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

Percentage Accurate: 79.8% → 90.1%

Time: 7.9s

Alternatives: 14

Speedup: 0.8×

• 36.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% 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: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-\mathsf{fma}\left(\frac{x}{z}, -9, -\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{y}\right) \cdot y}{c}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          (- (* (fma (/ x z) -9.0 (- (/ (fma (* a t) -4.0 (/ b z)) y))) y))
          c)))
   (if (<= z -1.15e+96)
     t_1
     (if (<= z 8.2e-26)
       (/ (+ (- (* (* x 9.0) y) (* (* (* 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((x / z), -9.0, -(fma((a * t), -4.0, (b / z)) / y)) * y) / c;
	double tmp;
	if (z <= -1.15e+96) {
		tmp = t_1;
	} else if (z <= 8.2e-26) {
		tmp = ((((x * 9.0) * y) - (((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(Float64(-Float64(fma(Float64(x / z), -9.0, Float64(-Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / y))) * y)) / c)
	tmp = 0.0
	if (z <= -1.15e+96)
		tmp = t_1;
	elseif (z <= 8.2e-26)
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - 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[(N[(x / z), $MachinePrecision] * -9.0 + (-N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision])), $MachinePrecision] * y), $MachinePrecision]) / c), $MachinePrecision]}, If[LessEqual[z, -1.15e+96], t$95$1, If[LessEqual[z, 8.2e-26], 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], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000008e96 or 8.1999999999999997e-26 < z

   1. Initial program 62.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 71.2%

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

   4. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   6. Applied rewrites 85.5%

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

   if -1.15000000000000008e96 < z < 8.1999999999999997e-26

   1. Initial program 93.8%

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

Alternative 2: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(t \cdot z\right) \cdot a, -4, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -4e+172)
     t_2
     (if (<= t_1 -5e+68)
       (* -4.0 (* t (/ a c)))
       (if (<= t_1 5e+99)
         (/ (fma (* (* t z) a) -4.0 b) (* z c))
         (if (<= t_1 2e+298) (/ (fma (* y x) 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 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -4e+172) {
		tmp = t_2;
	} else if (t_1 <= -5e+68) {
		tmp = -4.0 * (t * (a / c));
	} else if (t_1 <= 5e+99) {
		tmp = fma(((t * z) * a), -4.0, b) / (z * c);
	} else if (t_1 <= 2e+298) {
		tmp = fma((y * x), 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(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -4e+172)
		tmp = t_2;
	elseif (t_1 <= -5e+68)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t_1 <= 5e+99)
		tmp = Float64(fma(Float64(Float64(t * z) * a), -4.0, b) / Float64(z * c));
	elseif (t_1 <= 2e+298)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+172], t$95$2, If[LessEqual[t$95$1, -5e+68], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+99], N[(N[(N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] * -4.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+298], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000003e172 or 1.9999999999999999e298 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 69.4%

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

   2. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 81.5

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

   4. Applied rewrites 81.5%

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

   if -4.0000000000000003e172 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000004e68

   1. Initial program 79.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 35.1

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

   4. Applied rewrites 35.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 39.2

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

   6. Applied rewrites 39.2%

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

   if -5.0000000000000004e68 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000008e99

   1. Initial program 82.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 84.2

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

   3. Applied rewrites 84.2%

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

   4. Taylor expanded in x around 0

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

      1. metadata-eval N/A

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

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

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 71.6

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

   6. Applied rewrites 71.6%

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

   if 5.00000000000000008e99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e298

   1. Initial program 81.2%

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

   2. 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 70.6

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

   4. Applied rewrites 70.6%

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

Alternative 3: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+80}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -4e+172)
     t_2
     (if (<= t_1 5e+80)
       (/ (fma (* a t) -4.0 (/ b z)) c)
       (if (<= t_1 2e+298)
         (/ (fma -4.0 (* (* t z) a) (* (* y x) 9.0)) (* 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 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -4e+172) {
		tmp = t_2;
	} else if (t_1 <= 5e+80) {
		tmp = fma((a * t), -4.0, (b / z)) / c;
	} else if (t_1 <= 2e+298) {
		tmp = fma(-4.0, ((t * z) * a), ((y * x) * 9.0)) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -4e+172)
		tmp = t_2;
	elseif (t_1 <= 5e+80)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 2e+298)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+172], t$95$2, If[LessEqual[t$95$1, 5e+80], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+298], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / 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) < -4.0000000000000003e172 or 1.9999999999999999e298 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 69.4%

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

   2. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 81.5

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

   4. Applied rewrites 81.5%

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

   if -4.0000000000000003e172 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999961e80

   1. Initial program 82.5%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 69.9

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

   4. Applied rewrites 69.9%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 76.8

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

   7. Applied rewrites 76.8%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-/.f64 78.3

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

   10. Applied rewrites 78.3%

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

   if 4.99999999999999961e80 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e298

   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. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 71.0

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

   4. Applied rewrites 71.0%

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

Alternative 4: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot t, -4, \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -4e+172)
     t_2
     (if (<= t_1 5e+99)
       (/ (fma (* a t) -4.0 (/ b z)) c)
       (if (<= t_1 2e+298) (/ (fma (* y x) 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 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -4e+172) {
		tmp = t_2;
	} else if (t_1 <= 5e+99) {
		tmp = fma((a * t), -4.0, (b / z)) / c;
	} else if (t_1 <= 2e+298) {
		tmp = fma((y * x), 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(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -4e+172)
		tmp = t_2;
	elseif (t_1 <= 5e+99)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(b / z)) / c);
	elseif (t_1 <= 2e+298)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+172], t$95$2, If[LessEqual[t$95$1, 5e+99], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+298], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / 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) < -4.0000000000000003e172 or 1.9999999999999999e298 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 69.4%

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

   2. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 81.5

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

   4. Applied rewrites 81.5%

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

   if -4.0000000000000003e172 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000008e99

   1. Initial program 82.5%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 69.4

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

   4. Applied rewrites 69.4%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-*.f64 76.2

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

   7. Applied rewrites 76.2%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. lower-/.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-/.f64 77.7

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

   10. Applied rewrites 77.7%

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

   if 5.00000000000000008e99 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e298

   1. Initial program 81.2%

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

   2. 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 70.6

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

   4. Applied rewrites 70.6%

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

Alternative 5: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{9 \cdot x}{c} \cdot \frac{y}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{\left(t\_1 - \left(4 \cdot z\right) \cdot \left(a \cdot t\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)) (t_2 (* (/ (* 9.0 x) c) (/ y z))))
   (if (<= t_1 -5e+269)
     t_2
     (if (<= t_1 2e+298)
       (/ (+ (- t_1 (* (* 4.0 z) (* 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 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -5e+269) {
		tmp = t_2;
	} else if (t_1 <= 2e+298) {
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + 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 = ((9.0d0 * x) / c) * (y / z)
    if (t_1 <= (-5d+269)) then
        tmp = t_2
    else if (t_1 <= 2d+298) then
        tmp = ((t_1 - ((4.0d0 * z) * (a * t))) + 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 = ((9.0 * x) / c) * (y / z);
	double tmp;
	if (t_1 <= -5e+269) {
		tmp = t_2;
	} else if (t_1 <= 2e+298) {
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + 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 = ((9.0 * x) / c) * (y / z)
	tmp = 0
	if t_1 <= -5e+269:
		tmp = t_2
	elif t_1 <= 2e+298:
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + b) / (z * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(9.0 * x) / c) * Float64(y / z))
	tmp = 0.0
	if (t_1 <= -5e+269)
		tmp = t_2;
	elseif (t_1 <= 2e+298)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(4.0 * z) * Float64(a * t))) + 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 = ((9.0 * x) / c) * (y / z);
	tmp = 0.0;
	if (t_1 <= -5e+269)
		tmp = t_2;
	elseif (t_1 <= 2e+298)
		tmp = ((t_1 - ((4.0 * z) * (a * t))) + 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[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+269], t$95$2, If[LessEqual[t$95$1, 2e+298], N[(N[(N[(t$95$1 - N[(N[(4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.0000000000000002e269 or 1.9999999999999999e298 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 64.8%

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

   2. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. associate-*r* N/A

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

      3. times-frac N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 86.9

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

   4. Applied rewrites 86.9%

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

   if -5.0000000000000002e269 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e298

   1. Initial program 82.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 83.5

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

   3. Applied rewrites 83.5%

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

Alternative 6: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(t \cdot z\right) \cdot c}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(y \cdot x\right) \cdot 9 - \left(\left(\left(4 \cdot z\right) \cdot t\right) \cdot a - b\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2.5e-58)
   (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) (* (* t z) c))) t)
   (/ (/ (- (* (* y x) 9.0) (- (* (* (* 4.0 z) t) a) b)) z) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2.5e-58) {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / ((t * z) * c))) * t;
	} else {
		tmp = ((((y * x) * 9.0) - ((((4.0 * z) * t) * a) - b)) / z) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2.5e-58)
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / Float64(Float64(t * z) * c))) * t);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * x) * 9.0) - Float64(Float64(Float64(Float64(4.0 * z) * t) * a) - b)) / z) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2.5e-58], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] - N[(N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999989e-58

   1. Initial program 75.2%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   4. Applied rewrites 85.2%

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

   if -2.49999999999999989e-58 < t

   1. Initial program 81.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

   3. Applied rewrites 82.4%

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

Alternative 7: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-145}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 650000000000:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+103}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.5e+114)
   (/ (/ b c) z)
   (if (<= b 1.85e-145)
     (* -4.0 (* t (/ a c)))
     (if (<= b 650000000000.0)
       (/ (* (* y x) 9.0) (* z c))
       (if (<= b 8.2e+103) (* (* (/ t c) -4.0) a) (/ (/ b z) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.5e+114) {
		tmp = (b / c) / z;
	} else if (b <= 1.85e-145) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 650000000000.0) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (b <= 8.2e+103) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4.5d+114)) then
        tmp = (b / c) / z
    else if (b <= 1.85d-145) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 650000000000.0d0) then
        tmp = ((y * x) * 9.0d0) / (z * c)
    else if (b <= 8.2d+103) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.5e+114) {
		tmp = (b / c) / z;
	} else if (b <= 1.85e-145) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 650000000000.0) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (b <= 8.2e+103) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.5e+114:
		tmp = (b / c) / z
	elif b <= 1.85e-145:
		tmp = -4.0 * (t * (a / c))
	elif b <= 650000000000.0:
		tmp = ((y * x) * 9.0) / (z * c)
	elif b <= 8.2e+103:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = (b / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.5e+114)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 1.85e-145)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 650000000000.0)
		tmp = Float64(Float64(Float64(y * x) * 9.0) / Float64(z * c));
	elseif (b <= 8.2e+103)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4.5e+114)
		tmp = (b / c) / z;
	elseif (b <= 1.85e-145)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 650000000000.0)
		tmp = ((y * x) * 9.0) / (z * c);
	elseif (b <= 8.2e+103)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.5e+114], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 1.85e-145], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 650000000000.0], N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+103], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.5000000000000001e114

   1. Initial program 78.0%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 70.1

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

   4. Applied rewrites 70.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 61.7%

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

   if -4.5000000000000001e114 < b < 1.85000000000000006e-145

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 45.6

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

   4. Applied rewrites 45.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.8

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

   6. Applied rewrites 45.8%

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

   if 1.85000000000000006e-145 < b < 6.5e11

   1. Initial program 80.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 42.4

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

   4. Applied rewrites 42.4%

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

   if 6.5e11 < b < 8.2000000000000003e103

   1. Initial program 80.8%

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

   2. Taylor expanded in 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 78.5%

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

   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 38.6

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

   7. Applied rewrites 38.6%

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

   if 8.2000000000000003e103 < b

   1. Initial program 80.5%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 61.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 58.5

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

      6. associate-+l- 58.5

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

      7. associate-*l* 58.5

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

      8. *-commutative 58.5

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

      9. *-commutative 58.5

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

      10. associate-+l- 58.5

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

   6. Applied rewrites 58.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 49.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+103}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.5e+114)
   (/ (/ b c) z)
   (if (<= b -3.4e-183)
     (* -4.0 (* t (/ a c)))
     (if (<= b 8.2e+103) (* (* (/ t c) -4.0) a) (/ (/ b z) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.5e+114) {
		tmp = (b / c) / z;
	} else if (b <= -3.4e-183) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 8.2e+103) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4.5d+114)) then
        tmp = (b / c) / z
    else if (b <= (-3.4d-183)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 8.2d+103) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.5e+114) {
		tmp = (b / c) / z;
	} else if (b <= -3.4e-183) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 8.2e+103) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.5e+114:
		tmp = (b / c) / z
	elif b <= -3.4e-183:
		tmp = -4.0 * (t * (a / c))
	elif b <= 8.2e+103:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = (b / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.5e+114)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -3.4e-183)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 8.2e+103)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4.5e+114)
		tmp = (b / c) / z;
	elseif (b <= -3.4e-183)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 8.2e+103)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.5e+114], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -3.4e-183], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+103], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.5000000000000001e114

   1. Initial program 78.0%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 70.1

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

   4. Applied rewrites 70.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 61.7%

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

   if -4.5000000000000001e114 < b < -3.40000000000000014e-183

   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. 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 41.3

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

   4. Applied rewrites 41.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 42.0

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

   6. Applied rewrites 42.0%

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

   if -3.40000000000000014e-183 < b < 8.2000000000000003e103

   1. Initial program 79.7%

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

   2. Taylor expanded in 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 77.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 46.5

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

   7. Applied rewrites 46.5%

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

   if 8.2000000000000003e103 < b

   1. Initial program 80.5%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 61.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 58.5

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

      6. associate-+l- 58.5

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

      7. associate-*l* 58.5

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

      8. *-commutative 58.5

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

      9. *-commutative 58.5

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

      10. associate-+l- 58.5

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

   6. Applied rewrites 58.5%

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

Alternative 9: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -9.2e+111)
   (* -4.0 (* t (/ a c)))
   (if (<= t 1e-28) (/ (fma (* 9.0 x) y b) (* z c)) (* (* (/ t c) -4.0) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.2e+111) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1e-28) {
		tmp = fma((9.0 * x), y, b) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -9.2e+111)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 1e-28)
		tmp = Float64(fma(Float64(9.0 * x), y, b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -9.2e+111], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-28], N[(N[(N[(9.0 * x), $MachinePrecision] * y + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000008e111

   1. Initial program 72.0%

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

   2. Taylor expanded in 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 57.8

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

   4. Applied rewrites 57.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 62.7

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

   6. Applied rewrites 62.7%

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

   if -9.20000000000000008e111 < t < 9.99999999999999971e-29

   1. Initial program 84.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.2

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

   4. Applied rewrites 71.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 71.1

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

   6. Applied rewrites 71.1%

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

   if 9.99999999999999971e-29 < t

   1. Initial program 75.1%

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

   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 54.9

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

   7. Applied rewrites 54.9%

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

Alternative 10: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -9.2e+111)
   (* -4.0 (* t (/ a c)))
   (if (<= t 1e-28) (/ (fma x (* 9.0 y) b) (* z c)) (* (* (/ t c) -4.0) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.2e+111) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1e-28) {
		tmp = fma(x, (9.0 * y), b) / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -9.2e+111)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 1e-28)
		tmp = Float64(fma(x, Float64(9.0 * y), b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -9.2e+111], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-28], N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000008e111

   1. Initial program 72.0%

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

   2. Taylor expanded in 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 57.8

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

   4. Applied rewrites 57.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 62.7

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

   6. Applied rewrites 62.7%

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

   if -9.20000000000000008e111 < t < 9.99999999999999971e-29

   1. Initial program 84.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.2

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

   4. Applied rewrites 71.2%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 71.1

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

   6. Applied rewrites 71.1%

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

   if 9.99999999999999971e-29 < t

   1. Initial program 75.1%

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

   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 54.9

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

   7. Applied rewrites 54.9%

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

Alternative 11: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8.8e+14)
   (* -4.0 (* t (/ a c)))
   (if (<= t 2.2e-29) (/ (/ b c) z) (* (* (/ t c) -4.0) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.8e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.2e-29) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-8.8d+14)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 2.2d-29) then
        tmp = (b / c) / z
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.8e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.2e-29) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8.8e+14:
		tmp = -4.0 * (t * (a / c))
	elif t <= 2.2e-29:
		tmp = (b / c) / z
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8.8e+14)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 2.2e-29)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8.8e+14)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 2.2e-29)
		tmp = (b / c) / z;
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8.8e+14], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-29], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8e14

   1. Initial program 73.3%

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

   2. Taylor expanded in z around 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 54.2

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

   4. Applied rewrites 54.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.3

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

   6. Applied rewrites 58.3%

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

   if -8.8e14 < t < 2.1999999999999999e-29

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 54.2

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

   4. Applied rewrites 54.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 42.5%

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

   if 2.1999999999999999e-29 < t

   1. Initial program 75.2%

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

   2. Taylor expanded in 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 54.8

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

   7. Applied rewrites 54.8%

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

Alternative 12: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8.8e+14)
   (* -4.0 (* t (/ a c)))
   (if (<= t 8.5e-29) (/ b (* z c)) (* (* (/ t c) -4.0) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.8e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 8.5e-29) {
		tmp = b / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-8.8d+14)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 8.5d-29) then
        tmp = b / (z * c)
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.8e+14) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 8.5e-29) {
		tmp = b / (z * c);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8.8e+14:
		tmp = -4.0 * (t * (a / c))
	elif t <= 8.5e-29:
		tmp = b / (z * c)
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8.8e+14)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 8.5e-29)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8.8e+14)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 8.5e-29)
		tmp = b / (z * c);
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8.8e+14], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-29], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8e14

   1. Initial program 73.3%

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

   2. Taylor expanded in z around 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 54.2

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

   4. Applied rewrites 54.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.3

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

   6. Applied rewrites 58.3%

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

   if -8.8e14 < t < 8.5000000000000001e-29

   1. Initial program 85.5%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 42.6%

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

   if 8.5000000000000001e-29 < t

   1. Initial program 75.1%

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

   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 54.9

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

   7. Applied rewrites 54.9%

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

Alternative 13: 49.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= t -8.8e+14) t_1 (if (<= t 8.5e-29) (/ b (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -8.8e+14) {
		tmp = t_1;
	} else if (t <= 8.5e-29) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (t <= (-8.8d+14)) then
        tmp = t_1
    else if (t <= 8.5d-29) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -8.8e+14) {
		tmp = t_1;
	} else if (t <= 8.5e-29) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -8.8e+14:
		tmp = t_1
	elif t <= 8.5e-29:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -8.8e+14)
		tmp = t_1;
	elseif (t <= 8.5e-29)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -8.8e+14)
		tmp = t_1;
	elseif (t <= 8.5e-29)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+14], t$95$1, If[LessEqual[t, 8.5e-29], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8e14 or 8.5000000000000001e-29 < t

   1. Initial program 74.3%

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

   2. Taylor expanded in z around 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 52.5

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

   4. Applied rewrites 52.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 55.6

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

   6. Applied rewrites 55.6%

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

   if -8.8e14 < t < 8.5000000000000001e-29

   1. Initial program 85.5%

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

   2. Taylor expanded in b around inf

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

   4. Applied rewrites 42.6%

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

Alternative 14: 35.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

2. Taylor expanded in b around inf

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

4. Applied rewrites 35.5%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
5. Add Preprocessing

Developer Target 1: 80.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - 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 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2025096 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))