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

Percentage Accurate: 79.4% → 88.9%

Time: 5.9s

Alternatives: 17

Speedup: 0.1×

• 63.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 79.4% accurate, 1.0× speedup

Math

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

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: 88.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := z \cdot \left|c\right|\\ t_3 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{t\_2}\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{\left(t\_1 - \left(\left(a \cdot z\right) \cdot 4\right) \cdot t\right) + b}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{\frac{\left(t\_1 + b\right) - \left(\left(t \cdot a\right) \cdot 4\right) \cdot z}{z}}{\left|c\right|}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{\left|c\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y)))
       (t_2 (* z (fabs c)))
       (t_3 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) t_2)))
  (*
   (copysign 1.0 c)
   (if (<= t_3 -5e+43)
     (/ (+ (- t_1 (* (* (* a z) 4.0) t)) b) t_2)
     (if (<= t_3 2e-111)
       (/ (/ (- (+ t_1 b) (* (* (* t a) 4.0) z)) z) (fabs c))
       (if (<= t_3 INFINITY) t_3 (* (* -4.0 a) (/ t (fabs c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = z * fabs(c);
	double t_3 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	double tmp;
	if (t_3 <= -5e+43) {
		tmp = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	} else if (t_3 <= 2e-111) {
		tmp = (((t_1 + b) - (((t * a) * 4.0) * z)) / z) / fabs(c);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * a) * (t / fabs(c));
	}
	return copysign(1.0, c) * tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = z * Math.abs(c);
	double t_3 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	double tmp;
	if (t_3 <= -5e+43) {
		tmp = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	} else if (t_3 <= 2e-111) {
		tmp = (((t_1 + b) - (((t * a) * 4.0) * z)) / z) / Math.abs(c);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * a) * (t / Math.abs(c));
	}
	return Math.copySign(1.0, c) * tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	t_2 = z * math.fabs(c)
	t_3 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2
	tmp = 0
	if t_3 <= -5e+43:
		tmp = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2
	elif t_3 <= 2e-111:
		tmp = (((t_1 + b) - (((t * a) * 4.0) * z)) / z) / math.fabs(c)
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = (-4.0 * a) * (t / math.fabs(c))
	return math.copysign(1.0, c) * tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_2 = Float64(z * abs(c))
	t_3 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / t_2)
	tmp = 0.0
	if (t_3 <= -5e+43)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(a * z) * 4.0) * t)) + b) / t_2);
	elseif (t_3 <= 2e-111)
		tmp = Float64(Float64(Float64(Float64(t_1 + b) - Float64(Float64(Float64(t * a) * 4.0) * z)) / z) / abs(c));
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * a) * Float64(t / abs(c)));
	end
	return Float64(copysign(1.0, c) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (min(x, y) * 9.0) * max(x, y);
	t_2 = z * abs(c);
	t_3 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	tmp = 0.0;
	if (t_3 <= -5e+43)
		tmp = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	elseif (t_3 <= 2e-111)
		tmp = (((t_1 + b) - (((t * a) * 4.0) * z)) / z) / abs(c);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = (-4.0 * a) * (t / abs(c));
	end
	tmp_2 = (sign(c) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$3, -5e+43], N[(N[(N[(t$95$1 - N[(N[(N[(a * z), $MachinePrecision] * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 2e-111], N[(N[(N[(N[(t$95$1 + b), $MachinePrecision] - N[(N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, N[(N[(-4.0 * a), $MachinePrecision] * N[(t / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000004e43

   1. Initial program 79.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.5%

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

   3. Applied rewrites 79.5%

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

   if -5.0000000000000004e43 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 2.0000000000000002e-111

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   5. Applied rewrites 82.0%

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

   if 2.0000000000000002e-111 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 79.4%

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

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

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 2: 88.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ t_2 := z \cdot \left|c\right|\\ t_3 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot \mathsf{max}\left(t, a\right)\right) + b}{t\_2}\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;\frac{\left(t\_1 - \left(\left(\mathsf{max}\left(t, a\right) \cdot z\right) \cdot 4\right) \cdot \mathsf{min}\left(t, a\right)\right) + b}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 10^{+62}:\\ \;\;\;\;\frac{\frac{\left(b + \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)\right) - \mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot \left(4 \cdot z\right)\right)}{\left|c\right|}}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{\left|c\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y)))
       (t_2 (* z (fabs c)))
       (t_3
        (/
         (+ (- t_1 (* (* (* z 4.0) (fmin t a)) (fmax t a))) b)
         t_2)))
  (*
   (copysign 1.0 c)
   (if (<= t_3 -1e-236)
     (/ (+ (- t_1 (* (* (* (fmax t a) z) 4.0) (fmin t a))) b) t_2)
     (if (<= t_3 1e+62)
       (/
        (/
         (-
          (+ b (* (fmax x y) (* 9.0 (fmin x y))))
          (* (fmax t a) (* (fmin t a) (* 4.0 z))))
         (fabs c))
        z)
       (if (<= t_3 INFINITY)
         t_3
         (* (* -4.0 (fmax t a)) (/ (fmin t a) (fabs c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = z * fabs(c);
	double t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2;
	double tmp;
	if (t_3 <= -1e-236) {
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2;
	} else if (t_3 <= 1e+62) {
		tmp = (((b + (fmax(x, y) * (9.0 * fmin(x, y)))) - (fmax(t, a) * (fmin(t, a) * (4.0 * z)))) / fabs(c)) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / fabs(c));
	}
	return copysign(1.0, c) * tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double t_2 = z * Math.abs(c);
	double t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2;
	double tmp;
	if (t_3 <= -1e-236) {
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2;
	} else if (t_3 <= 1e+62) {
		tmp = (((b + (fmax(x, y) * (9.0 * fmin(x, y)))) - (fmax(t, a) * (fmin(t, a) * (4.0 * z)))) / Math.abs(c)) / z;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / Math.abs(c));
	}
	return Math.copySign(1.0, c) * tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	t_2 = z * math.fabs(c)
	t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2
	tmp = 0
	if t_3 <= -1e-236:
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2
	elif t_3 <= 1e+62:
		tmp = (((b + (fmax(x, y) * (9.0 * fmin(x, y)))) - (fmax(t, a) * (fmin(t, a) * (4.0 * z)))) / math.fabs(c)) / z
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / math.fabs(c))
	return math.copysign(1.0, c) * tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	t_2 = Float64(z * abs(c))
	t_3 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2)
	tmp = 0.0
	if (t_3 <= -1e-236)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2);
	elseif (t_3 <= 1e+62)
		tmp = Float64(Float64(Float64(Float64(b + Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) - Float64(fmax(t, a) * Float64(fmin(t, a) * Float64(4.0 * z)))) / abs(c)) / z);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / abs(c)));
	end
	return Float64(copysign(1.0, c) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (min(x, y) * 9.0) * max(x, y);
	t_2 = z * abs(c);
	t_3 = ((t_1 - (((z * 4.0) * min(t, a)) * max(t, a))) + b) / t_2;
	tmp = 0.0;
	if (t_3 <= -1e-236)
		tmp = ((t_1 - (((max(t, a) * z) * 4.0) * min(t, a))) + b) / t_2;
	elseif (t_3 <= 1e+62)
		tmp = (((b + (max(x, y) * (9.0 * min(x, y)))) - (max(t, a) * (min(t, a) * (4.0 * z)))) / abs(c)) / z;
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = (-4.0 * max(t, a)) * (min(t, a) / abs(c));
	end
	tmp_2 = (sign(c) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$3, -1e-236], N[(N[(N[(t$95$1 - N[(N[(N[(N[Max[t, a], $MachinePrecision] * z), $MachinePrecision] * 4.0), $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 1e+62], N[(N[(N[(N[(b + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1e-236

   1. Initial program 79.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.5%

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

   3. Applied rewrites 79.5%

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

   if -1e-236 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 1e62

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   if 1e62 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 79.4%

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

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

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 3: 87.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := z \cdot \left|c\right|\\ t_3 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot \mathsf{min}\left(t, a\right)\right) \cdot \mathsf{max}\left(t, a\right)\right) + b}{t\_2}\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;\frac{\left(t\_1 - \left(\left(\mathsf{max}\left(t, a\right) \cdot z\right) \cdot 4\right) \cdot \mathsf{min}\left(t, a\right)\right) + b}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\left(\left(\left(z \cdot \mathsf{min}\left(t, a\right)\right) \cdot \mathsf{max}\left(t, a\right)\right) \cdot -4 + b\right) \cdot \frac{1}{\left|c\right|}}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{\left|c\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* x 9.0) y))
       (t_2 (* z (fabs c)))
       (t_3
        (/
         (+ (- t_1 (* (* (* z 4.0) (fmin t a)) (fmax t a))) b)
         t_2)))
  (*
   (copysign 1.0 c)
   (if (<= t_3 -1e-236)
     (/ (+ (- t_1 (* (* (* (fmax t a) z) 4.0) (fmin t a))) b) t_2)
     (if (<= t_3 0.0)
       (/
        (*
         (+ (* (* (* z (fmin t a)) (fmax t a)) -4.0) b)
         (/ 1.0 (fabs c)))
        z)
       (if (<= t_3 INFINITY)
         t_3
         (* (* -4.0 (fmax t a)) (/ (fmin t a) (fabs c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = z * fabs(c);
	double t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2;
	double tmp;
	if (t_3 <= -1e-236) {
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2;
	} else if (t_3 <= 0.0) {
		tmp = (((((z * fmin(t, a)) * fmax(t, a)) * -4.0) + b) * (1.0 / fabs(c))) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / fabs(c));
	}
	return copysign(1.0, c) * tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = z * Math.abs(c);
	double t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2;
	double tmp;
	if (t_3 <= -1e-236) {
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2;
	} else if (t_3 <= 0.0) {
		tmp = (((((z * fmin(t, a)) * fmax(t, a)) * -4.0) + b) * (1.0 / Math.abs(c))) / z;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / Math.abs(c));
	}
	return Math.copySign(1.0, c) * tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = z * math.fabs(c)
	t_3 = ((t_1 - (((z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2
	tmp = 0
	if t_3 <= -1e-236:
		tmp = ((t_1 - (((fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2
	elif t_3 <= 0.0:
		tmp = (((((z * fmin(t, a)) * fmax(t, a)) * -4.0) + b) * (1.0 / math.fabs(c))) / z
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / math.fabs(c))
	return math.copysign(1.0, c) * tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(z * abs(c))
	t_3 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * fmin(t, a)) * fmax(t, a))) + b) / t_2)
	tmp = 0.0
	if (t_3 <= -1e-236)
		tmp = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(fmax(t, a) * z) * 4.0) * fmin(t, a))) + b) / t_2);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(z * fmin(t, a)) * fmax(t, a)) * -4.0) + b) * Float64(1.0 / abs(c))) / z);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / abs(c)));
	end
	return Float64(copysign(1.0, c) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = z * abs(c);
	t_3 = ((t_1 - (((z * 4.0) * min(t, a)) * max(t, a))) + b) / t_2;
	tmp = 0.0;
	if (t_3 <= -1e-236)
		tmp = ((t_1 - (((max(t, a) * z) * 4.0) * min(t, a))) + b) / t_2;
	elseif (t_3 <= 0.0)
		tmp = (((((z * min(t, a)) * max(t, a)) * -4.0) + b) * (1.0 / abs(c))) / z;
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = (-4.0 * max(t, a)) * (min(t, a) / abs(c));
	end
	tmp_2 = (sign(c) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$3, -1e-236], N[(N[(N[(t$95$1 - N[(N[(N[(N[Max[t, a], $MachinePrecision] * z), $MachinePrecision] * 4.0), $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(N[(N[(z * N[Min[t, a], $MachinePrecision]), $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + b), $MachinePrecision] * N[(1.0 / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1e-236

   1. Initial program 79.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.5%

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

   3. Applied rewrites 79.5%

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

   if -1e-236 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/r* N/A

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

      8. associate-*r/ N/A

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

      9. lower-/.f64 N/A

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

   6. Applied rewrites 55.9%

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

   if -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 79.4%

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

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

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 4: 87.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := z \cdot \left|c\right|\\ t_3 := \frac{\left(t\_1 - \left(\left(a \cdot z\right) \cdot 4\right) \cdot t\right) + b}{t\_2}\\ t_4 := \frac{\left(t\_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{t\_2}\\ \mathsf{copysign}\left(1, c\right) \cdot \begin{array}{l} \mathbf{if}\;t\_4 \leq -5 \cdot 10^{-227}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{\left(\left(z \cdot t\right) \cdot a\right) \cdot -4 + b}{z}}{\left|c\right|}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot \frac{t}{\left|c\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* x 9.0) y))
       (t_2 (* z (fabs c)))
       (t_3 (/ (+ (- t_1 (* (* (* a z) 4.0) t)) b) t_2))
       (t_4 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) t_2)))
  (*
   (copysign 1.0 c)
   (if (<= t_4 -5e-227)
     t_3
     (if (<= t_4 4e-224)
       (/ (/ (+ (* (* (* z t) a) -4.0) b) z) (fabs c))
       (if (<= t_4 INFINITY) t_3 (* (* -4.0 a) (/ t (fabs c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = z * fabs(c);
	double t_3 = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	double t_4 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	double tmp;
	if (t_4 <= -5e-227) {
		tmp = t_3;
	} else if (t_4 <= 4e-224) {
		tmp = (((((z * t) * a) * -4.0) + b) / z) / fabs(c);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * a) * (t / fabs(c));
	}
	return copysign(1.0, c) * tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = z * Math.abs(c);
	double t_3 = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	double t_4 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	double tmp;
	if (t_4 <= -5e-227) {
		tmp = t_3;
	} else if (t_4 <= 4e-224) {
		tmp = (((((z * t) * a) * -4.0) + b) / z) / Math.abs(c);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * a) * (t / Math.abs(c));
	}
	return Math.copySign(1.0, c) * tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = z * math.fabs(c)
	t_3 = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2
	t_4 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2
	tmp = 0
	if t_4 <= -5e-227:
		tmp = t_3
	elif t_4 <= 4e-224:
		tmp = (((((z * t) * a) * -4.0) + b) / z) / math.fabs(c)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = (-4.0 * a) * (t / math.fabs(c))
	return math.copysign(1.0, c) * tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(z * abs(c))
	t_3 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(a * z) * 4.0) * t)) + b) / t_2)
	t_4 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / t_2)
	tmp = 0.0
	if (t_4 <= -5e-227)
		tmp = t_3;
	elseif (t_4 <= 4e-224)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(z * t) * a) * -4.0) + b) / z) / abs(c));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * a) * Float64(t / abs(c)));
	end
	return Float64(copysign(1.0, c) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = z * abs(c);
	t_3 = ((t_1 - (((a * z) * 4.0) * t)) + b) / t_2;
	t_4 = ((t_1 - (((z * 4.0) * t) * a)) + b) / t_2;
	tmp = 0.0;
	if (t_4 <= -5e-227)
		tmp = t_3;
	elseif (t_4 <= 4e-224)
		tmp = (((((z * t) * a) * -4.0) + b) / z) / abs(c);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = (-4.0 * a) * (t / abs(c));
	end
	tmp_2 = (sign(c) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[Abs[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 - N[(N[(N[(a * z), $MachinePrecision] * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / t$95$2), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$4, -5e-227], t$95$3, If[LessEqual[t$95$4, 4e-224], N[(N[(N[(N[(N[(N[(z * t), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / N[Abs[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(-4.0 * a), $MachinePrecision] * N[(t / N[Abs[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999999999999996e-227 or 4.0000000000000001e-224 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 79.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 79.5%

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

   3. Applied rewrites 79.5%

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

   if -4.9999999999999996e-227 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 4.0000000000000001e-224

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 55.8%

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

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

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 5: 70.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{\left(\left(z \cdot t\right) \cdot a\right) \cdot -4 + b}{z}}{c}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-20}:\\ \;\;\;\;\frac{\frac{b + \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (/ (+ (* (* (* z t) a) -4.0) b) z) c)))
  (if (<= z -5.5e+97)
    (* -4.0 (/ (* a t) c))
    (if (<= z -2.3e-141)
      t_1
      (if (<= z 4e-20)
        (/ (/ (+ b (* (fmax x y) (* 9.0 (fmin x y)))) c) z)
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((((z * t) * a) * -4.0) + b) / z) / c;
	double tmp;
	if (z <= -5.5e+97) {
		tmp = -4.0 * ((a * t) / c);
	} else if (z <= -2.3e-141) {
		tmp = t_1;
	} else if (z <= 4e-20) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((z * t) * a) * (-4.0d0)) + b) / z) / c
    if (z <= (-5.5d+97)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (z <= (-2.3d-141)) then
        tmp = t_1
    else if (z <= 4d-20) then
        tmp = ((b + (fmax(x, y) * (9.0d0 * fmin(x, y)))) / c) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((((z * t) * a) * -4.0) + b) / z) / c;
	double tmp;
	if (z <= -5.5e+97) {
		tmp = -4.0 * ((a * t) / c);
	} else if (z <= -2.3e-141) {
		tmp = t_1;
	} else if (z <= 4e-20) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (((((z * t) * a) * -4.0) + b) / z) / c
	tmp = 0
	if z <= -5.5e+97:
		tmp = -4.0 * ((a * t) / c)
	elif z <= -2.3e-141:
		tmp = t_1
	elif z <= 4e-20:
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(z * t) * a) * -4.0) + b) / z) / c)
	tmp = 0.0
	if (z <= -5.5e+97)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (z <= -2.3e-141)
		tmp = t_1;
	elseif (z <= 4e-20)
		tmp = Float64(Float64(Float64(b + Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / c) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((((z * t) * a) * -4.0) + b) / z) / c;
	tmp = 0.0;
	if (z <= -5.5e+97)
		tmp = -4.0 * ((a * t) / c);
	elseif (z <= -2.3e-141)
		tmp = t_1;
	elseif (z <= 4e-20)
		tmp = ((b + (max(x, y) * (9.0 * min(x, y)))) / c) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(z * t), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -5.5e+97], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-141], t$95$1, If[LessEqual[z, 4e-20], N[(N[(N[(b + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e97

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -5.5000000000000002e97 < z < -2.2999999999999999e-141 or 3.9999999999999998e-20 < z

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 55.8%

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

   if -2.2999999999999999e-141 < z < 3.9999999999999998e-20

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 60.5%

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

Alternative 6: 68.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(x, y\right) \cdot 9\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{b + \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b - \left(\left(\mathsf{min}\left(t, a\right) \cdot \mathsf{max}\left(t, a\right)\right) \cdot 4\right) \cdot z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right) - 4 \cdot \left(\mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\right)}{c \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* (fmin x y) 9.0) (fmax x y))))
  (if (<= t_1 -1e-48)
    (/ (/ (+ b (* (fmax x y) (* 9.0 (fmin x y)))) c) z)
    (if (<= t_1 4e-75)
      (/
       (* (/ 1.0 c) (- b (* (* (* (fmin t a) (fmax t a)) 4.0) z)))
       z)
      (/
       (-
        (* 9.0 (* (fmin x y) (fmax x y)))
        (* 4.0 (* (fmax t a) (* (fmin t a) z))))
       (* c z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -1e-48) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (t_1 <= 4e-75) {
		tmp = ((1.0 / c) * (b - (((fmin(t, a) * fmax(t, a)) * 4.0) * z))) / z;
	} else {
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * (fmax(t, a) * (fmin(t, a) * z)))) / (c * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (fmin(x, y) * 9.0d0) * fmax(x, y)
    if (t_1 <= (-1d-48)) then
        tmp = ((b + (fmax(x, y) * (9.0d0 * fmin(x, y)))) / c) / z
    else if (t_1 <= 4d-75) then
        tmp = ((1.0d0 / c) * (b - (((fmin(t, a) * fmax(t, a)) * 4.0d0) * z))) / z
    else
        tmp = ((9.0d0 * (fmin(x, y) * fmax(x, y))) - (4.0d0 * (fmax(t, a) * (fmin(t, a) * z)))) / (c * z)
    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 = (fmin(x, y) * 9.0) * fmax(x, y);
	double tmp;
	if (t_1 <= -1e-48) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (t_1 <= 4e-75) {
		tmp = ((1.0 / c) * (b - (((fmin(t, a) * fmax(t, a)) * 4.0) * z))) / z;
	} else {
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * (fmax(t, a) * (fmin(t, a) * z)))) / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (fmin(x, y) * 9.0) * fmax(x, y)
	tmp = 0
	if t_1 <= -1e-48:
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z
	elif t_1 <= 4e-75:
		tmp = ((1.0 / c) * (b - (((fmin(t, a) * fmax(t, a)) * 4.0) * z))) / z
	else:
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * (fmax(t, a) * (fmin(t, a) * z)))) / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(fmin(x, y) * 9.0) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -1e-48)
		tmp = Float64(Float64(Float64(b + Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / c) / z);
	elseif (t_1 <= 4e-75)
		tmp = Float64(Float64(Float64(1.0 / c) * Float64(b - Float64(Float64(Float64(fmin(t, a) * fmax(t, a)) * 4.0) * z))) / z);
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(fmin(x, y) * fmax(x, y))) - Float64(4.0 * Float64(fmax(t, a) * Float64(fmin(t, a) * z)))) / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (min(x, y) * 9.0) * max(x, y);
	tmp = 0.0;
	if (t_1 <= -1e-48)
		tmp = ((b + (max(x, y) * (9.0 * min(x, y)))) / c) / z;
	elseif (t_1 <= 4e-75)
		tmp = ((1.0 / c) * (b - (((min(t, a) * max(t, a)) * 4.0) * z))) / z;
	else
		tmp = ((9.0 * (min(x, y) * max(x, y))) - (4.0 * (max(t, a) * (min(t, a) * z)))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * 9.0), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-48], N[(N[(N[(b + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e-75], N[(N[(N[(1.0 / c), $MachinePrecision] * N[(b - N[(N[(N[(N[Min[t, a], $MachinePrecision] * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.9999999999999997e-49

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 60.5%

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

   if -9.9999999999999997e-49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.9999999999999998e-75

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 79.7%

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 79.7%

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 79.7%

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.7%

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. associate-*r* N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*r* N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 80.3%

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 56.8%

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

   if 3.9999999999999998e-75 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 79.4%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 56.8%

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

   4. Applied rewrites 56.8%

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

Alternative 7: 68.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\\ \mathbf{if}\;\mathsf{min}\left(x, y\right) \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{b + \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)}{c}}{z}\\ \mathbf{elif}\;\mathsf{min}\left(x, y\right) \leq 1.05 \cdot 10^{-181}:\\ \;\;\;\;\frac{-4 \cdot t\_1 + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right) - 4 \cdot t\_1}{c \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (fmax t a) (* (fmin t a) z))))
  (if (<= (fmin x y) -5e+19)
    (/ (/ (+ b (* (fmax x y) (* 9.0 (fmin x y)))) c) z)
    (if (<= (fmin x y) 1.05e-181)
      (/ (+ (* -4.0 t_1) b) (* z c))
      (/ (- (* 9.0 (* (fmin x y) (fmax x y))) (* 4.0 t_1)) (* c z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fmax(t, a) * (fmin(t, a) * z);
	double tmp;
	if (fmin(x, y) <= -5e+19) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (fmin(x, y) <= 1.05e-181) {
		tmp = ((-4.0 * t_1) + b) / (z * c);
	} else {
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * t_1)) / (c * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = fmax(t, a) * (fmin(t, a) * z)
    if (fmin(x, y) <= (-5d+19)) then
        tmp = ((b + (fmax(x, y) * (9.0d0 * fmin(x, y)))) / c) / z
    else if (fmin(x, y) <= 1.05d-181) then
        tmp = (((-4.0d0) * t_1) + b) / (z * c)
    else
        tmp = ((9.0d0 * (fmin(x, y) * fmax(x, y))) - (4.0d0 * t_1)) / (c * z)
    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 = fmax(t, a) * (fmin(t, a) * z);
	double tmp;
	if (fmin(x, y) <= -5e+19) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (fmin(x, y) <= 1.05e-181) {
		tmp = ((-4.0 * t_1) + b) / (z * c);
	} else {
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * t_1)) / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = fmax(t, a) * (fmin(t, a) * z)
	tmp = 0
	if fmin(x, y) <= -5e+19:
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z
	elif fmin(x, y) <= 1.05e-181:
		tmp = ((-4.0 * t_1) + b) / (z * c)
	else:
		tmp = ((9.0 * (fmin(x, y) * fmax(x, y))) - (4.0 * t_1)) / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fmax(t, a) * Float64(fmin(t, a) * z))
	tmp = 0.0
	if (fmin(x, y) <= -5e+19)
		tmp = Float64(Float64(Float64(b + Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / c) / z);
	elseif (fmin(x, y) <= 1.05e-181)
		tmp = Float64(Float64(Float64(-4.0 * t_1) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(fmin(x, y) * fmax(x, y))) - Float64(4.0 * t_1)) / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = max(t, a) * (min(t, a) * z);
	tmp = 0.0;
	if (min(x, y) <= -5e+19)
		tmp = ((b + (max(x, y) * (9.0 * min(x, y)))) / c) / z;
	elseif (min(x, y) <= 1.05e-181)
		tmp = ((-4.0 * t_1) + b) / (z * c);
	else
		tmp = ((9.0 * (min(x, y) * max(x, y))) - (4.0 * t_1)) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Min[x, y], $MachinePrecision], -5e+19], N[(N[(N[(b + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[Min[x, y], $MachinePrecision], 1.05e-181], N[(N[(N[(-4.0 * t$95$1), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e19

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 60.5%

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

   if -5e19 < x < 1.05e-181

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

   if 1.05e-181 < x

   1. Initial program 79.4%

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

   2. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 56.8%

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

   4. Applied rewrites 56.8%

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

Alternative 8: 67.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(x, y\right) \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{b + \mathsf{max}\left(x, y\right) \cdot \left(9 \cdot \mathsf{min}\left(x, y\right)\right)}{c}}{z}\\ \mathbf{elif}\;\mathsf{min}\left(x, y\right) \leq 8600000000:\\ \;\;\;\;\frac{-4 \cdot \left(\mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right)}{c}}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (if (<= (fmin x y) -5e+19)
  (/ (/ (+ b (* (fmax x y) (* 9.0 (fmin x y)))) c) z)
  (if (<= (fmin x y) 8600000000.0)
    (/ (+ (* -4.0 (* (fmax t a) (* (fmin t a) z))) b) (* z c))
    (/ (/ (+ b (* 9.0 (* (fmin x y) (fmax x y)))) c) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (fmin(x, y) <= -5e+19) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (fmin(x, y) <= 8600000000.0) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else {
		tmp = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z;
	}
	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 (fmin(x, y) <= (-5d+19)) then
        tmp = ((b + (fmax(x, y) * (9.0d0 * fmin(x, y)))) / c) / z
    else if (fmin(x, y) <= 8600000000.0d0) then
        tmp = (((-4.0d0) * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
    else
        tmp = ((b + (9.0d0 * (fmin(x, y) * fmax(x, y)))) / c) / z
    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 (fmin(x, y) <= -5e+19) {
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z;
	} else if (fmin(x, y) <= 8600000000.0) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else {
		tmp = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if fmin(x, y) <= -5e+19:
		tmp = ((b + (fmax(x, y) * (9.0 * fmin(x, y)))) / c) / z
	elif fmin(x, y) <= 8600000000.0:
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
	else:
		tmp = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (fmin(x, y) <= -5e+19)
		tmp = Float64(Float64(Float64(b + Float64(fmax(x, y) * Float64(9.0 * fmin(x, y)))) / c) / z);
	elseif (fmin(x, y) <= 8600000000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(fmax(t, a) * Float64(fmin(t, a) * z))) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(fmin(x, y) * fmax(x, y)))) / c) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (min(x, y) <= -5e+19)
		tmp = ((b + (max(x, y) * (9.0 * min(x, y)))) / c) / z;
	elseif (min(x, y) <= 8600000000.0)
		tmp = ((-4.0 * (max(t, a) * (min(t, a) * z))) + b) / (z * c);
	else
		tmp = ((b + (9.0 * (min(x, y) * max(x, y)))) / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[Min[x, y], $MachinePrecision], -5e+19], N[(N[(N[(b + N[(N[Max[x, y], $MachinePrecision] * N[(9.0 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[Min[x, y], $MachinePrecision], 8600000000.0], N[(N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e19

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 60.5%

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

   if -5e19 < x < 8.6e9

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

   if 8.6e9 < x

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

Alternative 9: 67.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{b + 9 \cdot \left(\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\right)}{c}}{z}\\ \mathbf{if}\;\mathsf{min}\left(x, y\right) \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{min}\left(x, y\right) \leq 8600000000:\\ \;\;\;\;\frac{-4 \cdot \left(\mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (/ (/ (+ b (* 9.0 (* (fmin x y) (fmax x y)))) c) z)))
  (if (<= (fmin x y) -5e+19)
    t_1
    (if (<= (fmin x y) 8600000000.0)
      (/ (+ (* -4.0 (* (fmax t a) (* (fmin t a) z))) b) (* z c))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z;
	double tmp;
	if (fmin(x, y) <= -5e+19) {
		tmp = t_1;
	} else if (fmin(x, y) <= 8600000000.0) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b + (9.0d0 * (fmin(x, y) * fmax(x, y)))) / c) / z
    if (fmin(x, y) <= (-5d+19)) then
        tmp = t_1
    else if (fmin(x, y) <= 8600000000.0d0) then
        tmp = (((-4.0d0) * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z;
	double tmp;
	if (fmin(x, y) <= -5e+19) {
		tmp = t_1;
	} else if (fmin(x, y) <= 8600000000.0) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((b + (9.0 * (fmin(x, y) * fmax(x, y)))) / c) / z
	tmp = 0
	if fmin(x, y) <= -5e+19:
		tmp = t_1
	elif fmin(x, y) <= 8600000000.0:
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b + Float64(9.0 * Float64(fmin(x, y) * fmax(x, y)))) / c) / z)
	tmp = 0.0
	if (fmin(x, y) <= -5e+19)
		tmp = t_1;
	elseif (fmin(x, y) <= 8600000000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(fmax(t, a) * Float64(fmin(t, a) * z))) + b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((b + (9.0 * (min(x, y) * max(x, y)))) / c) / z;
	tmp = 0.0;
	if (min(x, y) <= -5e+19)
		tmp = t_1;
	elseif (min(x, y) <= 8600000000.0)
		tmp = ((-4.0 * (max(t, a) * (min(t, a) * z))) + b) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b + N[(9.0 * N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[Min[x, y], $MachinePrecision], -5e+19], t$95$1, If[LessEqual[N[Min[x, y], $MachinePrecision], 8600000000.0], N[(N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5e19 or 8.6e9 < x

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   if -5e19 < x < 8.6e9

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

Alternative 10: 67.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \frac{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}{c}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-141}:\\ \;\;\;\;\frac{-4 \cdot \left(\mathsf{max}\left(t, a\right) \cdot \left(\mathsf{min}\left(t, a\right) \cdot z\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (if (<= z -3.3e+97)
  (* -4.0 (/ (* (fmax t a) (fmin t a)) c))
  (if (<= z -2.3e-141)
    (/ (+ (* -4.0 (* (fmax t a) (* (fmin t a) z))) b) (* z c))
    (if (<= z 7.8e+105)
      (/ (+ b (* y (* 9.0 x))) (* z c))
      (* (* -4.0 (fmax t a)) (/ (fmin t a) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+97) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= -2.3e-141) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(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 (z <= (-3.3d+97)) then
        tmp = (-4.0d0) * ((fmax(t, a) * fmin(t, a)) / c)
    else if (z <= (-2.3d-141)) then
        tmp = (((-4.0d0) * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
    else if (z <= 7.8d+105) then
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    else
        tmp = ((-4.0d0) * fmax(t, a)) * (fmin(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 (z <= -3.3e+97) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= -2.3e-141) {
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.3e+97:
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c)
	elif z <= -2.3e-141:
		tmp = ((-4.0 * (fmax(t, a) * (fmin(t, a) * z))) + b) / (z * c)
	elif z <= 7.8e+105:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	else:
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.3e+97)
		tmp = Float64(-4.0 * Float64(Float64(fmax(t, a) * fmin(t, a)) / c));
	elseif (z <= -2.3e-141)
		tmp = Float64(Float64(Float64(-4.0 * Float64(fmax(t, a) * Float64(fmin(t, a) * z))) + b) / Float64(z * c));
	elseif (z <= 7.8e+105)
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.3e+97)
		tmp = -4.0 * ((max(t, a) * min(t, a)) / c);
	elseif (z <= -2.3e-141)
		tmp = ((-4.0 * (max(t, a) * (min(t, a) * z))) + b) / (z * c);
	elseif (z <= 7.8e+105)
		tmp = (b + (y * (9.0 * x))) / (z * c);
	else
		tmp = (-4.0 * max(t, a)) * (min(t, a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.3e+97], N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-141], N[(N[(N[(-4.0 * N[(N[Max[t, a], $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+105], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3000000000000001e97

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -3.3000000000000001e97 < z < -2.2999999999999999e-141

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 56.3%

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

   4. Applied rewrites 56.3%

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

   if -2.2999999999999999e-141 < z < 7.7999999999999996e105

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.8%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 59.8%

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

   6. Applied rewrites 59.8%

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

   if 7.7999999999999996e105 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 11: 67.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;-4 \cdot \frac{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (if (<= z -3.9e+65)
  (* -4.0 (/ (* (fmax t a) (fmin t a)) c))
  (if (<= z 7.8e+105)
    (/ (+ b (* y (* 9.0 x))) (* z c))
    (* (* -4.0 (fmax t a)) (/ (fmin t a) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e+65) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(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 (z <= (-3.9d+65)) then
        tmp = (-4.0d0) * ((fmax(t, a) * fmin(t, a)) / c)
    else if (z <= 7.8d+105) then
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    else
        tmp = ((-4.0d0) * fmax(t, a)) * (fmin(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 (z <= -3.9e+65) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.9e+65:
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c)
	elif z <= 7.8e+105:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	else:
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.9e+65)
		tmp = Float64(-4.0 * Float64(Float64(fmax(t, a) * fmin(t, a)) / c));
	elseif (z <= 7.8e+105)
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.9e+65)
		tmp = -4.0 * ((max(t, a) * min(t, a)) / c);
	elseif (z <= 7.8e+105)
		tmp = (b + (y * (9.0 * x))) / (z * c);
	else
		tmp = (-4.0 * max(t, a)) * (min(t, a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.9e+65], N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+105], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e65

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -3.8999999999999998e65 < z < 7.7999999999999996e105

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.8%

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 59.8%

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

   6. Applied rewrites 59.8%

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

   if 7.7999999999999996e105 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 12: 66.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;-4 \cdot \frac{\mathsf{max}\left(t, a\right) \cdot \mathsf{min}\left(t, a\right)}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (if (<= z -3.9e+65)
  (* -4.0 (/ (* (fmax t a) (fmin t a)) c))
  (if (<= z 7.8e+105)
    (/ (+ b (* 9.0 (* x y))) (* z c))
    (* (* -4.0 (fmax t a)) (/ (fmin t a) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e+65) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(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 (z <= (-3.9d+65)) then
        tmp = (-4.0d0) * ((fmax(t, a) * fmin(t, a)) / c)
    else if (z <= 7.8d+105) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = ((-4.0d0) * fmax(t, a)) * (fmin(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 (z <= -3.9e+65) {
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c);
	} else if (z <= 7.8e+105) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.9e+65:
		tmp = -4.0 * ((fmax(t, a) * fmin(t, a)) / c)
	elif z <= 7.8e+105:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = (-4.0 * fmax(t, a)) * (fmin(t, a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.9e+65)
		tmp = Float64(-4.0 * Float64(Float64(fmax(t, a) * fmin(t, a)) / c));
	elseif (z <= 7.8e+105)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.9e+65)
		tmp = -4.0 * ((max(t, a) * min(t, a)) / c);
	elseif (z <= 7.8e+105)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = (-4.0 * max(t, a)) * (min(t, a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.9e+65], N[(-4.0 * N[(N[(N[Max[t, a], $MachinePrecision] * N[Min[t, a], $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+105], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e65

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -3.8999999999999998e65 < z < 7.7999999999999996e105

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.9%

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

   4. Applied rewrites 59.9%

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

   if 7.7999999999999996e105 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 13: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-175}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+19}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* -4.0 (fmax t a)) (/ (fmin t a) c))))
  (if (<= z -2.75e-64)
    t_1
    (if (<= z 1.1e-175)
      (/ b (* c z))
      (if (<= z 9.5e+19) (* 9.0 (/ (* x y) (* c z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.1e-175) {
		tmp = b / (c * z);
	} else if (z <= 9.5e+19) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * fmax(t, a)) * (fmin(t, a) / c)
    if (z <= (-2.75d-64)) then
        tmp = t_1
    else if (z <= 1.1d-175) then
        tmp = b / (c * z)
    else if (z <= 9.5d+19) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.1e-175) {
		tmp = b / (c * z);
	} else if (z <= 9.5e+19) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c)
	tmp = 0
	if z <= -2.75e-64:
		tmp = t_1
	elif z <= 1.1e-175:
		tmp = b / (c * z)
	elif z <= 9.5e+19:
		tmp = 9.0 * ((x * y) / (c * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / c))
	tmp = 0.0
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.1e-175)
		tmp = Float64(b / Float64(c * z));
	elseif (z <= 9.5e+19)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * max(t, a)) * (min(t, a) / c);
	tmp = 0.0;
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.1e-175)
		tmp = b / (c * z);
	elseif (z <= 9.5e+19)
		tmp = 9.0 * ((x * y) / (c * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e-64], t$95$1, If[LessEqual[z, 1.1e-175], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+19], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7499999999999999e-64 or 9.5e19 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

   if -2.7499999999999999e-64 < z < 1.1e-175

   1. Initial program 79.4%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   if 1.1e-175 < z < 9.5e19

   1. Initial program 79.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 36.2%

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

   4. Applied rewrites 36.2%

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

Alternative 14: 49.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \left(-4 \cdot \mathsf{max}\left(t, a\right)\right) \cdot \frac{\mathsf{min}\left(t, a\right)}{c}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+23}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* (* -4.0 (fmax t a)) (/ (fmin t a) c))))
  (if (<= z -2.75e-64) t_1 (if (<= z 1.36e+23) (/ b (* c z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.36e+23) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * fmax(t, a)) * (fmin(t, a) / c)
    if (z <= (-2.75d-64)) then
        tmp = t_1
    else if (z <= 1.36d+23) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.36e+23) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-4.0 * fmax(t, a)) * (fmin(t, a) / c)
	tmp = 0
	if z <= -2.75e-64:
		tmp = t_1
	elif z <= 1.36e+23:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * fmax(t, a)) * Float64(fmin(t, a) / c))
	tmp = 0.0
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.36e+23)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (-4.0 * max(t, a)) * (min(t, a) / c);
	tmp = 0.0;
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.36e+23)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[Max[t, a], $MachinePrecision]), $MachinePrecision] * N[(N[Min[t, a], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e-64], t$95$1, If[LessEqual[z, 1.36e+23], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999999e-64 or 1.36e23 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

   if -2.7499999999999999e-64 < z < 1.36e23

   1. Initial program 79.4%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0%

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

   4. Applied rewrites 35.0%

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

Alternative 15: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+23}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (if (<= z -2.75e-64)
  (* -4.0 (/ (* a t) c))
  (if (<= z 1.36e+23) (/ 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 (z <= -2.75e-64) {
		tmp = -4.0 * ((a * t) / c);
	} else if (z <= 1.36e+23) {
		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 (z <= (-2.75d-64)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (z <= 1.36d+23) 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 (z <= -2.75e-64) {
		tmp = -4.0 * ((a * t) / c);
	} else if (z <= 1.36e+23) {
		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 z <= -2.75e-64:
		tmp = -4.0 * ((a * t) / c)
	elif z <= 1.36e+23:
		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 (z <= -2.75e-64)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (z <= 1.36e+23)
		tmp = Float64(b / Float64(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 (z <= -2.75e-64)
		tmp = -4.0 * ((a * t) / c);
	elseif (z <= 1.36e+23)
		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[z, -2.75e-64], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+23], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7499999999999999e-64

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -2.7499999999999999e-64 < z < 1.36e23

   1. Initial program 79.4%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0%

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

   4. Applied rewrites 35.0%

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

   if 1.36e23 < z

   1. Initial program 79.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

   3. Applied rewrites 79.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   6. Applied rewrites 38.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 40.7%

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

   8. Applied rewrites 40.7%

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

Alternative 16: 49.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+23}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  (let* ((t_1 (* -4.0 (/ (* a t) c))))
  (if (<= z -2.75e-64) t_1 (if (<= z 1.36e+23) (/ b (* c z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.36e+23) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((a * t) / c)
    if (z <= (-2.75d-64)) then
        tmp = t_1
    else if (z <= 1.36d+23) then
        tmp = b / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((a * t) / c);
	double tmp;
	if (z <= -2.75e-64) {
		tmp = t_1;
	} else if (z <= 1.36e+23) {
		tmp = b / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((a * t) / c)
	tmp = 0
	if z <= -2.75e-64:
		tmp = t_1
	elif z <= 1.36e+23:
		tmp = b / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.36e+23)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (z <= -2.75e-64)
		tmp = t_1;
	elseif (z <= 1.36e+23)
		tmp = b / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e-64], t$95$1, If[LessEqual[z, 1.36e+23], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999999e-64 or 1.36e23 < z

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.7%

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

   4. Applied rewrites 38.7%

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

   if -2.7499999999999999e-64 < z < 1.36e23

   1. Initial program 79.4%

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

   2. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0%

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

   4. Applied rewrites 35.0%

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

Alternative 17: 35.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.4%

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

2. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 35.0%

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

4. Applied rewrites 35.0%

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

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64
  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))