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

Percentage Accurate: 79.2% → 87.8%

Time: 9.6s

Alternatives: 17

Speedup: 0.9×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 47.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 47.2%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 94.8%

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

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

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.6%

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

Alternative 2: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -5 \cdot 10^{+278}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 9, \frac{x}{c \cdot z}, \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* (* x 9.0) y) -5e+278)
   (fma (* y 9.0) (/ x (* c z)) (/ (fma (* -4.0 z) (* a t) b) (* c z)))
   (/ (fma (* -4.0 a) t (/ (fma (* y x) 9.0 b) z)) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * 9.0) * y) <= -5e+278) {
		tmp = fma((y * 9.0), (x / (c * z)), (fma((-4.0 * z), (a * t), b) / (c * z)));
	} else {
		tmp = fma((-4.0 * a), t, (fma((y * x), 9.0, b) / z)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(x * 9.0) * y) <= -5e+278)
		tmp = fma(Float64(y * 9.0), Float64(x / Float64(c * z)), Float64(fma(Float64(-4.0 * z), Float64(a * t), b) / Float64(c * z)));
	else
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(y * x), 9.0, b) / z)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision], -5e+278], N[(N[(y * 9.0), $MachinePrecision] * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000029e278

   1. Initial program 51.9%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      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

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

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

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

      6. associate-+l+ N/A

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

      7. div-add N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-/l* N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 81.5%

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

   if -5.00000000000000029e278 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.9%

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

Alternative 3: 88.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 47.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 80.2%

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

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

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.6%

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

Alternative 4: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+128} \lor \neg \left(z \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{\left(-t\right) \cdot \mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -7.5e+128) (not (<= z 4.6e+115)))
   (/ (* (- t) (fma a 4.0 (/ (- b) (* t z)))) c)
   (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.5e+128) || !(z <= 4.6e+115)) {
		tmp = (-t * fma(a, 4.0, (-b / (t * z)))) / c;
	} else {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7.5e+128) || !(z <= 4.6e+115))
		tmp = Float64(Float64(Float64(-t) * fma(a, 4.0, Float64(Float64(-b) / Float64(t * z)))) / c);
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -7.5e+128], N[Not[LessEqual[z, 4.6e+115]], $MachinePrecision]], N[(N[((-t) * N[(a * 4.0 + N[((-b) / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000076e128 or 4.60000000000000007e115 < z

   1. Initial program 50.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.2%

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

   6. Taylor expanded in t around -inf

      \[\leadsto \frac{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.3%

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

   if -7.50000000000000076e128 < z < 4.60000000000000007e115

   1. Initial program 90.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 89.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+128} \lor \neg \left(z \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{\left(-t\right) \cdot \mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+158} \lor \neg \left(z \leq 1.25 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{\left(-t\right) \cdot \mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.1e+158) (not (<= z 1.25e+116)))
   (/ (* (- t) (fma a 4.0 (/ (- b) (* t z)))) c)
   (/ (fma (* 9.0 x) y (fma (* -4.0 z) (* a t) b)) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.1e+158) || !(z <= 1.25e+116)) {
		tmp = (-t * fma(a, 4.0, (-b / (t * z)))) / c;
	} else {
		tmp = fma((9.0 * x), y, fma((-4.0 * z), (a * t), b)) / (z * c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.1e+158) || !(z <= 1.25e+116))
		tmp = Float64(Float64(Float64(-t) * fma(a, 4.0, Float64(Float64(-b) / Float64(t * z)))) / c);
	else
		tmp = Float64(fma(Float64(9.0 * x), y, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.1e+158], N[Not[LessEqual[z, 1.25e+116]], $MachinePrecision]], N[(N[((-t) * N[(a * 4.0 + N[((-b) / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(9.0 * x), $MachinePrecision] * y + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000004e158 or 1.25000000000000006e116 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in t around -inf

      \[\leadsto \frac{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.8%

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

   if -4.10000000000000004e158 < z < 1.25000000000000006e116

   1. Initial program 90.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

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

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. distribute-lft-neg-in N/A

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+158} \lor \neg \left(z \leq 1.25 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{\left(-t\right) \cdot \mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9 \cdot x, y, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, t, \frac{\frac{b}{z}}{a}\right)}{c} \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-t\right) \cdot \mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.4e+49)
   (* (/ (fma -4.0 t (/ (/ b z) a)) c) a)
   (if (<= z 4.6e+115)
     (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) (* z c))
     (/ (* (- t) (fma a 4.0 (/ (- b) (* t z)))) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.4e+49) {
		tmp = (fma(-4.0, t, ((b / z) / a)) / c) * a;
	} else if (z <= 4.6e+115) {
		tmp = fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / (z * c);
	} else {
		tmp = (-t * fma(a, 4.0, (-b / (t * z)))) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.4e+49)
		tmp = Float64(Float64(fma(-4.0, t, Float64(Float64(b / z) / a)) / c) * a);
	elseif (z <= 4.6e+115)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(-t) * fma(a, 4.0, Float64(Float64(-b) / Float64(t * z)))) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.4e+49], N[(N[(N[(-4.0 * t + N[(N[(b / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 4.6e+115], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[((-t) * N[(a * 4.0 + N[((-b) / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000028e49

   1. Initial program 58.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 70.8%

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

   if -6.40000000000000028e49 < z < 4.60000000000000007e115

   1. Initial program 92.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 91.9%

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

   if 4.60000000000000007e115 < z

   1. Initial program 48.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in t around -inf

      \[\leadsto \frac{-1 \cdot \left(t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)\right)}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.3%

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

Alternative 7: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2800000000000 \lor \neg \left(t \leq 5.5 \cdot 10^{-93}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{\mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2800000000000.0) (not (<= t 5.5e-93)))
   (* (- t) (/ (fma a 4.0 (/ (- b) (* t z))) c))
   (/ (/ (fma (* y x) 9.0 b) z) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2800000000000.0) || !(t <= 5.5e-93)) {
		tmp = -t * (fma(a, 4.0, (-b / (t * z))) / c);
	} else {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2800000000000.0) || !(t <= 5.5e-93))
		tmp = Float64(Float64(-t) * Float64(fma(a, 4.0, Float64(Float64(-b) / Float64(t * z))) / c));
	else
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2800000000000.0], N[Not[LessEqual[t, 5.5e-93]], $MachinePrecision]], N[((-t) * N[(N[(a * 4.0 + N[((-b) / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e12 or 5.49999999999999968e-93 < t

   1. Initial program 75.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 73.9%

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

   if -2.8e12 < t < 5.49999999999999968e-93

   1. Initial program 81.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 80.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2800000000000 \lor \neg \left(t \leq 5.5 \cdot 10^{-93}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{\mathsf{fma}\left(a, 4, \frac{-b}{t \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+203}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.35e+203)
   (* (* -4.0 a) (/ t c))
   (if (<= t -4.2e+40)
     (/ (fma (* (* -4.0 z) a) t b) (* z c))
     (if (<= t 5.2e-37)
       (/ (/ (fma (* y x) 9.0 b) z) c)
       (* -4.0 (* t (/ a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.35e+203) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= -4.2e+40) {
		tmp = fma(((-4.0 * z) * a), t, b) / (z * c);
	} else if (t <= 5.2e-37) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.35e+203)
		tmp = Float64(Float64(-4.0 * a) * Float64(t / c));
	elseif (t <= -4.2e+40)
		tmp = Float64(fma(Float64(Float64(-4.0 * z) * a), t, b) / Float64(z * c));
	elseif (t <= 5.2e-37)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.35e+203], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e+40], N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-37], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e203

   1. Initial program 64.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 52.1%

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

   7. Applied rewrites 56.8%

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

   if -1.35e203 < t < -4.2000000000000002e40

   1. Initial program 75.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-neg-in N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 78.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 75.8%

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

   if -4.2000000000000002e40 < t < 5.19999999999999959e-37

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 78.0%

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

   if 5.19999999999999959e-37 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.0%

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

   7. Applied rewrites 49.7%

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

Alternative 9: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-113}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{z \cdot c}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.2e+40)
   (* (* -4.0 a) (/ t c))
   (if (<= t -2.15e-113)
     (/ (* (* y x) 9.0) (* z c))
     (if (<= t 3.3e-37) (/ (/ b z) c) (* -4.0 (* t (/ a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.2e+40) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= -2.15e-113) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (t <= 3.3e-37) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= (-4.2d+40)) then
        tmp = ((-4.0d0) * a) * (t / c)
    else if (t <= (-2.15d-113)) then
        tmp = ((y * x) * 9.0d0) / (z * c)
    else if (t <= 3.3d-37) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (t * (a / 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 (t <= -4.2e+40) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= -2.15e-113) {
		tmp = ((y * x) * 9.0) / (z * c);
	} else if (t <= 3.3e-37) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -4.2e+40:
		tmp = (-4.0 * a) * (t / c)
	elif t <= -2.15e-113:
		tmp = ((y * x) * 9.0) / (z * c)
	elif t <= 3.3e-37:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.2e+40)
		tmp = Float64(Float64(-4.0 * a) * Float64(t / c));
	elseif (t <= -2.15e-113)
		tmp = Float64(Float64(Float64(y * x) * 9.0) / Float64(z * c));
	elseif (t <= 3.3e-37)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -4.2e+40)
		tmp = (-4.0 * a) * (t / c);
	elseif (t <= -2.15e-113)
		tmp = ((y * x) * 9.0) / (z * c);
	elseif (t <= 3.3e-37)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.2e+40], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e-113], N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-37], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.2000000000000002e40

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 51.8%

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

   7. Applied rewrites 61.6%

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

   if -4.2000000000000002e40 < t < -2.15e-113

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.5%

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

   if -2.15e-113 < t < 3.29999999999999982e-37

   1. Initial program 77.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.0%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   6. 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 48.1

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

   7. Applied rewrites 48.1%

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

   if 3.29999999999999982e-37 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.0%

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

   7. Applied rewrites 49.7%

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

Alternative 10: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+128}:\\ \;\;\;\;\frac{\left(-4 \cdot a\right) \cdot t}{c}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.36e+128)
   (/ (* (* -4.0 a) t) c)
   (if (<= z 7.2e+42) (/ (fma (* y x) 9.0 b) (* z c)) (* -4.0 (/ (* a t) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.36e+128) {
		tmp = ((-4.0 * a) * t) / c;
	} else if (z <= 7.2e+42) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.36e+128)
		tmp = Float64(Float64(Float64(-4.0 * a) * t) / c);
	elseif (z <= 7.2e+42)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.36e+128], N[(N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7.2e+42], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35999999999999991e128

   1. Initial program 54.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 59.7%

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

   if -1.35999999999999991e128 < z < 7.2000000000000002e42

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 77.3%

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

   if 7.2000000000000002e42 < z

   1. Initial program 56.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 67.0%

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

Alternative 11: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+128}:\\ \;\;\;\;\frac{\left(-4 \cdot a\right) \cdot t}{c}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.36e+128)
   (/ (* (* -4.0 a) t) c)
   (if (<= z 7.2e+42) (/ (fma (* y 9.0) x b) (* z c)) (* -4.0 (/ (* a t) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.36e+128) {
		tmp = ((-4.0 * a) * t) / c;
	} else if (z <= 7.2e+42) {
		tmp = fma((y * 9.0), x, b) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.36e+128)
		tmp = Float64(Float64(Float64(-4.0 * a) * t) / c);
	elseif (z <= 7.2e+42)
		tmp = Float64(fma(Float64(y * 9.0), x, b) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.36e+128], N[(N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7.2e+42], N[(N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35999999999999991e128

   1. Initial program 54.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 59.7%

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

   if -1.35999999999999991e128 < z < 7.2000000000000002e42

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 77.3%

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

   7. Applied rewrites 77.3%

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

   if 7.2000000000000002e42 < z

   1. Initial program 56.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 67.0%

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

Alternative 12: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+14}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.02e+14)
   (* (* -4.0 a) (/ t c))
   (if (<= t 3.3e-37) (/ (/ b z) c) (* -4.0 (* t (/ a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.02e+14) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 3.3e-37) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= (-1.02d+14)) then
        tmp = ((-4.0d0) * a) * (t / c)
    else if (t <= 3.3d-37) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (t * (a / 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 (t <= -1.02e+14) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 3.3e-37) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.02e+14:
		tmp = (-4.0 * a) * (t / c)
	elif t <= 3.3e-37:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.02e+14)
		tmp = Float64(Float64(-4.0 * a) * Float64(t / c));
	elseif (t <= 3.3e-37)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.02e+14)
		tmp = (-4.0 * a) * (t / c);
	elseif (t <= 3.3e-37)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.02e+14], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-37], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e14

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 48.8%

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

   7. Applied rewrites 57.5%

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

   if -1.02e14 < t < 3.29999999999999982e-37

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 44.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 45.7

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

   7. Applied rewrites 45.7%

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

   if 3.29999999999999982e-37 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.0%

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

   7. Applied rewrites 49.7%

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

Alternative 13: 49.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.6e+81)
   (* (* -4.0 a) (/ t c))
   (if (<= t 1.7e-38) (/ (/ b c) z) (* -4.0 (* t (/ a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.6e+81) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 1.7e-38) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= (-1.6d+81)) then
        tmp = ((-4.0d0) * a) * (t / c)
    else if (t <= 1.7d-38) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t * (a / 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 (t <= -1.6e+81) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 1.7e-38) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.6e+81:
		tmp = (-4.0 * a) * (t / c)
	elif t <= 1.7e-38:
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.6e+81)
		tmp = Float64(Float64(-4.0 * a) * Float64(t / c));
	elseif (t <= 1.7e-38)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.6e+81)
		tmp = (-4.0 * a) * (t / c);
	elseif (t <= 1.7e-38)
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.6e+81], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-38], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e81

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 48.1%

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

   7. Applied rewrites 59.5%

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

   if -1.6e81 < t < 1.7000000000000001e-38

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 42.1%

      \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
   6. 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. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 43.4

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

   7. Applied rewrites 43.4%

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

   if 1.7000000000000001e-38 < t

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.0%

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

   7. Applied rewrites 49.7%

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

Alternative 14: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-37} \lor \neg \left(z \leq 7 \cdot 10^{+42}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.3e-37) (not (<= z 7e+42)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e-37) || !(z <= 7e+42)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.3d-37)) .or. (.not. (z <= 7d+42))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e-37) || !(z <= 7e+42)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.3e-37) or not (z <= 7e+42):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.3e-37) || !(z <= 7e+42))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.3e-37) || ~((z <= 7e+42)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.3e-37], N[Not[LessEqual[z, 7e+42]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e-37 or 7.00000000000000047e42 < z

   1. Initial program 61.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 55.6%

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

   7. Applied rewrites 57.3%

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

   if -1.2999999999999999e-37 < z < 7.00000000000000047e42

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-37} \lor \neg \left(z \leq 7 \cdot 10^{+42}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.6e+81)
   (* (* -4.0 a) (/ t c))
   (if (<= t 9.5e-45) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.6e+81) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 9.5e-45) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / 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 (t <= (-1.6d+81)) then
        tmp = ((-4.0d0) * a) * (t / c)
    else if (t <= 9.5d-45) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / 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 (t <= -1.6e+81) {
		tmp = (-4.0 * a) * (t / c);
	} else if (t <= 9.5e-45) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.6e+81:
		tmp = (-4.0 * a) * (t / c)
	elif t <= 9.5e-45:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.6e+81)
		tmp = Float64(Float64(-4.0 * a) * Float64(t / c));
	elseif (t <= 9.5e-45)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.6e+81)
		tmp = (-4.0 * a) * (t / c);
	elseif (t <= 9.5e-45)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.6e+81], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-45], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e81

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 48.1%

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

   7. Applied rewrites 59.5%

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

   if -1.6e81 < t < 9.5000000000000002e-45

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 42.4%

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

   if 9.5000000000000002e-45 < t

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 47.8%

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

   7. Applied rewrites 50.4%

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

Alternative 16: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-37}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.3e-37)
   (* -4.0 (* t (/ a c)))
   (if (<= z 7e+42) (/ b (* z c)) (* -4.0 (/ (* a t) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.3e-37) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 7e+42) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.3d-37)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= 7d+42) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.3e-37) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 7e+42) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.3e-37:
		tmp = -4.0 * (t * (a / c))
	elif z <= 7e+42:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.3e-37)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= 7e+42)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.3e-37)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= 7e+42)
		tmp = b / (z * c);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.3e-37], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+42], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e-37

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 44.1%

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

   7. Applied rewrites 47.1%

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

   if -1.2999999999999999e-37 < z < 7.00000000000000047e42

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 49.6%

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

   if 7.00000000000000047e42 < z

   1. Initial program 56.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 67.0%

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

Alternative 17: 34.9% 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 77.7%

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

3. Taylor expanded in b around inf

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

5. Applied rewrites 35.9%

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

Developer Target 1: 80.3% 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 2025025 
(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)))