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

Percentage Accurate: 79.2% → 93.9%

Time: 16.5s

Alternatives: 17

Speedup: 0.8×

• 38.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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: 93.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, \mathsf{fma}\left(a, t \cdot 4, \frac{b}{-z}\right)\right)}{-c}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma x (/ (* y -9.0) z) (fma a (* t 4.0) (/ b (- z)))) (- c))))
   (if (<= z -2.35e-39)
     t_1
     (if (<= z 1.1e-85)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, ((y * -9.0) / z), fma(a, (t * 4.0), (b / -z))) / -c;
	double tmp;
	if (z <= -2.35e-39) {
		tmp = t_1;
	} else if (z <= 1.1e-85) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(Float64(y * -9.0) / z), fma(a, Float64(t * 4.0), Float64(b / Float64(-z)))) / Float64(-c))
	tmp = 0.0
	if (z <= -2.35e-39)
		tmp = t_1;
	elseif (z <= 1.1e-85)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(a * N[(t * 4.0), $MachinePrecision] + N[(b / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision]}, If[LessEqual[z, -2.35e-39], t$95$1, If[LessEqual[z, 1.1e-85], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3500000000000001e-39 or 1.1e-85 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 83.7%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

   8. Simplified 95.0%

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

   if -2.3500000000000001e-39 < z < 1.1e-85

   1. Initial program 98.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, \mathsf{fma}\left(a, t \cdot 4, \frac{b}{-z}\right)\right)}{-c}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y \cdot -9}{z}, \mathsf{fma}\left(a, t \cdot 4, \frac{b}{-z}\right)\right)}{-c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 INFINITY)
     t_1
     (/ (fma x (/ (* y -9.0) z) (* 4.0 (* a t))) (- c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(x, ((y * -9.0) / z), (4.0 * (a * t))) / -c;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(fma(x, Float64(Float64(y * -9.0) / z), Float64(4.0 * Float64(a * t))) / Float64(-c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision]]]

Derivation

1. Split input into 2 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)) < +inf.0

   1. Initial program 90.5%

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

   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 0.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

   8. Simplified 74.0%

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

   9. Taylor expanded in a around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-lowering-*.f64 74.0

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

   11. Simplified 74.0%

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

4. Final simplification 89.8%

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

Alternative 3: 85.7% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* z -4.0) (* a t) (fma x (* y 9.0) b)) (* z c))
   (/ (fma x (/ (* y -9.0) z) (* 4.0 (* a t))) (- c))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * -4.0), $MachinePrecision] * N[(a * t), $MachinePrecision] + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision] + N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision]]

Derivation

1. Split input into 2 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)) < +inf.0

   1. Initial program 90.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. *-lowering-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-lowering-*.f64 91.2

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

   4. Applied egg-rr 91.2%

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

   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 0.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

   8. Simplified 74.0%

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

   9. Taylor expanded in a around inf

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

       1. *-lowering-*.f64 N/A

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

       2. *-lowering-*.f64 74.0

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

   11. Simplified 74.0%

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

4. Final simplification 90.5%

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

Alternative 4: 85.4% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* z -4.0) (* a t) (fma x (* y 9.0) b)) (* z c))
   (* -4.0 (* a (/ t c)))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * -4.0), $MachinePrecision] * N[(a * t), $MachinePrecision] + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 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)) < +inf.0

   1. Initial program 90.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. *-lowering-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-lowering-*.f64 91.2

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

   4. Applied egg-rr 91.2%

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

   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 0.0%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 10.6%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 54.9

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

   7. Simplified 54.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 65.3

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

   9. Applied egg-rr 65.3%

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

4. Final simplification 90.1%

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

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1000000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, a \cdot -4, b\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_1 -4e+290)
     t_2
     (if (<= t_1 -1000000000000.0)
       (/ (/ (fma x (* y 9.0) b) c) z)
       (if (<= t_1 2e+86)
         (* (fma (* z t) (* a -4.0) b) (/ 1.0 (* z c)))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_1 <= -4e+290) {
		tmp = t_2;
	} else if (t_1 <= -1000000000000.0) {
		tmp = (fma(x, (y * 9.0), b) / c) / z;
	} else if (t_1 <= 2e+86) {
		tmp = fma((z * t), (a * -4.0), b) * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_1 <= -4e+290)
		tmp = t_2;
	elseif (t_1 <= -1000000000000.0)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / c) / z);
	elseif (t_1 <= 2e+86)
		tmp = Float64(fma(Float64(z * t), Float64(a * -4.0), b) * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+290], t$95$2, If[LessEqual[t$95$1, -1000000000000.0], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(N[(z * t), $MachinePrecision] * N[(a * -4.0), $MachinePrecision] + b), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000025e290 or 2e86 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 81.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 75.8

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

   7. Simplified 75.8%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 80.3

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

   9. Applied egg-rr 80.3%

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

   if -4.00000000000000025e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e12

   1. Initial program 81.3%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 75.1%

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

   if -1e12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e86

   1. Initial program 89.9%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 83.6

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

   7. Simplified 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot z, -4 \cdot a, b\right)} \cdot \frac{1}{z \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+290}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1000000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, a \cdot -4, b\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+45}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_1 -4e+290)
     t_2
     (if (<= t_1 -5e+35)
       (/ (fma 9.0 (* x y) b) (* z c))
       (if (<= t_1 1e+45) (/ (- (/ b z) (* 4.0 (* a t))) c) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_1 <= -4e+290) {
		tmp = t_2;
	} else if (t_1 <= -5e+35) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (t_1 <= 1e+45) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_1 <= -4e+290)
		tmp = t_2;
	elseif (t_1 <= -5e+35)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (t_1 <= 1e+45)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+290], t$95$2, If[LessEqual[t$95$1, -5e+35], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+45], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000025e290 or 9.9999999999999993e44 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.2%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 79.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 70.5

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

   7. Simplified 70.5%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 74.2

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

   9. Applied egg-rr 74.2%

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

   if -4.00000000000000025e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000021e35

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 74.3

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

   5. Simplified 74.3%

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

   if -5.00000000000000021e35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999993e44

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 79.7%

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

   6. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

   8. Simplified 91.3%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. mul-1-neg N/A

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

       3. unsub-neg N/A

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

       4. --lowering--.f64 N/A

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

       5. *-lowering-*.f64 N/A

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

       6. *-lowering-*.f64 N/A

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

       7. /-lowering-/.f64 89.2

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

   11. Simplified 89.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+290}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+45}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1000000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_1 -4e+290)
     t_2
     (if (<= t_1 -1000000000000.0)
       (/ (/ (fma x (* y 9.0) b) c) z)
       (if (<= t_1 2e+86) (/ (fma a (* -4.0 (* z t)) b) (* z c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_1 <= -4e+290) {
		tmp = t_2;
	} else if (t_1 <= -1000000000000.0) {
		tmp = (fma(x, (y * 9.0), b) / c) / z;
	} else if (t_1 <= 2e+86) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_1 <= -4e+290)
		tmp = t_2;
	elseif (t_1 <= -1000000000000.0)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / c) / z);
	elseif (t_1 <= 2e+86)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+290], t$95$2, If[LessEqual[t$95$1, -1000000000000.0], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000025e290 or 2e86 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 81.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 75.8

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

   7. Simplified 75.8%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 80.3

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

   9. Applied egg-rr 80.3%

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

   if -4.00000000000000025e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e12

   1. Initial program 81.3%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 75.1%

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

   if -1e12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e86

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 83.5

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

   5. Simplified 83.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+290}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1000000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1000000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (/ (* y 9.0) z) (/ x c))))
   (if (<= t_1 -4e+290)
     t_2
     (if (<= t_1 -1000000000000.0)
       (/ (fma 9.0 (* x y) b) (* z c))
       (if (<= t_1 2e+86) (/ (fma a (* -4.0 (* z t)) b) (* z c)) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = ((y * 9.0) / z) * (x / c);
	double tmp;
	if (t_1 <= -4e+290) {
		tmp = t_2;
	} else if (t_1 <= -1000000000000.0) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (t_1 <= 2e+86) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c))
	tmp = 0.0
	if (t_1 <= -4e+290)
		tmp = t_2;
	elseif (t_1 <= -1000000000000.0)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (t_1 <= 2e+86)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+290], t$95$2, If[LessEqual[t$95$1, -1000000000000.0], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000025e290 or 2e86 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 81.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 75.8

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

   7. Simplified 75.8%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. /-lowering-/.f64 80.3

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

   9. Applied egg-rr 80.3%

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

   if -4.00000000000000025e290 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e12

   1. Initial program 81.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 70.6

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

   5. Simplified 70.6%

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

   if -1e12 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e86

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 83.5

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

   5. Simplified 83.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+290}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1000000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (* x 9.0) (/ y (* z c)))))
   (if (<= t_1 -5e+35)
     t_2
     (if (<= t_1 -1e-204)
       (* b (/ 1.0 (* z c)))
       (if (<= t_1 5e+54) (* t (/ a (* c -0.25))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (x * 9.0) * (y / (z * c));
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = t_2;
	} else if (t_1 <= -1e-204) {
		tmp = b * (1.0 / (z * c));
	} else if (t_1 <= 5e+54) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    t_2 = (x * 9.0d0) * (y / (z * c))
    if (t_1 <= (-5d+35)) then
        tmp = t_2
    else if (t_1 <= (-1d-204)) then
        tmp = b * (1.0d0 / (z * c))
    else if (t_1 <= 5d+54) then
        tmp = t * (a / (c * (-0.25d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (x * 9.0) * (y / (z * c));
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = t_2;
	} else if (t_1 <= -1e-204) {
		tmp = b * (1.0 / (z * c));
	} else if (t_1 <= 5e+54) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	t_2 = (x * 9.0) * (y / (z * c))
	tmp = 0
	if t_1 <= -5e+35:
		tmp = t_2
	elif t_1 <= -1e-204:
		tmp = b * (1.0 / (z * c))
	elif t_1 <= 5e+54:
		tmp = t * (a / (c * -0.25))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)))
	tmp = 0.0
	if (t_1 <= -5e+35)
		tmp = t_2;
	elseif (t_1 <= -1e-204)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (t_1 <= 5e+54)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	t_2 = (x * 9.0) * (y / (z * c));
	tmp = 0.0;
	if (t_1 <= -5e+35)
		tmp = t_2;
	elseif (t_1 <= -1e-204)
		tmp = b * (1.0 / (z * c));
	elseif (t_1 <= 5e+54)
		tmp = t * (a / (c * -0.25));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+35], t$95$2, If[LessEqual[t$95$1, -1e-204], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+54], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000021e35 or 5.00000000000000005e54 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.7%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 63.8

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

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. un-div-inv N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. *-lowering-*.f64 64.7

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

   9. Applied egg-rr 64.7%

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

   if -5.00000000000000021e35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-204

   1. Initial program 90.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 58.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 58.3

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

   7. Applied egg-rr 58.3%

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

   if -1e-204 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000005e54

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

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

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 51.6

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

   5. Simplified 51.6%

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. *-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. clear-num N/A

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

      13. un-div-inv N/A

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

      14. /-lowering-/.f64 N/A

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

      15. div-inv N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      17. metadata-eval 60.1

          \[\leadsto \frac{a}{c \cdot \color{blue}{-0.25}} \cdot t \]

   7. Applied egg-rr 60.1%

      \[\leadsto \color{blue}{\frac{a}{c \cdot -0.25} \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* x (* 9.0 (/ y (* z c))))))
   (if (<= t_1 -5e+35)
     t_2
     (if (<= t_1 -1e-204)
       (* b (/ 1.0 (* z c)))
       (if (<= t_1 5e+54) (* t (/ a (* c -0.25))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = x * (9.0 * (y / (z * c)));
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = t_2;
	} else if (t_1 <= -1e-204) {
		tmp = b * (1.0 / (z * c));
	} else if (t_1 <= 5e+54) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    t_2 = x * (9.0d0 * (y / (z * c)))
    if (t_1 <= (-5d+35)) then
        tmp = t_2
    else if (t_1 <= (-1d-204)) then
        tmp = b * (1.0d0 / (z * c))
    else if (t_1 <= 5d+54) then
        tmp = t * (a / (c * (-0.25d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = x * (9.0 * (y / (z * c)));
	double tmp;
	if (t_1 <= -5e+35) {
		tmp = t_2;
	} else if (t_1 <= -1e-204) {
		tmp = b * (1.0 / (z * c));
	} else if (t_1 <= 5e+54) {
		tmp = t * (a / (c * -0.25));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	t_2 = x * (9.0 * (y / (z * c)))
	tmp = 0
	if t_1 <= -5e+35:
		tmp = t_2
	elif t_1 <= -1e-204:
		tmp = b * (1.0 / (z * c))
	elif t_1 <= 5e+54:
		tmp = t * (a / (c * -0.25))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -5e+35)
		tmp = t_2;
	elseif (t_1 <= -1e-204)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (t_1 <= 5e+54)
		tmp = Float64(t * Float64(a / Float64(c * -0.25)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	t_2 = x * (9.0 * (y / (z * c)));
	tmp = 0.0;
	if (t_1 <= -5e+35)
		tmp = t_2;
	elseif (t_1 <= -1e-204)
		tmp = b * (1.0 / (z * c));
	elseif (t_1 <= 5e+54)
		tmp = t * (a / (c * -0.25));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(9.0 * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+35], t$95$2, If[LessEqual[t$95$1, -1e-204], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+54], N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000021e35 or 5.00000000000000005e54 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.7%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 63.8

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

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)} \cdot \frac{1}{z \cdot c} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-*l* N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-lowering-*.f64 64.8

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

   9. Applied egg-rr 64.8%

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

   if -5.00000000000000021e35 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e-204

   1. Initial program 90.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 58.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 58.3

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

   7. Applied egg-rr 58.3%

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

   if -1e-204 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.00000000000000005e54

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

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

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 51.6

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

   5. Simplified 51.6%

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. *-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. clear-num N/A

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

      13. un-div-inv N/A

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

      14. /-lowering-/.f64 N/A

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

      15. div-inv N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      17. metadata-eval 60.1

          \[\leadsto \frac{a}{c \cdot \color{blue}{-0.25}} \cdot t \]

   7. Applied egg-rr 60.1%

      \[\leadsto \color{blue}{\frac{a}{c \cdot -0.25} \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.1e-40)
   (* (/ (fma x (* y 9.0) (fma (* a t) (* z -4.0) b)) z) (/ 1.0 c))
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.1e-40) {
		tmp = (fma(x, (y * 9.0), fma((a * t), (z * -4.0), b)) / z) * (1.0 / c);
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.1e-40)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), fma(Float64(a * t), Float64(z * -4.0), b)) / z) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5.1e-40], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000037e-40

   1. Initial program 72.1%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

      3. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 92.4%

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

   if -5.10000000000000037e-40 < z

   1. Initial program 91.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+164}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ a (* c -0.25)))))
   (if (<= a -1.1e-50)
     t_1
     (if (<= a 2.05e+164) (/ (fma 9.0 (* x y) b) (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a / (c * -0.25));
	double tmp;
	if (a <= -1.1e-50) {
		tmp = t_1;
	} else if (a <= 2.05e+164) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a / Float64(c * -0.25)))
	tmp = 0.0
	if (a <= -1.1e-50)
		tmp = t_1;
	elseif (a <= 2.05e+164)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e-50], t$95$1, If[LessEqual[a, 2.05e+164], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e-50 or 2.05000000000000008e164 < a

   1. Initial program 88.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

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

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 52.5

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

   5. Simplified 52.5%

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

      1. times-frac N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. *-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-lowering-*.f64 N/A

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

      12. clear-num N/A

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

      13. un-div-inv N/A

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

      14. /-lowering-/.f64 N/A

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

      15. div-inv N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \frac{a}{\color{blue}{c \cdot \frac{1}{-4}}} \cdot t \]

      17. metadata-eval 60.4

          \[\leadsto \frac{a}{c \cdot \color{blue}{-0.25}} \cdot t \]

   7. Applied egg-rr 60.4%

      \[\leadsto \color{blue}{\frac{a}{c \cdot -0.25} \cdot t} \]

   if -1.0999999999999999e-50 < a < 2.05000000000000008e164

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 72.5

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

   5. Simplified 72.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+164}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{c \cdot -0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.6e+29)
   (/ (/ b z) c)
   (if (<= b 6e+103) (* -4.0 (/ (* a t) c)) (* b (/ 1.0 (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+29) {
		tmp = (b / z) / c;
	} else if (b <= 6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.6d+29)) then
        tmp = (b / z) / c
    else if (b <= 6d+103) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b * (1.0d0 / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+29) {
		tmp = (b / z) / c;
	} else if (b <= 6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.6e+29:
		tmp = (b / z) / c
	elif b <= 6e+103:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.6e+29)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 6e+103)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.6e+29)
		tmp = (b / z) / c;
	elseif (b <= 6e+103)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b * (1.0 / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.6e+29], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 6e+103], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6e29

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 59.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 60.5

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

   7. Applied egg-rr 60.5%

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

   if -2.6e29 < b < 6e103

   1. Initial program 84.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 55.1

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

   7. Simplified 55.1%

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

   if 6e103 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 68.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 68.4

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

   7. Applied egg-rr 68.4%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.45e+29)
   (/ b (* z c))
   (if (<= b 6.6e+103) (* -4.0 (/ (* a t) c)) (* b (/ 1.0 (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.45e+29) {
		tmp = b / (z * c);
	} else if (b <= 6.6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.45d+29)) then
        tmp = b / (z * c)
    else if (b <= 6.6d+103) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b * (1.0d0 / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.45e+29) {
		tmp = b / (z * c);
	} else if (b <= 6.6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.45e+29:
		tmp = b / (z * c)
	elif b <= 6.6e+103:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.45e+29)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 6.6e+103)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.45e+29)
		tmp = b / (z * c);
	elseif (b <= 6.6e+103)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b * (1.0 / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.45e+29], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+103], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.45e29

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 59.0%

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

   if -1.45e29 < b < 6.60000000000000017e103

   1. Initial program 84.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 55.1

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

   7. Simplified 55.1%

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

   if 6.60000000000000017e103 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 68.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 68.4

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

   7. Applied egg-rr 68.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -1.4e+19) t_1 (if (<= b 4.6e+103) (* -4.0 (/ (* a t) c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.4e+19) {
		tmp = t_1;
	} else if (b <= 4.6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b / (z * c)
    if (b <= (-1.4d+19)) then
        tmp = t_1
    else if (b <= 4.6d+103) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.4e+19) {
		tmp = t_1;
	} else if (b <= 4.6e+103) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -1.4e+19:
		tmp = t_1
	elif b <= 4.6e+103:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -1.4e+19)
		tmp = t_1;
	elseif (b <= 4.6e+103)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -1.4e+19)
		tmp = t_1;
	elseif (b <= 4.6e+103)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+19], t$95$1, If[LessEqual[b, 4.6e+103], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4e19 or 4.60000000000000017e103 < b

   1. Initial program 89.4%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 62.7%

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

   if -1.4e19 < b < 4.60000000000000017e103

   1. Initial program 84.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 55.1

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

   7. Simplified 55.1%

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

Alternative 16: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -1.7e+27) t_1 (if (<= b 5.8e+103) (* -4.0 (* a (/ t c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.7e+27) {
		tmp = t_1;
	} else if (b <= 5.8e+103) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b / (z * c)
    if (b <= (-1.7d+27)) then
        tmp = t_1
    else if (b <= 5.8d+103) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.7e+27) {
		tmp = t_1;
	} else if (b <= 5.8e+103) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -1.7e+27:
		tmp = t_1
	elif b <= 5.8e+103:
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -1.7e+27)
		tmp = t_1;
	elseif (b <= 5.8e+103)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -1.7e+27)
		tmp = t_1;
	elseif (b <= 5.8e+103)
		tmp = -4.0 * (a * (t / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+27], t$95$1, If[LessEqual[b, 5.8e+103], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e27 or 5.7999999999999997e103 < b

   1. Initial program 89.4%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 62.7%

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

   if -1.7e27 < b < 5.7999999999999997e103

   1. Initial program 84.8%

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

      1. div-inv N/A

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

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

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 55.1

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

   7. Simplified 55.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 51.6

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

   9. Applied egg-rr 51.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

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

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in b around inf

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

5. Simplified 36.0%

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

Developer Target 1: 80.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

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

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