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

Percentage Accurate: 79.3% → 89.8%

Time: 5.4s

Alternatives: 19

Speedup: 0.6×

• 37.4% 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: 79.3% 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: 89.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{fma}\left(\frac{y}{z}, -9, -\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{x}\right) \cdot x}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 (- INFINITY))
     (- (* (* (/ (/ y c) z) -9.0) x))
     (if (<= t_1 2e-15)
       (/ (fma (fma (* x y) 9.0 b) (/ 1.0 z) (* (* a t) -4.0)) c)
       (if (<= t_1 5e+185)
         (fma -4.0 (* a (/ t c)) (/ (fma (* y x) 9.0 b) (* c z)))
         (/
          (- (* (fma (/ y z) -9.0 (- (/ (fma (* a t) -4.0 (/ b z)) x))) 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 <= -((double) INFINITY)) {
		tmp = -((((y / c) / z) * -9.0) * x);
	} else if (t_1 <= 2e-15) {
		tmp = fma(fma((x * y), 9.0, b), (1.0 / z), ((a * t) * -4.0)) / c;
	} else if (t_1 <= 5e+185) {
		tmp = fma(-4.0, (a * (t / c)), (fma((y * x), 9.0, b) / (c * z)));
	} else {
		tmp = -(fma((y / z), -9.0, -(fma((a * t), -4.0, (b / z)) / x)) * 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 <= Float64(-Inf))
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	elseif (t_1 <= 2e-15)
		tmp = Float64(fma(fma(Float64(x * y), 9.0, b), Float64(1.0 / z), Float64(Float64(a * t) * -4.0)) / c);
	elseif (t_1 <= 5e+185)
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z)));
	else
		tmp = Float64(Float64(-Float64(fma(Float64(y / z), -9.0, Float64(-Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / x))) * 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, (-Infinity)], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, 2e-15], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] * N[(1.0 / z), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+185], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[(N[(N[(y / z), $MachinePrecision] * -9.0 + (-N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision])), $MachinePrecision] * x), $MachinePrecision]) / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 91.5

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

   9. Applied rewrites 91.5%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000002e-15

   1. Initial program 81.4%

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

      1. lift-*.f64 N/A

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

      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 81.1%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 90.4

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

   6. Applied rewrites 90.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. mult-flip N/A

         \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + b\right) \cdot \frac{1}{z} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(b + \left(y \cdot x\right) \cdot 9\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. *-commutative N/A

          \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(b + 9 \cdot \left(x \cdot y\right), \color{blue}{\frac{1}{z}}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      13. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot \left(x \cdot y\right) + b, \frac{\color{blue}{1}}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(x \cdot y\right) \cdot 9 + b, \frac{1}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{\color{blue}{1}}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{\color{blue}{z}}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      18. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

      20. lift-*.f64 90.7

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

   8. Applied rewrites 90.7%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \color{blue}{\frac{1}{z}}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

   if 2.0000000000000002e-15 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e185

   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. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 87.8

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

   4. Applied rewrites 87.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 87.9

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

   6. Applied rewrites 87.9%

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

   if 4.9999999999999999e185 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.2%

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

      1. lift-*.f64 N/A

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

      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 71.6%

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

   4. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{z} + -1 \cdot \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{x}\right)\right)}{c} \]

      2. lower-neg.f64 N/A

         \[\leadsto \frac{-x \cdot \left(-9 \cdot \frac{y}{z} + -1 \cdot \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{x}\right)}{c} \]

      3. *-commutative N/A

         \[\leadsto \frac{-\left(-9 \cdot \frac{y}{z} + -1 \cdot \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{x}\right) \cdot x}{c} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{-\left(-9 \cdot \frac{y}{z} + -1 \cdot \frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{x}\right) \cdot x}{c} \]

   6. Applied rewrites 81.5%

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

Alternative 2: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \mathbf{elif}\;t\_2 \leq 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* (* (/ (/ y c) z) -9.0) x))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e-15)
       (/ (fma (fma (* x y) 9.0 b) (/ 1.0 z) (* (* a t) -4.0)) c)
       (if (<= t_2 1e+281)
         (fma -4.0 (* a (/ t c)) (/ (fma (* y x) 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 = -((((y / c) / z) * -9.0) * x);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e-15) {
		tmp = fma(fma((x * y), 9.0, b), (1.0 / z), ((a * t) * -4.0)) / c;
	} else if (t_2 <= 1e+281) {
		tmp = fma(-4.0, (a * (t / c)), (fma((y * x), 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(Float64(Float64(y / c) / z) * -9.0) * x))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e-15)
		tmp = Float64(fma(fma(Float64(x * y), 9.0, b), Float64(1.0 / z), Float64(Float64(a * t) * -4.0)) / c);
	elseif (t_2 <= 1e+281)
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(fma(Float64(y * x), 9.0, b) / Float64(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[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision])}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e-15], N[(N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] * N[(1.0 / z), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 1e+281], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0 or 1e281 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 63.7%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.3

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

   7. Applied rewrites 81.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 89.2

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

   9. Applied rewrites 89.2%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000002e-15

   1. Initial program 81.4%

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

      1. lift-*.f64 N/A

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

      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 81.1%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 90.4

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

   6. Applied rewrites 90.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. mult-flip N/A

         \[\leadsto \frac{\left(\left(y \cdot x\right) \cdot 9 + b\right) \cdot \frac{1}{z} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(b + \left(y \cdot x\right) \cdot 9\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      11. *-commutative N/A

          \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(b + 9 \cdot \left(x \cdot y\right), \color{blue}{\frac{1}{z}}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      13. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(9 \cdot \left(x \cdot y\right) + b, \frac{\color{blue}{1}}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(x \cdot y\right) \cdot 9 + b, \frac{1}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{\color{blue}{1}}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{\color{blue}{z}}, -4 \cdot \left(a \cdot t\right)\right)}{c} \]

      18. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

      20. lift-*.f64 90.7

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \frac{1}{z}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

   8. Applied rewrites 90.7%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot y, 9, b\right), \color{blue}{\frac{1}{z}}, \left(a \cdot t\right) \cdot -4\right)}{c} \]

   if 2.0000000000000002e-15 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e281

   1. Initial program 83.4%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 87.5

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

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 86.9

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

   6. Applied rewrites 86.9%

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

Alternative 3: 89.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ t_3 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{t\_2}{z}\right)}{c}\\ \mathbf{elif}\;t\_3 \leq 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{t\_2}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* (* (/ (/ y c) z) -9.0) x)))
        (t_2 (fma (* y x) 9.0 b))
        (t_3 (* (* x 9.0) y)))
   (if (<= t_3 (- INFINITY))
     t_1
     (if (<= t_3 2e-93)
       (/ (fma (* a t) -4.0 (/ t_2 z)) c)
       (if (<= t_3 1e+281) (fma -4.0 (* a (/ t c)) (/ t_2 (* c z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -((((y / c) / z) * -9.0) * x);
	double t_2 = fma((y * x), 9.0, b);
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_3 <= 2e-93) {
		tmp = fma((a * t), -4.0, (t_2 / z)) / c;
	} else if (t_3 <= 1e+281) {
		tmp = fma(-4.0, (a * (t / c)), (t_2 / (c * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x))
	t_2 = fma(Float64(y * x), 9.0, b)
	t_3 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_3 <= 2e-93)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(t_2 / z)) / c);
	elseif (t_3 <= 1e+281)
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(t_2 / Float64(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[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision])}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$1, If[LessEqual[t$95$3, 2e-93], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$3, 1e+281], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0 or 1e281 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 63.7%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.3

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

   7. Applied rewrites 81.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 89.2

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

   9. Applied rewrites 89.2%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999998e-93

   1. Initial program 81.2%

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

      1. lift-*.f64 N/A

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

      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 80.8%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 90.4

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

   6. Applied rewrites 90.4%

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

   if 1.9999999999999998e-93 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e281

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 88.0

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

   4. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 87.4

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

   6. Applied rewrites 87.4%

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

Alternative 4: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ t_2 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+281}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* (* (/ (/ y c) z) -9.0) x))) (t_2 (* (* x 9.0) y)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 1e+281)
       (/ (fma (* a t) -4.0 (/ (fma (* y x) 9.0 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 = -((((y / c) / z) * -9.0) * x);
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+281) {
		tmp = fma((a * t), -4.0, (fma((y * x), 9.0, b) / z)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x))
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+281)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(fma(Float64(y * x), 9.0, b) / 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[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision])}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+281], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0 or 1e281 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 63.7%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.3

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

   7. Applied rewrites 81.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 89.2

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

   9. Applied rewrites 89.2%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e281

   1. Initial program 81.9%

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

      1. lift-*.f64 N/A

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

      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 80.9%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 89.9

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

   6. Applied rewrites 89.9%

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

Alternative 5: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{y}{c} \cdot -9 - \frac{b}{c \cdot x}}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 (- INFINITY))
     (- (* (* (/ (/ y c) z) -9.0) x))
     (if (<= t_1 -2e-72)
       (/ (fma (* a t) -4.0 (* (/ (* x y) z) 9.0)) c)
       (if (<= t_1 2e+111)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (- (* (/ (- (* (/ y c) -9.0) (/ b (* c x))) z) x)))))))

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 <= -((double) INFINITY)) {
		tmp = -((((y / c) / z) * -9.0) * x);
	} else if (t_1 <= -2e-72) {
		tmp = fma((a * t), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (t_1 <= 2e+111) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else {
		tmp = -(((((y / c) * -9.0) - (b / (c * x))) / z) * x);
	}
	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 <= Float64(-Inf))
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	elseif (t_1 <= -2e-72)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (t_1 <= 2e+111)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	else
		tmp = Float64(-Float64(Float64(Float64(Float64(Float64(y / c) * -9.0) - Float64(b / Float64(c * x))) / z) * x));
	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, (-Infinity)], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, -2e-72], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], (-N[(N[(N[(N[(N[(y / c), $MachinePrecision] * -9.0), $MachinePrecision] - N[(b / N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision])]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 91.5

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

   9. Applied rewrites 91.5%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e-72

   1. Initial program 81.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.5%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 88.4

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

   6. Applied rewrites 88.4%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 71.1

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

   9. Applied rewrites 71.1%

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

   if -1.9999999999999999e-72 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   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 82.2%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 91.1

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

   6. Applied rewrites 91.1%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 81.9

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

   9. Applied rewrites 81.9%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 82.0

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

   11. Applied rewrites 82.0%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 72.9

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

   7. Applied rewrites 72.9%

      \[\leadsto -\frac{\frac{y}{c} \cdot -9 - \frac{b}{c \cdot x}}{z} \cdot x \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 78.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\left(\frac{y}{c} \cdot -9 - \frac{b}{c \cdot x}\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 (- INFINITY))
     (- (* (* (/ (/ y c) z) -9.0) x))
     (if (<= t_1 -2e-72)
       (/ (fma (* a t) -4.0 (* (/ (* x y) z) 9.0)) c)
       (if (<= t_1 4e+25)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (- (/ (* (- (* (/ y c) -9.0) (/ b (* c x))) x) z)))))))

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 <= -((double) INFINITY)) {
		tmp = -((((y / c) / z) * -9.0) * x);
	} else if (t_1 <= -2e-72) {
		tmp = fma((a * t), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (t_1 <= 4e+25) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else {
		tmp = -(((((y / c) * -9.0) - (b / (c * x))) * x) / z);
	}
	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 <= Float64(-Inf))
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	elseif (t_1 <= -2e-72)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (t_1 <= 4e+25)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	else
		tmp = Float64(-Float64(Float64(Float64(Float64(Float64(y / c) * -9.0) - Float64(b / Float64(c * x))) * x) / z));
	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, (-Infinity)], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, -2e-72], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 4e+25], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], (-N[(N[(N[(N[(N[(y / c), $MachinePrecision] * -9.0), $MachinePrecision] - N[(b / N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision])]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 91.5

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

   9. Applied rewrites 91.5%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e-72

   1. Initial program 81.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.5%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 88.4

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

   6. Applied rewrites 88.4%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 71.1

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

   9. Applied rewrites 71.1%

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

   if -1.9999999999999999e-72 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.00000000000000036e25

   1. Initial program 81.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 82.1%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 91.3

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

   6. Applied rewrites 91.3%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 85.1

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

   9. Applied rewrites 85.1%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 85.2

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

   11. Applied rewrites 85.2%

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

   if 4.00000000000000036e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.9%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 68.2

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

   7. Applied rewrites 68.2%

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

Alternative 7: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 (- INFINITY))
     (- (* (* (/ (/ y c) z) -9.0) x))
     (if (<= t_1 -2e-72)
       (/ (fma (* a t) -4.0 (* (/ (* x y) z) 9.0)) c)
       (if (<= t_1 2e+111)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (* (/ (* x 1.0) (* c (/ z y))) 9.0))))))

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 <= -((double) INFINITY)) {
		tmp = -((((y / c) / z) * -9.0) * x);
	} else if (t_1 <= -2e-72) {
		tmp = fma((a * t), -4.0, (((x * y) / z) * 9.0)) / c;
	} else if (t_1 <= 2e+111) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else {
		tmp = ((x * 1.0) / (c * (z / y))) * 9.0;
	}
	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 <= Float64(-Inf))
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	elseif (t_1 <= -2e-72)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(Float64(Float64(x * y) / z) * 9.0)) / c);
	elseif (t_1 <= 2e+111)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(x * 1.0) / Float64(c * Float64(z / y))) * 9.0);
	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, (-Infinity)], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, -2e-72], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * 1.0), $MachinePrecision] / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 91.5

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

   9. Applied rewrites 91.5%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e-72

   1. Initial program 81.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 79.5%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 88.4

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

   6. Applied rewrites 88.4%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 71.1

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

   9. Applied rewrites 71.1%

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

   if -1.9999999999999999e-72 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   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 82.2%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 91.1

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

   6. Applied rewrites 91.1%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 81.9

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

   9. Applied rewrites 81.9%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 82.0

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

   11. Applied rewrites 82.0%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

      1. lift-*.f64 N/A

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

      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 73.3%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 79.3

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

   6. Applied rewrites 79.3%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-+l- N/A

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 67.5

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

   9. Applied rewrites 67.5%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-/l* N/A

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

       5. times-frac N/A

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

       6. division-flip N/A

          \[\leadsto \left(\frac{x}{c} \cdot \frac{1}{\frac{z}{y}}\right) \cdot 9 \]

       7. frac-times N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       8. lower-/.f64 N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       10. lower-*.f64 N/A

           \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       11. lower-/.f64 68.7

           \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

   11. Applied rewrites 68.7%

       \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+275}:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -5e+275)
     (- (* (* (/ (/ y c) z) -9.0) x))
     (if (<= t_1 -5e+25)
       (/ (fma (* y x) 9.0 b) (* z c))
       (if (<= t_1 2e+111)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (* (/ (* x 1.0) (* c (/ z y))) 9.0))))))

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+275) {
		tmp = -((((y / c) / z) * -9.0) * x);
	} else if (t_1 <= -5e+25) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 2e+111) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else {
		tmp = ((x * 1.0) / (c * (z / y))) * 9.0;
	}
	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+275)
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	elseif (t_1 <= -5e+25)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 2e+111)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(x * 1.0) / Float64(c * Float64(z / y))) * 9.0);
	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+275], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, -5e+25], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * 1.0), $MachinePrecision] / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000003e275

   1. Initial program 62.6%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.3%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 79.1

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

   7. Applied rewrites 79.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 87.6

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

   9. Applied rewrites 87.6%

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

   if -5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000024e25

   1. Initial program 81.8%

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

   2. 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 66.2

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

   4. Applied rewrites 66.2%

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

   if -5.00000000000000024e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   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 82.1%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 91.1

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

   6. Applied rewrites 91.1%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 80.6

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

   9. Applied rewrites 80.6%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 80.7

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

   11. Applied rewrites 80.7%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

      1. lift-*.f64 N/A

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

      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 73.3%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 79.3

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

   6. Applied rewrites 79.3%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-+l- N/A

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 67.5

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

   9. Applied rewrites 67.5%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-/l* N/A

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

       5. times-frac N/A

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

       6. division-flip N/A

          \[\leadsto \left(\frac{x}{c} \cdot \frac{1}{\frac{z}{y}}\right) \cdot 9 \]

       7. frac-times N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       8. lower-/.f64 N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       10. lower-*.f64 N/A

           \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

       11. lower-/.f64 68.7

           \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]

   11. Applied rewrites 68.7%

       \[\leadsto \frac{x \cdot 1}{c \cdot \frac{z}{y}} \cdot 9 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := -\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (- (* (* (/ (/ y c) z) -9.0) x))))
   (if (<= t_1 -5e+275)
     t_2
     (if (<= t_1 -5e+25)
       (/ (fma (* y x) 9.0 b) (* z c))
       (if (<= t_1 2e+111) (/ (fma (* -4.0 a) t (/ b z)) c) t_2)))))

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 = -((((y / c) / z) * -9.0) * x);
	double tmp;
	if (t_1 <= -5e+275) {
		tmp = t_2;
	} else if (t_1 <= -5e+25) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 2e+111) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else {
		tmp = t_2;
	}
	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(Float64(Float64(y / c) / z) * -9.0) * x))
	tmp = 0.0
	if (t_1 <= -5e+275)
		tmp = t_2;
	elseif (t_1 <= -5e+25)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 2e+111)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	else
		tmp = t_2;
	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[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[t$95$1, -5e+275], t$95$2, If[LessEqual[t$95$1, -5e+25], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000003e275 or 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 71.4%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 71.0

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

   7. Applied rewrites 71.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 75.9

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

   9. Applied rewrites 75.9%

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

   if -5.0000000000000003e275 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000024e25

   1. Initial program 81.8%

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

   2. 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 66.2

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

   4. Applied rewrites 66.2%

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

   if -5.00000000000000024e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   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 82.1%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 91.1

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

   6. Applied rewrites 91.1%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 80.6

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

   9. Applied rewrites 80.6%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 80.7

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

   11. Applied rewrites 80.7%

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

Alternative 10: 67.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+207}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+103}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.6e+207)
   (* (* a (/ t c)) -4.0)
   (if (<= z 2.7e+103)
     (/ (fma (* y x) 9.0 b) (* z c))
     (* -4.0 (/ (* a t) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.6e+207) {
		tmp = (a * (t / c)) * -4.0;
	} else if (z <= 2.7e+103) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.6e+207)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	elseif (z <= 2.7e+103)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.6e+207], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 2.7e+103], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999998e207

   1. Initial program 46.5%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 78.4

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 66.3

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

   9. Applied rewrites 66.3%

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

   if -2.5999999999999998e207 < z < 2.69999999999999993e103

   1. Initial program 88.6%

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

   2. Taylor expanded in 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 69.0

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

   4. Applied rewrites 69.0%

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

   if 2.69999999999999993e103 < z

   1. Initial program 54.8%

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

   2. 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 60.6

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

   4. Applied rewrites 60.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot \frac{t}{c}\right) \cdot -4\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a (/ t c)) -4.0))
        (t_2 (* (* x 9.0) y))
        (t_3 (* (* x (/ (/ y c) z)) 9.0)))
   (if (<= t_2 -5e+25)
     t_3
     (if (<= t_2 -1e-98)
       t_1
       (if (<= t_2 5e-230) (/ (/ b z) c) (if (<= t_2 2e+111) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * (t / c)) * -4.0;
	double t_2 = (x * 9.0) * y;
	double t_3 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_3;
	} else if (t_2 <= -1e-98) {
		tmp = t_1;
	} else if (t_2 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_2 <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * (t / c)) * (-4.0d0)
    t_2 = (x * 9.0d0) * y
    t_3 = (x * ((y / c) / z)) * 9.0d0
    if (t_2 <= (-5d+25)) then
        tmp = t_3
    else if (t_2 <= (-1d-98)) then
        tmp = t_1
    else if (t_2 <= 5d-230) then
        tmp = (b / z) / c
    else if (t_2 <= 2d+111) then
        tmp = t_1
    else
        tmp = t_3
    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 * (t / c)) * -4.0;
	double t_2 = (x * 9.0) * y;
	double t_3 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_3;
	} else if (t_2 <= -1e-98) {
		tmp = t_1;
	} else if (t_2 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_2 <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * (t / c)) * -4.0
	t_2 = (x * 9.0) * y
	t_3 = (x * ((y / c) / z)) * 9.0
	tmp = 0
	if t_2 <= -5e+25:
		tmp = t_3
	elif t_2 <= -1e-98:
		tmp = t_1
	elif t_2 <= 5e-230:
		tmp = (b / z) / c
	elif t_2 <= 2e+111:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * Float64(t / c)) * -4.0)
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(Float64(x * Float64(Float64(y / c) / z)) * 9.0)
	tmp = 0.0
	if (t_2 <= -5e+25)
		tmp = t_3;
	elseif (t_2 <= -1e-98)
		tmp = t_1;
	elseif (t_2 <= 5e-230)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_2 <= 2e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * (t / c)) * -4.0;
	t_2 = (x * 9.0) * y;
	t_3 = (x * ((y / c) / z)) * 9.0;
	tmp = 0.0;
	if (t_2 <= -5e+25)
		tmp = t_3;
	elseif (t_2 <= -1e-98)
		tmp = t_1;
	elseif (t_2 <= 5e-230)
		tmp = (b / z) / c;
	elseif (t_2 <= 2e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+25], t$95$3, If[LessEqual[t$95$2, -1e-98], t$95$1, If[LessEqual[t$95$2, 5e-230], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 2e+111], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000024e25 or 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

      1. lift-*.f64 N/A

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

      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 73.3%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 79.5

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

   6. Applied rewrites 79.5%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-+l- N/A

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 62.0

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

   9. Applied rewrites 62.0%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/r* N/A

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

       4. lower-/.f64 N/A

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

       5. lower-/.f64 65.1

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

   11. Applied rewrites 65.1%

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

   if -5.00000000000000024e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-99 or 5.00000000000000035e-230 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   1. Initial program 82.9%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 89.0

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

   4. Applied rewrites 89.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 46.2

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

   9. Applied rewrites 46.2%

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

   if -9.99999999999999939e-99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000035e-230

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 50.0%

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

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

   6. Applied rewrites 48.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-98}:\\ \;\;\;\;\left(\frac{x}{c} \cdot \frac{y}{z}\right) \cdot 9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-\left(\frac{\frac{y}{c}}{z} \cdot -9\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -1e-98)
     (* (* (/ x c) (/ y z)) 9.0)
     (if (<= t_1 5e-230)
       (/ (/ b z) c)
       (if (<= t_1 2e+111)
         (* (* a (/ t c)) -4.0)
         (- (* (* (/ (/ y c) z) -9.0) x)))))))

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 <= -1e-98) {
		tmp = ((x / c) * (y / z)) * 9.0;
	} else if (t_1 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+111) {
		tmp = (a * (t / c)) * -4.0;
	} else {
		tmp = -((((y / c) / z) * -9.0) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, 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 = (x * 9.0d0) * y
    if (t_1 <= (-1d-98)) then
        tmp = ((x / c) * (y / z)) * 9.0d0
    else if (t_1 <= 5d-230) then
        tmp = (b / z) / c
    else if (t_1 <= 2d+111) then
        tmp = (a * (t / c)) * (-4.0d0)
    else
        tmp = -((((y / c) / z) * (-9.0d0)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -1e-98) {
		tmp = ((x / c) * (y / z)) * 9.0;
	} else if (t_1 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+111) {
		tmp = (a * (t / c)) * -4.0;
	} else {
		tmp = -((((y / c) / z) * -9.0) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -1e-98:
		tmp = ((x / c) * (y / z)) * 9.0
	elif t_1 <= 5e-230:
		tmp = (b / z) / c
	elif t_1 <= 2e+111:
		tmp = (a * (t / c)) * -4.0
	else:
		tmp = -((((y / c) / z) * -9.0) * x)
	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 <= -1e-98)
		tmp = Float64(Float64(Float64(x / c) * Float64(y / z)) * 9.0);
	elseif (t_1 <= 5e-230)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e+111)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	else
		tmp = Float64(-Float64(Float64(Float64(Float64(y / c) / z) * -9.0) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -1e-98)
		tmp = ((x / c) * (y / z)) * 9.0;
	elseif (t_1 <= 5e-230)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e+111)
		tmp = (a * (t / c)) * -4.0;
	else
		tmp = -((((y / c) / z) * -9.0) * x);
	end
	tmp_2 = 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, -1e-98], N[(N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-230], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], (-N[(N[(N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision] * -9.0), $MachinePrecision] * x), $MachinePrecision])]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-99

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 75.4%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 82.9

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

   6. Applied rewrites 82.9%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-+l- N/A

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 49.1

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

   9. Applied rewrites 49.1%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-/l* N/A

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

       5. times-frac N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. lower-/.f64 50.5

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

   11. Applied rewrites 50.5%

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

   if -9.99999999999999939e-99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000035e-230

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 50.0%

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

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

   6. Applied rewrites 48.9%

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

   if 5.00000000000000035e-230 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 45.9

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

   9. Applied rewrites 45.9%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-9 \cdot \frac{y}{c \cdot z} + -1 \cdot \frac{\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}}{x}\right) \cdot x \]

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 67.5

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

   7. Applied rewrites 67.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 70.7

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

   9. Applied rewrites 70.7%

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

Alternative 13: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-98}:\\ \;\;\;\;\left(\frac{x}{c} \cdot \frac{y}{z}\right) \cdot 9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -1e-98)
     (* (* (/ x c) (/ y z)) 9.0)
     (if (<= t_1 5e-230)
       (/ (/ b z) c)
       (if (<= t_1 2e+111)
         (* (* a (/ t c)) -4.0)
         (* (* x (/ (/ y c) z)) 9.0))))))

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 <= -1e-98) {
		tmp = ((x / c) * (y / z)) * 9.0;
	} else if (t_1 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+111) {
		tmp = (a * (t / c)) * -4.0;
	} else {
		tmp = (x * ((y / c) / z)) * 9.0;
	}
	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 = (x * 9.0d0) * y
    if (t_1 <= (-1d-98)) then
        tmp = ((x / c) * (y / z)) * 9.0d0
    else if (t_1 <= 5d-230) then
        tmp = (b / z) / c
    else if (t_1 <= 2d+111) then
        tmp = (a * (t / c)) * (-4.0d0)
    else
        tmp = (x * ((y / c) / z)) * 9.0d0
    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 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -1e-98) {
		tmp = ((x / c) * (y / z)) * 9.0;
	} else if (t_1 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+111) {
		tmp = (a * (t / c)) * -4.0;
	} else {
		tmp = (x * ((y / c) / z)) * 9.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	tmp = 0
	if t_1 <= -1e-98:
		tmp = ((x / c) * (y / z)) * 9.0
	elif t_1 <= 5e-230:
		tmp = (b / z) / c
	elif t_1 <= 2e+111:
		tmp = (a * (t / c)) * -4.0
	else:
		tmp = (x * ((y / c) / z)) * 9.0
	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 <= -1e-98)
		tmp = Float64(Float64(Float64(x / c) * Float64(y / z)) * 9.0);
	elseif (t_1 <= 5e-230)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e+111)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	else
		tmp = Float64(Float64(x * Float64(Float64(y / c) / z)) * 9.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_1 <= -1e-98)
		tmp = ((x / c) * (y / z)) * 9.0;
	elseif (t_1 <= 5e-230)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e+111)
		tmp = (a * (t / c)) * -4.0;
	else
		tmp = (x * ((y / c) / z)) * 9.0;
	end
	tmp_2 = 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, -1e-98], N[(N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e-230], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-99

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 75.4%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 82.9

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

   6. Applied rewrites 82.9%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-+l- N/A

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 49.1

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

   9. Applied rewrites 49.1%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-/l* N/A

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

       5. times-frac N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. lower-/.f64 50.5

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

   11. Applied rewrites 50.5%

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

   if -9.99999999999999939e-99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000035e-230

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 50.0%

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

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

   6. Applied rewrites 48.9%

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

   if 5.00000000000000035e-230 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 45.9

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

   9. Applied rewrites 45.9%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

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

      1. lift-*.f64 N/A

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

      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 73.3%

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

   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. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-*r/ N/A

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

      9. div-add N/A

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

      10. lower-/.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 79.3

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 79.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      4. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      5. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      6. associate-+l- N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{9} \cdot \frac{x \cdot y}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      10. associate-/l* N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      12. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      13. lift-*.f64 67.5

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

   9. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       2. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       3. associate-/r* N/A

          \[\leadsto \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9 \]

       4. lower-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9 \]

       5. lower-/.f64 70.7

          \[\leadsto \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9 \]

   11. Applied rewrites 70.7%

       \[\leadsto \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{c \cdot z}\\ t_2 := \left(a \cdot \frac{t}{c}\right) \cdot -4\\ t_3 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(t\_1 \cdot 9\right)\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\_1\right) \cdot 9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ y (* c z))) (t_2 (* (* a (/ t c)) -4.0)) (t_3 (* (* x 9.0) y)))
   (if (<= t_3 -5e+25)
     (* x (* t_1 9.0))
     (if (<= t_3 -1e-98)
       t_2
       (if (<= t_3 5e-230)
         (/ (/ b z) c)
         (if (<= t_3 2e+111) t_2 (* (* x t_1) 9.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y / (c * z);
	double t_2 = (a * (t / c)) * -4.0;
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -5e+25) {
		tmp = x * (t_1 * 9.0);
	} else if (t_3 <= -1e-98) {
		tmp = t_2;
	} else if (t_3 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_3 <= 2e+111) {
		tmp = t_2;
	} else {
		tmp = (x * t_1) * 9.0;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y / (c * z)
    t_2 = (a * (t / c)) * (-4.0d0)
    t_3 = (x * 9.0d0) * y
    if (t_3 <= (-5d+25)) then
        tmp = x * (t_1 * 9.0d0)
    else if (t_3 <= (-1d-98)) then
        tmp = t_2
    else if (t_3 <= 5d-230) then
        tmp = (b / z) / c
    else if (t_3 <= 2d+111) then
        tmp = t_2
    else
        tmp = (x * t_1) * 9.0d0
    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 = y / (c * z);
	double t_2 = (a * (t / c)) * -4.0;
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -5e+25) {
		tmp = x * (t_1 * 9.0);
	} else if (t_3 <= -1e-98) {
		tmp = t_2;
	} else if (t_3 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_3 <= 2e+111) {
		tmp = t_2;
	} else {
		tmp = (x * t_1) * 9.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = y / (c * z)
	t_2 = (a * (t / c)) * -4.0
	t_3 = (x * 9.0) * y
	tmp = 0
	if t_3 <= -5e+25:
		tmp = x * (t_1 * 9.0)
	elif t_3 <= -1e-98:
		tmp = t_2
	elif t_3 <= 5e-230:
		tmp = (b / z) / c
	elif t_3 <= 2e+111:
		tmp = t_2
	else:
		tmp = (x * t_1) * 9.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(y / Float64(c * z))
	t_2 = Float64(Float64(a * Float64(t / c)) * -4.0)
	t_3 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_3 <= -5e+25)
		tmp = Float64(x * Float64(t_1 * 9.0));
	elseif (t_3 <= -1e-98)
		tmp = t_2;
	elseif (t_3 <= 5e-230)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_3 <= 2e+111)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * t_1) * 9.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y / (c * z);
	t_2 = (a * (t / c)) * -4.0;
	t_3 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_3 <= -5e+25)
		tmp = x * (t_1 * 9.0);
	elseif (t_3 <= -1e-98)
		tmp = t_2;
	elseif (t_3 <= 5e-230)
		tmp = (b / z) / c;
	elseif (t_3 <= 2e+111)
		tmp = t_2;
	else
		tmp = (x * t_1) * 9.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+25], N[(x * N[(t$95$1 * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-98], t$95$2, If[LessEqual[t$95$3, 5e-230], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$3, 2e+111], t$95$2, N[(N[(x * t$95$1), $MachinePrecision] * 9.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000024e25

   1. Initial program 75.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      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 73.3%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   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. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      9. div-add N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      15. lift-*.f64 79.6

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 79.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      4. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      5. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      6. associate-+l- N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{9} \cdot \frac{x \cdot y}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      10. associate-/l* N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      12. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      13. lift-*.f64 57.8

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

   9. Applied rewrites 57.8%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot \color{blue}{9} \]

       2. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       3. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       4. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       5. associate-*l* N/A

          \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot 9\right)} \]

       6. *-commutative N/A

          \[\leadsto x \cdot \left(9 \cdot \color{blue}{\frac{y}{c \cdot z}}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

       8. *-commutative N/A

          \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot \color{blue}{9}\right) \]

       9. lower-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot \color{blue}{9}\right) \]

       10. lift-/.f64 N/A

           \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) \]

       11. lift-*.f64 57.8

           \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) \]

   11. Applied rewrites 57.8%

       \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot 9\right)} \]

   if -5.00000000000000024e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-99 or 5.00000000000000035e-230 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   3. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{\frac{a \cdot t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + \frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      9. div-add N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{9 \cdot \left(x \cdot y\right) + b}{c \cdot z}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\left(x \cdot y\right) \cdot 9 + b}{c \cdot z}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      16. lower-*.f64 89.0

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

   4. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      5. lower-/.f64 46.2

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   9. Applied rewrites 46.2%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -9.99999999999999939e-99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000035e-230

   1. Initial program 81.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   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

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   6. Applied rewrites 48.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      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 82.5%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   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. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      9. div-add N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      15. lift-*.f64 90.7

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 90.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      4. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      5. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      6. associate-+l- N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{9} \cdot \frac{x \cdot y}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      10. associate-/l* N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      12. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      13. lift-*.f64 25.9

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

   9. Applied rewrites 25.9%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot \frac{t}{c}\right) \cdot -4\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a (/ t c)) -4.0))
        (t_2 (* (* x 9.0) y))
        (t_3 (* x (* (/ y (* c z)) 9.0))))
   (if (<= t_2 -5e+25)
     t_3
     (if (<= t_2 -1e-98)
       t_1
       (if (<= t_2 5e-230) (/ (/ b z) c) (if (<= t_2 2e+111) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * (t / c)) * -4.0;
	double t_2 = (x * 9.0) * y;
	double t_3 = x * ((y / (c * z)) * 9.0);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_3;
	} else if (t_2 <= -1e-98) {
		tmp = t_1;
	} else if (t_2 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_2 <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * (t / c)) * (-4.0d0)
    t_2 = (x * 9.0d0) * y
    t_3 = x * ((y / (c * z)) * 9.0d0)
    if (t_2 <= (-5d+25)) then
        tmp = t_3
    else if (t_2 <= (-1d-98)) then
        tmp = t_1
    else if (t_2 <= 5d-230) then
        tmp = (b / z) / c
    else if (t_2 <= 2d+111) then
        tmp = t_1
    else
        tmp = t_3
    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 * (t / c)) * -4.0;
	double t_2 = (x * 9.0) * y;
	double t_3 = x * ((y / (c * z)) * 9.0);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_3;
	} else if (t_2 <= -1e-98) {
		tmp = t_1;
	} else if (t_2 <= 5e-230) {
		tmp = (b / z) / c;
	} else if (t_2 <= 2e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * (t / c)) * -4.0
	t_2 = (x * 9.0) * y
	t_3 = x * ((y / (c * z)) * 9.0)
	tmp = 0
	if t_2 <= -5e+25:
		tmp = t_3
	elif t_2 <= -1e-98:
		tmp = t_1
	elif t_2 <= 5e-230:
		tmp = (b / z) / c
	elif t_2 <= 2e+111:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * Float64(t / c)) * -4.0)
	t_2 = Float64(Float64(x * 9.0) * y)
	t_3 = Float64(x * Float64(Float64(y / Float64(c * z)) * 9.0))
	tmp = 0.0
	if (t_2 <= -5e+25)
		tmp = t_3;
	elseif (t_2 <= -1e-98)
		tmp = t_1;
	elseif (t_2 <= 5e-230)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_2 <= 2e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * (t / c)) * -4.0;
	t_2 = (x * 9.0) * y;
	t_3 = x * ((y / (c * z)) * 9.0);
	tmp = 0.0;
	if (t_2 <= -5e+25)
		tmp = t_3;
	elseif (t_2 <= -1e-98)
		tmp = t_1;
	elseif (t_2 <= 5e-230)
		tmp = (b / z) / c;
	elseif (t_2 <= 2e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+25], t$95$3, If[LessEqual[t$95$2, -1e-98], t$95$1, If[LessEqual[t$95$2, 5e-230], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 2e+111], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000024e25 or 1.99999999999999991e111 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      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 73.3%

      \[\leadsto \color{blue}{\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}} \]

   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. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c} \]

      7. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z} + \frac{9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      9. div-add N/A

         \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      10. lower-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}{c} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{9 \cdot \left(x \cdot y\right) + b}{z}\right)}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\left(x \cdot y\right) \cdot 9 + b}{z}\right)}{c} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

      15. lift-*.f64 79.5

          \[\leadsto \frac{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c} \]

   6. Applied rewrites 79.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(a \cdot t, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}}{c} \]

   7. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      4. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      5. *-commutative N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      6. associate-+l- N/A

         \[\leadsto 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{9} \cdot \frac{x \cdot y}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9} \]

      10. associate-/l* N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      12. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

      13. lift-*.f64 62.0

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

   9. Applied rewrites 62.0%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot \color{blue}{9} \]

       2. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       3. lift-*.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       4. lift-/.f64 N/A

          \[\leadsto \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9 \]

       5. associate-*l* N/A

          \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot 9\right)} \]

       6. *-commutative N/A

          \[\leadsto x \cdot \left(9 \cdot \color{blue}{\frac{y}{c \cdot z}}\right) \]

       7. lower-*.f64 N/A

          \[\leadsto x \cdot \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \]

       8. *-commutative N/A

          \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot \color{blue}{9}\right) \]

       9. lower-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot \color{blue}{9}\right) \]

       10. lift-/.f64 N/A

           \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) \]

       11. lift-*.f64 62.0

           \[\leadsto x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right) \]

   11. Applied rewrites 62.0%

       \[\leadsto x \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot 9\right)} \]

   if -5.00000000000000024e25 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999939e-99 or 5.00000000000000035e-230 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999991e111

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   3. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{\frac{a \cdot t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + \frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      9. div-add N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{9 \cdot \left(x \cdot y\right) + b}{c \cdot z}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\left(x \cdot y\right) \cdot 9 + b}{c \cdot z}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      16. lower-*.f64 89.0

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

   4. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      5. lower-/.f64 46.2

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   9. Applied rewrites 46.2%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -9.99999999999999939e-99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000035e-230

   1. Initial program 81.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 50.0%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   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

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   6. Applied rewrites 48.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 49.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;\left(a \cdot \frac{t}{c}\right) \cdot -4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.4e-81)
   (* (* a (/ t c)) -4.0)
   (if (<= z 7e+101) (/ b (* z c)) (* -4.0 (/ (* a t) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.4e-81) {
		tmp = (a * (t / c)) * -4.0;
	} else if (z <= 7e+101) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	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 (z <= (-6.4d-81)) then
        tmp = (a * (t / c)) * (-4.0d0)
    else if (z <= 7d+101) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    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 (z <= -6.4e-81) {
		tmp = (a * (t / c)) * -4.0;
	} else if (z <= 7e+101) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -6.4e-81:
		tmp = (a * (t / c)) * -4.0
	elif z <= 7e+101:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.4e-81)
		tmp = Float64(Float64(a * Float64(t / c)) * -4.0);
	elseif (z <= 7e+101)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -6.4e-81)
		tmp = (a * (t / c)) * -4.0;
	elseif (z <= 7e+101)
		tmp = b / (z * c);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.4e-81], N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 7e+101], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4e-81

   1. Initial program 70.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   3. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval N/A

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{\frac{a \cdot t}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{\color{blue}{c}}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z} + \frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      9. div-add N/A

         \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{9 \cdot \left(x \cdot y\right) + b}{c \cdot z}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\left(x \cdot y\right) \cdot 9 + b}{c \cdot z}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{c \cdot z}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

      16. lower-*.f64 83.0

          \[\leadsto \mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right) \]

   4. Applied rewrites 83.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      4. associate-*l* N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      5. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      6. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      7. *-commutative N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      8. associate--r- N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      9. lift-*.f64 N/A

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      10. lift-*.f64 N/A

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

      11. associate-/l/ N/A

          \[\leadsto \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{-4} \]

   7. Applied rewrites 49.2%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 \]

      3. associate-/l* N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

      5. lower-/.f64 50.2

         \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   9. Applied rewrites 50.2%

      \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -6.4e-81 < z < 7.00000000000000046e101

   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. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 44.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]

   if 7.00000000000000046e101 < z

   1. Initial program 54.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in 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 60.4

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

   4. Applied rewrites 60.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 48.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* a t) c))))
   (if (<= z -1.4e-80) t_1 (if (<= z 7e+101) (/ 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 = -4.0 * ((a * t) / c);
	double tmp;
	if (z <= -1.4e-80) {
		tmp = t_1;
	} else if (z <= 7e+101) {
		tmp = b / (z * c);
	} 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 (z <= (-1.4d-80)) then
        tmp = t_1
    else if (z <= 7d+101) then
        tmp = b / (z * c)
    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 (z <= -1.4e-80) {
		tmp = t_1;
	} else if (z <= 7e+101) {
		tmp = b / (z * c);
	} 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 z <= -1.4e-80:
		tmp = t_1
	elif z <= 7e+101:
		tmp = b / (z * c)
	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 (z <= -1.4e-80)
		tmp = t_1;
	elseif (z <= 7e+101)
		tmp = Float64(b / Float64(z * c));
	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 (z <= -1.4e-80)
		tmp = t_1;
	elseif (z <= 7e+101)
		tmp = b / (z * c);
	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[z, -1.4e-80], t$95$1, If[LessEqual[z, 7e+101], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999995e-80 or 7.00000000000000046e101 < z

   1. Initial program 64.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. 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 53.3

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} \]

   4. Applied rewrites 53.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -1.39999999999999995e-80 < z < 7.00000000000000046e101

   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. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 44.8%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 34.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 4.5e+57) (/ (/ b z) c) (/ b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.5e+57) {
		tmp = (b / z) / c;
	} else {
		tmp = b / (z * c);
	}
	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 <= 4.5d+57) then
        tmp = (b / z) / c
    else
        tmp = b / (z * c)
    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 <= 4.5e+57) {
		tmp = (b / z) / c;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 4.5e+57:
		tmp = (b / z) / c
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 4.5e+57)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 4.5e+57)
		tmp = (b / z) / c;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 4.5e+57], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.49999999999999996e57

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 36.5%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   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

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   6. Applied rewrites 35.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if 4.49999999999999996e57 < a

   1. Initial program 77.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Taylor expanded in b around inf

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   3. Step-by-step derivation

   4. Applied rewrites 27.2%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 33.6% 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 79.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

2. Taylor expanded in b around inf

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
3. Step-by-step derivation

4. Applied rewrites 34.6%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(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)))