z) / c;
	} else if (a <= 18000000000000.0) {
		tmp = ((y * 9.0) * x) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
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), intent (in) :: c
    real(8) :: tmp
    if (a <= (-3.5d-137)) then
        tmp = ((a / c) * (-4.0d0)) * t
    else if (a <= 7.4d-269) then
        tmp = (b / z) / c
    else if (a <= 18000000000000.0d0) then
        tmp = ((y * 9.0d0) * x) / (z * c)
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 7.4e-269) {
		tmp = (b / z) / c;
	} else if (a <= 18000000000000.0) {
		tmp = ((y * 9.0) * x) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.5e-137:
		tmp = ((a / c) * -4.0) * t
	elif a <= 7.4e-269:
		tmp = (b / z) / c
	elif a <= 18000000000000.0:
		tmp = ((y * 9.0) * x) / (z * c)
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.5e-137)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (a <= 7.4e-269)
		tmp = Float64(Float64(b / z) / c);
	elseif (a <= 18000000000000.0)
		tmp = Float64(Float64(Float64(y * 9.0) * x) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -3.5e-137)
		tmp = ((a / c) * -4.0) * t;
	elseif (a <= 7.4e-269)
		tmp = (b / z) / c;
	elseif (a <= 18000000000000.0)
		tmp = ((y * 9.0) * x) / (z * c);
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -3.5e-137], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 7.4e-269], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 18000000000000.0], N[(N[(N[(y * 9.0), $MachinePrecision] * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5000000000000001e-137

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 48.9

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 48.9%

      \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   if -3.5000000000000001e-137 < a < 7.39999999999999955e-269

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 47.3%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

      5. lower-/.f64 46.4

         \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

      6. associate-+l- 46.4

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      7. associate-*l* 46.4

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      8. *-commutative 46.4

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      9. *-commutative 46.4

         \[\leadsto \frac{\frac{b}{z}}{c} \]

      10. associate-+l- 46.4

          \[\leadsto \frac{\frac{b}{z}}{c} \]

   6. Applied rewrites 46.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if 7.39999999999999955e-269 < a < 1.8e13

   1. Initial program 79.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{\left(\left(9 \cdot y + \frac{b}{x}\right) - 4 \cdot \frac{a \cdot \left(t \cdot z\right)}{x}\right) \cdot \color{blue}{x}}{z \cdot c} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(9 \cdot y + \frac{b}{x}\right) - 4 \cdot \frac{a \cdot \left(t \cdot z\right)}{x}\right) \cdot \color{blue}{x}}{z \cdot c} \]

   4. Applied rewrites 73.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 9, \frac{b - \left(\left(t \cdot z\right) \cdot a\right) \cdot 4}{x}\right) \cdot x}}{z \cdot c} \]

   5. Taylor expanded in x around inf

      \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(y \cdot 9\right) \cdot x}{z \cdot c} \]

      2. lower-*.f64 40.0

         \[\leadsto \frac{\left(y \cdot 9\right) \cdot x}{z \cdot c} \]

   7. Applied rewrites 40.0%

      \[\leadsto \frac{\left(y \cdot 9\right) \cdot x}{z \cdot c} \]

   if 1.8e13 < a

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(c \cdot z\right) \cdot a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      3. lift-/.f64 55.6

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   7. Applied rewrites 55.6%

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

Alternative 11: 48.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;\left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{elif}\;a \leq 16500000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -3.5e-137)
   (* (* (/ a c) -4.0) t)
   (if (<= a 16500000000000.0) (/ (/ b c) z) (* (* (/ t c) -4.0) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
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), intent (in) :: c
    real(8) :: tmp
    if (a <= (-3.5d-137)) then
        tmp = ((a / c) * (-4.0d0)) * t
    else if (a <= 16500000000000.0d0) then
        tmp = (b / c) / z
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.5e-137) {
		tmp = ((a / c) * -4.0) * t;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.5e-137:
		tmp = ((a / c) * -4.0) * t
	elif a <= 16500000000000.0:
		tmp = (b / c) / z
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.5e-137)
		tmp = Float64(Float64(Float64(a / c) * -4.0) * t);
	elseif (a <= 16500000000000.0)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -3.5e-137)
		tmp = ((a / c) * -4.0) * t;
	elseif (a <= 16500000000000.0)
		tmp = (b / c) / z;
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -3.5e-137], N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 16500000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5000000000000001e-137

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 48.9

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 48.9%

      \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   if -3.5000000000000001e-137 < a < 1.65e13

   1. Initial program 79.5%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 84.8

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 84.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 77.0

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in b around inf

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 42.9

         \[\leadsto \frac{\frac{b}{c}}{z} \]

   9. Applied rewrites 42.9%

      \[\leadsto \frac{\frac{b}{c}}{z} \]

   if 1.65e13 < a

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(c \cdot z\right) \cdot a}\right) \cdot a} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

      3. lift-/.f64 55.5

         \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   7. Applied rewrites 55.5%

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

Alternative 12: 47.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{a}{c} \cdot -4\right) \cdot t\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 16500000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ a c) -4.0) t)))
   (if (<= a -3.5e-137) t_1 (if (<= a 16500000000000.0) (/ (/ b c) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * -4.0) * t;
	double tmp;
	if (a <= -3.5e-137) {
		tmp = t_1;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a / c) * (-4.0d0)) * t
    if (a <= (-3.5d-137)) then
        tmp = t_1
    else if (a <= 16500000000000.0d0) then
        tmp = (b / c) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((a / c) * -4.0) * t;
	double tmp;
	if (a <= -3.5e-137) {
		tmp = t_1;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((a / c) * -4.0) * t
	tmp = 0
	if a <= -3.5e-137:
		tmp = t_1
	elif a <= 16500000000000.0:
		tmp = (b / c) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(a / c) * -4.0) * t)
	tmp = 0.0
	if (a <= -3.5e-137)
		tmp = t_1;
	elseif (a <= 16500000000000.0)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((a / c) * -4.0) * t;
	tmp = 0.0;
	if (a <= -3.5e-137)
		tmp = t_1;
	elseif (a <= 16500000000000.0)
		tmp = (b / c) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[a, -3.5e-137], t$95$1, If[LessEqual[a, 16500000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000001e-137 or 1.65e13 < a

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot \color{blue}{t} \]

   4. Applied rewrites 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{a}{c}\right) \cdot t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

      3. lift-/.f64 52.1

         \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   7. Applied rewrites 52.1%

      \[\leadsto \left(\frac{a}{c} \cdot -4\right) \cdot t \]

   if -3.5000000000000001e-137 < a < 1.65e13

   1. Initial program 79.5%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 84.8

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 84.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 77.0

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in b around inf

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 42.9

         \[\leadsto \frac{\frac{b}{c}}{z} \]

   9. Applied rewrites 42.9%

      \[\leadsto \frac{\frac{b}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 46.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 16500000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c))))
   (if (<= a -3.5e-137) t_1 (if (<= a 16500000000000.0) (/ (/ b c) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double tmp;
	if (a <= -3.5e-137) {
		tmp = t_1;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    if (a <= (-3.5d-137)) then
        tmp = t_1
    else if (a <= 16500000000000.0d0) then
        tmp = (b / c) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double tmp;
	if (a <= -3.5e-137) {
		tmp = t_1;
	} else if (a <= 16500000000000.0) {
		tmp = (b / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	tmp = 0
	if a <= -3.5e-137:
		tmp = t_1
	elif a <= 16500000000000.0:
		tmp = (b / c) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (a <= -3.5e-137)
		tmp = t_1;
	elseif (a <= 16500000000000.0)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (a <= -3.5e-137)
		tmp = t_1;
	elseif (a <= 16500000000000.0)
		tmp = (b / c) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-137], t$95$1, If[LessEqual[a, 16500000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000001e-137 or 1.65e13 < a

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{\color{blue}{c}} \]

      3. lower-*.f64 48.0

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

   4. Applied rewrites 48.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -3.5000000000000001e-137 < a < 1.65e13

   1. Initial program 79.5%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

      4. associate-*l* N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

      9. lower-*.f64 84.8

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   3. Applied rewrites 84.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      12. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

      13. lower-/.f64 77.0

          \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   6. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

   7. Taylor expanded in b around inf

      \[\leadsto \frac{\frac{b}{c}}{z} \]
   8. Step-by-step derivation

      1. lift-/.f64 42.9

         \[\leadsto \frac{\frac{b}{c}}{z} \]

   9. Applied rewrites 42.9%

      \[\leadsto \frac{\frac{b}{c}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 34.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ (/ b c) z))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

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, c)
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), intent (in) :: c
    code = (b / c) / z
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Python

def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 79.2%

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

   1. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right)} \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right)} \cdot a\right) + b}{z \cdot c} \]

   4. associate-*l* N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   5. *-commutative N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   6. lower-*.f64 N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   7. *-commutative N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right)} \cdot \left(a \cdot t\right)\right) + b}{z \cdot c} \]

   9. lower-*.f64 80.0

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)}\right) + b}{z \cdot c} \]

3. Applied rewrites 80.0%

   \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(4 \cdot z\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

4. Taylor expanded in z around 0

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

   1. lower-/.f64 N/A

      \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{\color{blue}{z}} \]

   2. *-commutative N/A

      \[\leadsto \frac{\frac{a \cdot \left(t \cdot z\right)}{c} \cdot -4 + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   3. lower-fma.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{a \cdot \left(t \cdot z\right)}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   5. *-commutative N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

   8. *-commutative N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \frac{x \cdot y}{c} \cdot 9 + \frac{b}{c}\right)}{z} \]

   9. lower-fma.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   10. lower-/.f64 N/A

       \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{x \cdot y}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   11. *-commutative N/A

       \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   12. lift-*.f64 N/A

       \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

   13. lower-/.f64 75.2

       \[\leadsto \frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z} \]

6. Applied rewrites 75.2%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\left(t \cdot z\right) \cdot a}{c}, -4, \mathsf{fma}\left(\frac{y \cdot x}{c}, 9, \frac{b}{c}\right)\right)}{z}} \]

7. Taylor expanded in b around inf

   \[\leadsto \frac{\frac{b}{c}}{z} \]
8. Step-by-step derivation

   1. lift-/.f64 34.2

      \[\leadsto \frac{\frac{b}{c}}{z} \]

9. Applied rewrites 34.2%

   \[\leadsto \frac{\frac{b}{c}}{z} \]
10. Add Preprocessing

Alternative 15: 34.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

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, c)
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), intent (in) :: c
    code = b / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. Taylor expanded in b around inf

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Step-by-step derivation

4. Applied rewrites 34.9%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))