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

Percentage Accurate: 78.8% → 91.5%

Time: 5.5s

Alternatives: 14

Speedup: 0.8×

• 36.7% 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: 78.8% 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: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+78}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\frac{y}{z}, 9, \frac{b}{z \cdot x}\right) \cdot x\right)}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-59}:\\ \;\;\;\;\frac{\left(x \cdot \left(y \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -9.5e+78)
   (/ (fma (* -4.0 a) t (* (fma (/ y z) 9.0 (/ b (* z x))) x)) c)
   (if (<= z 1.55e-59)
     (/ (+ (- (* x (* y 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))
     (/ (fma (* -4.0 a) t (/ (fma (* x y) 9.0 b) z)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -9.5e+78) {
		tmp = fma((-4.0 * a), t, (fma((y / z), 9.0, (b / (z * x))) * x)) / c;
	} else if (z <= 1.55e-59) {
		tmp = (((x * (y * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = fma((-4.0 * a), t, (fma((x * y), 9.0, b) / z)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -9.5e+78)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(y / z), 9.0, Float64(b / Float64(z * x))) * x)) / c);
	elseif (z <= 1.55e-59)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x * y), 9.0, b) / z)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -9.5e+78], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y / z), $MachinePrecision] * 9.0 + N[(b / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.55e-59], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000006e78

   1. Initial program 55.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 61.5

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

   3. Applied rewrites 61.5%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 87.1%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-fma.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 88.7

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

   11. Applied rewrites 88.7%

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

   if -9.5000000000000006e78 < z < 1.55e-59

   1. Initial program 93.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.6

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

   3. Applied rewrites 93.6%

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

   if 1.55e-59 < z

   1. Initial program 68.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 71.7

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

   3. Applied rewrites 71.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 88.9%

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

Alternative 2: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-59}:\\ \;\;\;\;\frac{\left(x \cdot \left(y \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* -4.0 a) t (/ (fma (* x y) 9.0 b) z)) c)))
   (if (<= z -3.5e-9)
     t_1
     (if (<= z 1.55e-59)
       (/ (+ (- (* x (* y 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((-4.0 * a), t, (fma((x * y), 9.0, b) / z)) / c;
	double tmp;
	if (z <= -3.5e-9) {
		tmp = t_1;
	} else if (z <= 1.55e-59) {
		tmp = (((x * (y * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x * y), 9.0, b) / z)) / c)
	tmp = 0.0
	if (z <= -3.5e-9)
		tmp = t_1;
	elseif (z <= 1.55e-59)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.5e-9], t$95$1, If[LessEqual[z, 1.55e-59], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e-9 or 1.55e-59 < z

   1. Initial program 65.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 69.8

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

   3. Applied rewrites 69.8%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 88.4%

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

   if -3.4999999999999999e-9 < z < 1.55e-59

   1. Initial program 95.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.3

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

   3. Applied rewrites 95.3%

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

Alternative 3: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* x (/ (/ y c) z)) 9.0)))
   (if (<= t_1 -1e+285)
     t_2
     (if (<= t_1 5e+267)
       (/ (fma (* -4.0 a) t (/ (fma (* x y) 9.0 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 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_1 <= -1e+285) {
		tmp = t_2;
	} else if (t_1 <= 5e+267) {
		tmp = fma((-4.0 * a), t, (fma((x * y), 9.0, 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(x * Float64(Float64(y / c) / z)) * 9.0)
	tmp = 0.0
	if (t_1 <= -1e+285)
		tmp = t_2;
	elseif (t_1 <= 5e+267)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(x * y), 9.0, 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[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+285], t$95$2, If[LessEqual[t$95$1, 5e+267], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999998e284 or 4.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 64.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 63.4

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

   3. Applied rewrites 63.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 86.2

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

   10. Applied rewrites 86.2%

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

   if -9.9999999999999998e284 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e267

   1. Initial program 81.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 82.4

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

   3. Applied rewrites 82.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 89.9%

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

Alternative 4: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* x (/ (/ y c) z)) 9.0)))
   (if (<= t_1 -1e+290)
     t_2
     (if (<= t_1 -4000000.0)
       (/ (fma (* y x) 9.0 b) (* z c))
       (if (<= t_1 2e-21)
         (/ (fma (* -4.0 a) t (/ b z)) c)
         (if (<= t_1 5e+267)
           (/ (fma (* -4.0 a) t (* (/ (* y x) z) 9.0)) 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 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_1 <= -1e+290) {
		tmp = t_2;
	} else if (t_1 <= -4000000.0) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 2e-21) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else if (t_1 <= 5e+267) {
		tmp = fma((-4.0 * a), t, (((y * x) / z) * 9.0)) / 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(x * Float64(Float64(y / c) / z)) * 9.0)
	tmp = 0.0
	if (t_1 <= -1e+290)
		tmp = t_2;
	elseif (t_1 <= -4000000.0)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 2e-21)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	elseif (t_1 <= 5e+267)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(y * x) / z) * 9.0)) / 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[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+290], t$95$2, If[LessEqual[t$95$1, -4000000.0], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000006e290 or 4.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 64.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 63.3

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

   3. Applied rewrites 63.3%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 86.2

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

   10. Applied rewrites 86.2%

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

   if -1.00000000000000006e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4e6

   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 67.1

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

   4. Applied rewrites 67.1%

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

   if -4e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999982e-21

   1. Initial program 80.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 81.7

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

   3. Applied rewrites 81.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 91.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.1%

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

   if 1.99999999999999982e-21 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e267

   1. Initial program 83.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 84.7

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

   3. Applied rewrites 84.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 88.6%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 71.1

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

   11. Applied rewrites 71.1%

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

Alternative 5: 77.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -500000000000:\\ \;\;\;\;-\frac{\frac{y}{c} \cdot -9 - \frac{b}{c \cdot x}}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{y \cdot x}{z} \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -500000000000.0)
     (- (* (/ (- (* (/ y c) -9.0) (/ b (* c x))) z) x))
     (if (<= t_1 2e-21)
       (/ (fma (* -4.0 a) t (/ b z)) c)
       (if (<= t_1 5e+267)
         (/ (fma (* -4.0 a) t (* (/ (* y x) z) 9.0)) c)
         (* (* 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 <= -500000000000.0) {
		tmp = -(((((y / c) * -9.0) - (b / (c * x))) / z) * x);
	} else if (t_1 <= 2e-21) {
		tmp = fma((-4.0 * a), t, (b / z)) / c;
	} else if (t_1 <= 5e+267) {
		tmp = fma((-4.0 * a), t, (((y * x) / z) * 9.0)) / c;
	} 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 <= -500000000000.0)
		tmp = Float64(-Float64(Float64(Float64(Float64(Float64(y / c) * -9.0) - Float64(b / Float64(c * x))) / z) * x));
	elseif (t_1 <= 2e-21)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(b / z)) / c);
	elseif (t_1 <= 5e+267)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(Float64(y * x) / z) * 9.0)) / c);
	else
		tmp = Float64(Float64(x * Float64(Float64(y / c) / z)) * 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, -500000000000.0], (-N[(N[(N[(N[(N[(y / c), $MachinePrecision] * -9.0), $MachinePrecision] - N[(b / N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[t$95$1, 2e-21], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c), $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) < -5e11

   1. Initial program 76.9%

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

   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 76.5%

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

   5. Taylor expanded in z around 0

      \[\leadsto -\frac{-9 \cdot \frac{y}{c} - \frac{b}{c \cdot x}}{z} \cdot x \]
   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 68.0

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

   7. Applied rewrites 68.0%

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

   if -5e11 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999982e-21

   1. Initial program 80.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 81.7

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

   3. Applied rewrites 81.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 91.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.0%

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

   if 1.99999999999999982e-21 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e267

   1. Initial program 83.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 84.7

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

   3. Applied rewrites 84.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 88.6%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 71.1

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

   11. Applied rewrites 71.1%

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

   if 4.9999999999999999e267 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 62.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 62.7

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

   3. Applied rewrites 62.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 85.6

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

   10. Applied rewrites 85.6%

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

Alternative 6: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -4000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+243}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* x (/ (/ y c) z)) 9.0)))
   (if (<= t_1 -1e+290)
     t_2
     (if (<= t_1 -4000000.0)
       (/ (fma (* y x) 9.0 b) (* z c))
       (if (<= t_1 5e+243) (/ (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 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_1 <= -1e+290) {
		tmp = t_2;
	} else if (t_1 <= -4000000.0) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else if (t_1 <= 5e+243) {
		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(x * Float64(Float64(y / c) / z)) * 9.0)
	tmp = 0.0
	if (t_1 <= -1e+290)
		tmp = t_2;
	elseif (t_1 <= -4000000.0)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	elseif (t_1 <= 5e+243)
		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[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+290], t$95$2, If[LessEqual[t$95$1, -4000000.0], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+243], 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) < -1.00000000000000006e290 or 5.00000000000000037e243 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 65.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 64.7

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

   3. Applied rewrites 64.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 79.2%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 85.4

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

   10. Applied rewrites 85.4%

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

   if -1.00000000000000006e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4e6

   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 67.1

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

   4. Applied rewrites 67.1%

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

   if -4e6 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000037e243

   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

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 82.5

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

   3. Applied rewrites 82.5%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate--r- N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. metadata-eval N/A

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

   8. Applied rewrites 90.8%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 77.1%

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

Alternative 7: 66.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+23}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ t c) -4.0) a)))
   (if (<= t -2.2e+38)
     t_1
     (if (<= t 2.95e+23) (/ (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 = ((t / c) * -4.0) * a;
	double tmp;
	if (t <= -2.2e+38) {
		tmp = t_1;
	} else if (t <= 2.95e+23) {
		tmp = 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(t / c) * -4.0) * a)
	tmp = 0.0
	if (t <= -2.2e+38)
		tmp = t_1;
	elseif (t <= 2.95e+23)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -2.2e+38], t$95$1, If[LessEqual[t, 2.95e+23], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000006e38 or 2.94999999999999994e23 < t

   1. Initial program 72.1%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 59.9

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

   7. Applied rewrites 59.9%

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

   if -2.20000000000000006e38 < t < 2.94999999999999994e23

   1. Initial program 84.4%

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

   2. Taylor expanded in 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 72.3

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

   4. Applied rewrites 72.3%

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

Alternative 8: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(x \cdot \frac{\frac{y}{c}}{z}\right) \cdot 9\\ \mathbf{if}\;t\_1 \leq -500000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* x (/ (/ y c) z)) 9.0)))
   (if (<= t_1 -500000000000.0)
     t_2
     (if (<= t_1 5e-138)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 2e-21) (/ 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 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 2e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = (x * ((y / c) / z)) * 9.0d0
    if (t_1 <= (-500000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-138) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 2d-21) then
        tmp = b / (z * c)
    else
        tmp = t_2
    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 t_2 = (x * ((y / c) / z)) * 9.0;
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 2e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = (x * ((y / c) / z)) * 9.0
	tmp = 0
	if t_1 <= -500000000000.0:
		tmp = t_2
	elif t_1 <= 5e-138:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 2e-21:
		tmp = 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(x * Float64(Float64(y / c) / z)) * 9.0)
	tmp = 0.0
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 2e-21)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = (x * ((y / c) / z)) * 9.0;
	tmp = 0.0;
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 2e-21)
		tmp = b / (z * c);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -500000000000.0], t$95$2, If[LessEqual[t$95$1, 5e-138], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e11 or 1.99999999999999982e-21 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 77.3

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

   3. Applied rewrites 77.3%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 60.4

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

   10. Applied rewrites 60.4%

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

   if -5e11 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999989e-138

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 48.9

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

   4. Applied rewrites 48.9%

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

   if 4.99999999999999989e-138 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999982e-21

   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 b around inf

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

   4. Applied rewrites 42.5%

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

Alternative 9: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9\\ \mathbf{if}\;t\_1 \leq -500000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+31}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (* x (/ y (* c z))) 9.0)))
   (if (<= t_1 -500000000000.0)
     t_2
     (if (<= t_1 5e-138)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 5e+31) (/ 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 = (x * (y / (c * z))) * 9.0;
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 5e+31) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = (x * (y / (c * z))) * 9.0d0
    if (t_1 <= (-500000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-138) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 5d+31) then
        tmp = b / (z * c)
    else
        tmp = t_2
    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 t_2 = (x * (y / (c * z))) * 9.0;
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 5e+31) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = (x * (y / (c * z))) * 9.0
	tmp = 0
	if t_1 <= -500000000000.0:
		tmp = t_2
	elif t_1 <= 5e-138:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 5e+31:
		tmp = 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(x * Float64(y / Float64(c * z))) * 9.0)
	tmp = 0.0
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 5e+31)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = (x * (y / (c * z))) * 9.0;
	tmp = 0.0;
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 5e+31)
		tmp = b / (z * c);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]}, If[LessEqual[t$95$1, -500000000000.0], t$95$2, If[LessEqual[t$95$1, 5e-138], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+31], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e11 or 5.00000000000000027e31 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 76.3

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

   3. Applied rewrites 76.3%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 60.1%

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

   if -5e11 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999989e-138

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 48.9

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

   4. Applied rewrites 48.9%

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

   if 4.99999999999999989e-138 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000027e31

   1. Initial program 84.8%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 41.3%

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

Alternative 10: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -500000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* x (* (/ y (* c z)) 9.0))))
   (if (<= t_1 -500000000000.0)
     t_2
     (if (<= t_1 5e-138)
       (* -4.0 (/ (* a t) c))
       (if (<= t_1 2e-21) (/ 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 = x * ((y / (c * z)) * 9.0);
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 2e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (x * 9.0d0) * y
    t_2 = x * ((y / (c * z)) * 9.0d0)
    if (t_1 <= (-500000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-138) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t_1 <= 2d-21) then
        tmp = b / (z * c)
    else
        tmp = t_2
    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 t_2 = x * ((y / (c * z)) * 9.0);
	double tmp;
	if (t_1 <= -500000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-138) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t_1 <= 2e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = x * ((y / (c * z)) * 9.0)
	tmp = 0
	if t_1 <= -500000000000.0:
		tmp = t_2
	elif t_1 <= 5e-138:
		tmp = -4.0 * ((a * t) / c)
	elif t_1 <= 2e-21:
		tmp = 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(x * Float64(Float64(y / Float64(c * z)) * 9.0))
	tmp = 0.0
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t_1 <= 2e-21)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = x * ((y / (c * z)) * 9.0);
	tmp = 0.0;
	if (t_1 <= -500000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-138)
		tmp = -4.0 * ((a * t) / c);
	elseif (t_1 <= 2e-21)
		tmp = b / (z * c);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -500000000000.0], t$95$2, If[LessEqual[t$95$1, 5e-138], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-21], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e11 or 1.99999999999999982e-21 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 77.3

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

   3. Applied rewrites 77.3%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around inf

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 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. lift-*.f64 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. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

   8. Applied rewrites 58.1%

      \[\leadsto \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9} \]
   9. 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 58.1

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

   10. Applied rewrites 58.1%

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

   if -5e11 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999989e-138

   1. Initial program 80.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 48.9

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

   4. Applied rewrites 48.9%

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

   if 4.99999999999999989e-138 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999982e-21

   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 b around inf

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

   4. Applied rewrites 42.5%

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

Alternative 11: 50.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 118000000:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* (/ t c) -4.0) a)))
   (if (<= t -1.75e+37)
     t_1
     (if (<= t 118000000.0) (* b (/ 1.0 (* c z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t / c) * -4.0) * a;
	double tmp;
	if (t <= -1.75e+37) {
		tmp = t_1;
	} else if (t <= 118000000.0) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t / c) * (-4.0d0)) * a
    if (t <= (-1.75d+37)) then
        tmp = t_1
    else if (t <= 118000000.0d0) then
        tmp = b * (1.0d0 / (c * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t / c) * -4.0) * a;
	double tmp;
	if (t <= -1.75e+37) {
		tmp = t_1;
	} else if (t <= 118000000.0) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t / c) * -4.0) * a
	tmp = 0
	if t <= -1.75e+37:
		tmp = t_1
	elif t <= 118000000.0:
		tmp = b * (1.0 / (c * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t / c) * -4.0) * a)
	tmp = 0.0
	if (t <= -1.75e+37)
		tmp = t_1;
	elseif (t <= 118000000.0)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t / c) * -4.0) * a;
	tmp = 0.0;
	if (t <= -1.75e+37)
		tmp = t_1;
	elseif (t <= 118000000.0)
		tmp = b * (1.0 / (c * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -1.75e+37], t$95$1, If[LessEqual[t, 118000000.0], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e37 or 1.18e8 < t

   1. Initial program 72.5%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 76.9%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 59.5

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

   7. Applied rewrites 59.5%

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

   if -1.75e37 < t < 1.18e8

   1. Initial program 84.5%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 42.4%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \frac{1}{\color{blue}{z \cdot c}} \]

      4. *-commutative N/A

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]

      6. associate-+l- N/A

         \[\leadsto b \cdot \frac{1}{c \cdot z} \]

      7. associate-*l* N/A

         \[\leadsto b \cdot \frac{1}{c \cdot z} \]

      8. *-commutative N/A

         \[\leadsto b \cdot \frac{1}{c \cdot z} \]

      9. *-commutative N/A

         \[\leadsto b \cdot \frac{1}{c \cdot z} \]

      10. associate-+l- N/A

          \[\leadsto b \cdot \frac{1}{c \cdot z} \]

      11. associate-+l- N/A

          \[\leadsto b \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{1}{c \cdot z}\right)\right) \]

      12. associate-+l- N/A

          \[\leadsto b \cdot \frac{1}{\mathsf{Rewrite<=}\left(lift-*.f64, \left(c \cdot z\right)\right)} \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 48.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1250000:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -1.75e+217)
     t_1
     (if (<= b 1250000.0) (* (* (/ t c) -4.0) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.75e+217) {
		tmp = t_1;
	} else if (b <= 1250000.0) {
		tmp = ((t / c) * -4.0) * a;
	} 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 = b / (z * c)
    if (b <= (-1.75d+217)) then
        tmp = t_1
    else if (b <= 1250000.0d0) then
        tmp = ((t / c) * (-4.0d0)) * a
    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 = b / (z * c);
	double tmp;
	if (b <= -1.75e+217) {
		tmp = t_1;
	} else if (b <= 1250000.0) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -1.75e+217:
		tmp = t_1
	elif b <= 1250000.0:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -1.75e+217)
		tmp = t_1;
	elseif (b <= 1250000.0)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -1.75e+217)
		tmp = t_1;
	elseif (b <= 1250000.0)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+217], t$95$1, If[LessEqual[b, 1250000.0], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7499999999999999e217 or 1.25e6 < b

   1. Initial program 79.0%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 53.2%

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

   if -1.7499999999999999e217 < b < 1.25e6

   1. Initial program 78.7%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 44.0

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

   7. Applied rewrites 44.0%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 46.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1250000:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -1.35e+73) t_1 (if (<= b 1250000.0) (* -4.0 (/ (* a t) c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.35e+73) {
		tmp = t_1;
	} else if (b <= 1250000.0) {
		tmp = -4.0 * ((a * t) / 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 = b / (z * c)
    if (b <= (-1.35d+73)) then
        tmp = t_1
    else if (b <= 1250000.0d0) then
        tmp = (-4.0d0) * ((a * t) / 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 = b / (z * c);
	double tmp;
	if (b <= -1.35e+73) {
		tmp = t_1;
	} else if (b <= 1250000.0) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -1.35e+73:
		tmp = t_1
	elif b <= 1250000.0:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -1.35e+73)
		tmp = t_1;
	elseif (b <= 1250000.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -1.35e+73)
		tmp = t_1;
	elseif (b <= 1250000.0)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+73], t$95$1, If[LessEqual[b, 1250000.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e73 or 1.25e6 < b

   1. Initial program 78.7%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 52.0%

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

   if -1.35e73 < b < 1.25e6

   1. Initial program 78.9%

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

   2. Taylor expanded in 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 45.2

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

   4. Applied rewrites 45.2%

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

Alternative 14: 34.0% 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 78.8%

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

2. Taylor expanded in b around inf

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

4. Applied rewrites 34.0%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025128 
(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)))