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

Percentage Accurate: 79.4% → 91.4%

Time: 15.7s

Alternatives: 15

Speedup: 0.8×

• 37.2% 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: 79.4% 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: 91.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{b}{c \cdot z} + t_1\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+126}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (/ t (/ c a)) -4.0 (/ (* x 9.0) (* z (/ c y))))))
   (if (<= c -2.8e+144)
     (+ (/ b (* c z)) t_1)
     (if (<= c 1.02e+126)
       (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
       (+ t_1 (/ (/ b c) z))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t / (c / a)), -4.0, ((x * 9.0) / (z * (c / y))));
	double tmp;
	if (c <= -2.8e+144) {
		tmp = (b / (c * z)) + t_1;
	} else if (c <= 1.02e+126) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else {
		tmp = t_1 + ((b / c) / z);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(t / Float64(c / a)), -4.0, Float64(Float64(x * 9.0) / Float64(z * Float64(c / y))))
	tmp = 0.0
	if (c <= -2.8e+144)
		tmp = Float64(Float64(b / Float64(c * z)) + t_1);
	elseif (c <= 1.02e+126)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	else
		tmp = Float64(t_1 + Float64(Float64(b / c) / z));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+144], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 1.02e+126], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 + N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.80000000000000007e144

   1. Initial program 63.4%

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

      1. associate-*l* 63.4%

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

      2. associate-*l* 57.2%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in x around 0 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-/r* 66.3%

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

      3. cancel-sign-sub-inv 66.3%

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

      4. metadata-eval 66.3%

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

      5. +-commutative 66.3%

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

      6. *-commutative 66.3%

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

      7. fma-def 66.3%

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

      8. *-commutative 66.3%

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

      9. associate-/l* 74.6%

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

      10. associate-*r/ 74.6%

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

      11. *-commutative 74.6%

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

      12. times-frac 78.7%

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

      13. *-commutative 78.7%

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

      14. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. frac-times 82.7%

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

   8. Applied egg-rr 82.7%

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

   9. Taylor expanded in b around 0 87.0%

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

   if -2.80000000000000007e144 < c < 1.02e126

   1. Initial program 86.8%

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

      1. associate-/r* 90.1%

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

   3. Simplified 95.5%

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

   if 1.02e126 < c

   1. Initial program 62.3%

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

      1. associate-*l* 62.1%

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

      2. associate-*l* 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in x around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-/r* 65.9%

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

      3. cancel-sign-sub-inv 65.9%

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

      4. metadata-eval 65.9%

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

      5. +-commutative 65.9%

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

      6. *-commutative 65.9%

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

      7. fma-def 65.9%

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

      8. *-commutative 65.9%

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

      9. associate-/l* 76.7%

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

      10. associate-*r/ 76.7%

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

      11. *-commutative 76.7%

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

      12. times-frac 82.3%

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

      13. *-commutative 82.3%

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

      14. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

      1. frac-times 93.7%

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

   8. Applied egg-rr 93.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+144}:\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+126}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right) + \frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 2: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+141} \lor \neg \left(c \leq 8.8 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -7e+141) (not (<= c 8.8e+60)))
   (+ (/ b (* c z)) (fma (/ t (/ c a)) -4.0 (/ (* x 9.0) (* z (/ c y)))))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -7e+141) || !(c <= 8.8e+60)) {
		tmp = (b / (c * z)) + fma((t / (c / a)), -4.0, ((x * 9.0) / (z * (c / y))));
	} else {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -7e+141) || !(c <= 8.8e+60))
		tmp = Float64(Float64(b / Float64(c * z)) + fma(Float64(t / Float64(c / a)), -4.0, Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)))));
	else
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -7e+141], N[Not[LessEqual[c, 8.8e+60]], $MachinePrecision]], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.9999999999999999e141 or 8.79999999999999984e60 < c

   1. Initial program 64.0%

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

      1. associate-*l* 64.0%

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

      2. associate-*l* 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in x around 0 70.0%

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

      1. associate--l+ 70.0%

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

      2. associate-/r* 68.0%

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

      3. cancel-sign-sub-inv 68.0%

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

      4. metadata-eval 68.0%

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

      5. +-commutative 68.0%

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

      6. *-commutative 68.0%

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

      7. fma-def 68.0%

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

      8. *-commutative 68.0%

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

      9. associate-/l* 76.6%

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

      10. associate-*r/ 76.6%

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

      11. *-commutative 76.6%

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

      12. times-frac 80.9%

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

      13. *-commutative 80.9%

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

      14. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

      1. frac-times 87.4%

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

   8. Applied egg-rr 87.4%

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

   9. Taylor expanded in b around 0 89.2%

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

   if -6.9999999999999999e141 < c < 8.79999999999999984e60

   1. Initial program 87.4%

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

      1. associate-/r* 90.2%

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

   3. Simplified 94.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+141} \lor \neg \left(c \leq 8.8 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 3: 91.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{c \cdot z} + t_1\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (/ t (/ c a)) -4.0 (/ (* x 9.0) (* z (/ c y))))))
   (if (<= c -3.5e+139)
     (+ (/ b (* c z)) t_1)
     (if (<= c 8.4e+60)
       (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
       (+ t_1 (/ (/ b c) z))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t / (c / a)), -4.0, ((x * 9.0) / (z * (c / y))));
	double tmp;
	if (c <= -3.5e+139) {
		tmp = (b / (c * z)) + t_1;
	} else if (c <= 8.4e+60) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = t_1 + ((b / c) / z);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(t / Float64(c / a)), -4.0, Float64(Float64(x * 9.0) / Float64(z * Float64(c / y))))
	tmp = 0.0
	if (c <= -3.5e+139)
		tmp = Float64(Float64(b / Float64(c * z)) + t_1);
	elseif (c <= 8.4e+60)
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(t_1 + Float64(Float64(b / c) / z));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+139], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 8.4e+60], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 + N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.49999999999999978e139

   1. Initial program 63.4%

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

      1. associate-*l* 63.4%

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

      2. associate-*l* 57.2%

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

   3. Simplified 57.2%

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

   4. Taylor expanded in x around 0 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-/r* 66.3%

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

      3. cancel-sign-sub-inv 66.3%

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

      4. metadata-eval 66.3%

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

      5. +-commutative 66.3%

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

      6. *-commutative 66.3%

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

      7. fma-def 66.3%

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

      8. *-commutative 66.3%

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

      9. associate-/l* 74.6%

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

      10. associate-*r/ 74.6%

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

      11. *-commutative 74.6%

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

      12. times-frac 78.7%

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

      13. *-commutative 78.7%

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

      14. associate-/l* 84.8%

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

   6. Simplified 84.8%

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

      1. frac-times 82.7%

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

   8. Applied egg-rr 82.7%

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

   9. Taylor expanded in b around 0 87.0%

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

   if -3.49999999999999978e139 < c < 8.4000000000000004e60

   1. Initial program 87.4%

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

      1. associate-/r* 90.2%

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

   3. Simplified 94.1%

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

   if 8.4000000000000004e60 < c

   1. Initial program 64.7%

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

      1. associate-*l* 64.6%

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

      2. associate-*l* 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-/r* 69.9%

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

      3. cancel-sign-sub-inv 69.9%

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

      4. metadata-eval 69.9%

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

      5. +-commutative 69.9%

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

      6. *-commutative 69.9%

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

      7. fma-def 69.9%

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

      8. *-commutative 69.9%

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

      9. associate-/l* 78.7%

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

      10. associate-*r/ 78.7%

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

      11. *-commutative 78.7%

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

      12. times-frac 83.2%

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

      13. *-commutative 83.2%

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

      14. associate-/l* 90.2%

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

   6. Simplified 90.2%

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

      1. frac-times 92.5%

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

   8. Applied egg-rr 92.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right)\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\frac{c}{a}}, -4, \frac{x \cdot 9}{z \cdot \frac{c}{y}}\right) + \frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 4: 92.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6e+25) (not (<= z 1.45e-30)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* (* x 9.0) y) (* a (* t (* z 4.0))))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6e+25) || !(z <= 1.45e-30)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6e+25) || !(z <= 1.45e-30))
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6e+25], N[Not[LessEqual[z, 1.45e-30]], $MachinePrecision]], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000011e25 or 1.44999999999999995e-30 < z

   1. Initial program 67.3%

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

      1. associate-/r* 76.5%

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

   3. Simplified 90.3%

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

   if -6.00000000000000011e25 < z < 1.44999999999999995e-30

   1. Initial program 92.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 5: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+121} \lor \neg \left(z \leq 1.95 \cdot 10^{+178}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9.5e+121) (not (<= z 1.95e+178)))
   (/ (+ (* t (* a -4.0)) (* 9.0 (/ y (/ z x)))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.5e+121) || !(z <= 1.95e+178)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z <= (-9.5d+121)) .or. (.not. (z <= 1.95d+178))) then
        tmp = ((t * (a * (-4.0d0))) + (9.0d0 * (y / (z / x)))) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.5e+121) || !(z <= 1.95e+178)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9.5e+121) or not (z <= 1.95e+178):
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9.5e+121) || !(z <= 1.95e+178))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -9.5e+121) || ~((z <= 1.95e+178)))
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9.5e+121], N[Not[LessEqual[z, 1.95e+178]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999949e121 or 1.9499999999999999e178 < z

   1. Initial program 52.5%

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

      1. associate-/r* 64.3%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around inf 78.7%

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

      1. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   if -9.49999999999999949e121 < z < 1.9499999999999999e178

   1. Initial program 89.2%

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

      1. associate-*l* 89.2%

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

      2. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+121} \lor \neg \left(z \leq 1.95 \cdot 10^{+178}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 6: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+121} \lor \neg \left(z \leq 4.2 \cdot 10^{+133}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6e+121) (not (<= z 4.2e+133)))
   (/ (+ (* t (* a -4.0)) (* 9.0 (/ y (/ z x)))) c)
   (/ (+ b (- (* (* x 9.0) y) (* a (* t (* z 4.0))))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6e+121) || !(z <= 4.2e+133)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z <= (-6d+121)) .or. (.not. (z <= 4.2d+133))) then
        tmp = ((t * (a * (-4.0d0))) + (9.0d0 * (y / (z / x)))) / c
    else
        tmp = (b + (((x * 9.0d0) * y) - (a * (t * (z * 4.0d0))))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6e+121) || !(z <= 4.2e+133)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -6e+121) or not (z <= 4.2e+133):
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c
	else:
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6e+121) || !(z <= 4.2e+133))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -6e+121) || ~((z <= 4.2e+133)))
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	else
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6e+121], N[Not[LessEqual[z, 4.2e+133]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000005e121 or 4.2e133 < z

   1. Initial program 57.1%

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

      1. associate-/r* 68.1%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 78.8%

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

      1. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   if -6.0000000000000005e121 < z < 4.2e133

   1. Initial program 90.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+121} \lor \neg \left(z \leq 4.2 \cdot 10^{+133}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 7: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= y -3.15e-38)
     t_1
     (if (<= y 2.1e-144)
       (* -4.0 (/ a (/ c t)))
       (if (<= y 3e-84)
         (/ (/ b z) c)
         (if (<= y 3.5e+92) (* -4.0 (* t (/ a c))) t_1))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -3.15e-38) {
		tmp = t_1;
	} else if (y <= 2.1e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3e-84) {
		tmp = (b / z) / c;
	} else if (y <= 3.5e+92) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 = 9.0d0 * ((y / c) * (x / z))
    if (y <= (-3.15d-38)) then
        tmp = t_1
    else if (y <= 2.1d-144) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (y <= 3d-84) then
        tmp = (b / z) / c
    else if (y <= 3.5d+92) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -3.15e-38) {
		tmp = t_1;
	} else if (y <= 2.1e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3e-84) {
		tmp = (b / z) / c;
	} else if (y <= 3.5e+92) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if y <= -3.15e-38:
		tmp = t_1
	elif y <= 2.1e-144:
		tmp = -4.0 * (a / (c / t))
	elif y <= 3e-84:
		tmp = (b / z) / c
	elif y <= 3.5e+92:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (y <= -3.15e-38)
		tmp = t_1;
	elseif (y <= 2.1e-144)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (y <= 3e-84)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 3.5e+92)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (y <= -3.15e-38)
		tmp = t_1;
	elseif (y <= 2.1e-144)
		tmp = -4.0 * (a / (c / t));
	elseif (y <= 3e-84)
		tmp = (b / z) / c;
	elseif (y <= 3.5e+92)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e-38], t$95$1, If[LessEqual[y, 2.1e-144], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-84], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 3.5e+92], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1499999999999998e-38 or 3.49999999999999986e92 < y

   1. Initial program 74.8%

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

      1. associate-*l* 73.9%

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

      2. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in x around inf 43.4%

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

      1. expm1-log1p-u 24.3%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 22.5%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 28.0%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 28.0%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 34.7%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 56.8%

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

   8. Simplified 56.8%

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

   if -3.1499999999999998e-38 < y < 2.1000000000000001e-144

   1. Initial program 87.0%

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

      1. associate-*l* 87.0%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 51.2%

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

   6. Simplified 51.2%

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

   if 2.1000000000000001e-144 < y < 3.0000000000000001e-84

   1. Initial program 88.0%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in b around inf 61.5%

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

   if 3.0000000000000001e-84 < y < 3.49999999999999986e92

   1. Initial program 73.3%

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

      1. associate-/r* 75.7%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in x around 0 77.7%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

      3. *-commutative 77.7%

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

   6. Simplified 77.7%

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

   7. Taylor expanded in b around 0 53.5%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 53.2%

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

   9. Simplified 53.2%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 8: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+116}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c \cdot z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.15e-38)
   (* 9.0 (* (/ y c) (/ x z)))
   (if (<= y 8.5e-144)
     (* -4.0 (/ a (/ c t)))
     (if (<= y 5e-86)
       (/ (/ b z) c)
       (if (<= y 2.9e+116)
         (* -4.0 (* t (/ a c)))
         (* 9.0 (/ y (/ (* c z) x))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 8.5e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 5e-86) {
		tmp = (b / z) / c;
	} else if (y <= 2.9e+116) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / ((c * z) / x));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (y <= (-3.15d-38)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (y <= 8.5d-144) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (y <= 5d-86) then
        tmp = (b / z) / c
    else if (y <= 2.9d+116) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = 9.0d0 * (y / ((c * z) / x))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 8.5e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 5e-86) {
		tmp = (b / z) / c;
	} else if (y <= 2.9e+116) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / ((c * z) / x));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.15e-38:
		tmp = 9.0 * ((y / c) * (x / z))
	elif y <= 8.5e-144:
		tmp = -4.0 * (a / (c / t))
	elif y <= 5e-86:
		tmp = (b / z) / c
	elif y <= 2.9e+116:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = 9.0 * (y / ((c * z) / x))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.15e-38)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (y <= 8.5e-144)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (y <= 5e-86)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 2.9e+116)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(9.0 * Float64(y / Float64(Float64(c * z) / x)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.15e-38)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (y <= 8.5e-144)
		tmp = -4.0 * (a / (c / t));
	elseif (y <= 5e-86)
		tmp = (b / z) / c;
	elseif (y <= 2.9e+116)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = 9.0 * (y / ((c * z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.15e-38], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-144], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-86], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 2.9e+116], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y / N[(N[(c * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1499999999999998e-38

   1. Initial program 79.0%

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

      1. associate-*l* 79.0%

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

      2. associate-*l* 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in x around inf 46.1%

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

      1. expm1-log1p-u 21.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 20.1%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 21.6%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 21.6%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 26.3%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 54.9%

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

   8. Simplified 54.9%

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

   if -3.1499999999999998e-38 < y < 8.49999999999999958e-144

   1. Initial program 87.2%

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

      1. associate-*l* 87.1%

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

      2. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 50.7%

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

   6. Simplified 50.7%

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

   if 8.49999999999999958e-144 < y < 4.9999999999999999e-86

   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. Step-by-step derivation

      1. associate-/r* 78.5%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. associate-*r* 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

   6. Simplified 79.3%

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

   7. Taylor expanded in b around inf 57.2%

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

   if 4.9999999999999999e-86 < y < 2.9000000000000001e116

   1. Initial program 73.4%

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

      1. associate-/r* 73.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in b around 0 49.3%

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

      1. associate-/l* 49.4%

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

      2. associate-/r/ 51.0%

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

   9. Simplified 51.0%

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

   if 2.9000000000000001e116 < y

   1. Initial program 68.4%

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

      1. associate-*l* 66.0%

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

      2. associate-*l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in x around inf 38.6%

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

      1. expm1-log1p-u 28.2%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 26.0%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 37.8%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 37.8%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 46.2%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 58.0%

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

   8. Simplified 58.0%

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

      1. frac-times 38.6%

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

      2. associate-/l* 56.2%

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

   10. Applied egg-rr 56.2%

       \[\leadsto 9 \cdot \color{blue}{\frac{y}{\frac{c \cdot z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+116}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c \cdot z}{x}}\\ \end{array} \]

Alternative 9: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.15e-38)
   (* 9.0 (* (/ y c) (/ x z)))
   (if (<= y 2.1e-144)
     (* -4.0 (/ a (/ c t)))
     (if (<= y 3.05e-83)
       (/ (/ b z) c)
       (if (<= y 4.6e+117)
         (* -4.0 (* t (/ a c)))
         (* (/ x (/ c y)) (/ 9.0 z)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 2.1e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3.05e-83) {
		tmp = (b / z) / c;
	} else if (y <= 4.6e+117) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (x / (c / y)) * (9.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (y <= (-3.15d-38)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (y <= 2.1d-144) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (y <= 3.05d-83) then
        tmp = (b / z) / c
    else if (y <= 4.6d+117) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (x / (c / y)) * (9.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 2.1e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3.05e-83) {
		tmp = (b / z) / c;
	} else if (y <= 4.6e+117) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (x / (c / y)) * (9.0 / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.15e-38:
		tmp = 9.0 * ((y / c) * (x / z))
	elif y <= 2.1e-144:
		tmp = -4.0 * (a / (c / t))
	elif y <= 3.05e-83:
		tmp = (b / z) / c
	elif y <= 4.6e+117:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (x / (c / y)) * (9.0 / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.15e-38)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (y <= 2.1e-144)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (y <= 3.05e-83)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 4.6e+117)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(x / Float64(c / y)) * Float64(9.0 / z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.15e-38)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (y <= 2.1e-144)
		tmp = -4.0 * (a / (c / t));
	elseif (y <= 3.05e-83)
		tmp = (b / z) / c;
	elseif (y <= 4.6e+117)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (x / (c / y)) * (9.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.15e-38], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-144], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-83], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 4.6e+117], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1499999999999998e-38

   1. Initial program 79.0%

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

      1. associate-*l* 79.0%

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

      2. associate-*l* 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in x around inf 46.1%

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

      1. expm1-log1p-u 21.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 20.1%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 21.6%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 21.6%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 26.3%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 54.9%

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

   8. Simplified 54.9%

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

   if -3.1499999999999998e-38 < y < 2.1000000000000001e-144

   1. Initial program 87.0%

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

      1. associate-*l* 87.0%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 51.2%

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

   6. Simplified 51.2%

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

   if 2.1000000000000001e-144 < y < 3.05000000000000001e-83

   1. Initial program 88.0%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in b around inf 61.5%

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

   if 3.05000000000000001e-83 < y < 4.59999999999999976e117

   1. Initial program 73.4%

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

      1. associate-/r* 73.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in b around 0 49.3%

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

      1. associate-/l* 49.4%

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

      2. associate-/r/ 51.0%

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

   9. Simplified 51.0%

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

   if 4.59999999999999976e117 < y

   1. Initial program 68.4%

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

      1. associate-*l* 66.0%

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

      2. associate-*l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in x around inf 38.6%

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

      1. associate-*r/ 38.5%

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

      2. *-commutative 38.5%

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

      3. times-frac 44.9%

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

      4. *-commutative 44.9%

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

      5. associate-/l* 60.3%

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

   6. Simplified 60.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \end{array} \]

Alternative 10: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+116}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.15e-38)
   (* 9.0 (* (/ y c) (/ x z)))
   (if (<= y 1.2e-144)
     (* -4.0 (/ a (/ c t)))
     (if (<= y 3.05e-83)
       (/ (/ b z) c)
       (if (<= y 2.4e+116)
         (* -4.0 (* t (/ a c)))
         (/ (* x (/ (* 9.0 y) c)) z))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 1.2e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3.05e-83) {
		tmp = (b / z) / c;
	} else if (y <= 2.4e+116) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (x * ((9.0 * y) / c)) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (y <= (-3.15d-38)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (y <= 1.2d-144) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (y <= 3.05d-83) then
        tmp = (b / z) / c
    else if (y <= 2.4d+116) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (x * ((9.0d0 * y) / c)) / z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.15e-38) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 1.2e-144) {
		tmp = -4.0 * (a / (c / t));
	} else if (y <= 3.05e-83) {
		tmp = (b / z) / c;
	} else if (y <= 2.4e+116) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (x * ((9.0 * y) / c)) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.15e-38:
		tmp = 9.0 * ((y / c) * (x / z))
	elif y <= 1.2e-144:
		tmp = -4.0 * (a / (c / t))
	elif y <= 3.05e-83:
		tmp = (b / z) / c
	elif y <= 2.4e+116:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (x * ((9.0 * y) / c)) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.15e-38)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (y <= 1.2e-144)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (y <= 3.05e-83)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 2.4e+116)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(9.0 * y) / c)) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.15e-38)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (y <= 1.2e-144)
		tmp = -4.0 * (a / (c / t));
	elseif (y <= 3.05e-83)
		tmp = (b / z) / c;
	elseif (y <= 2.4e+116)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (x * ((9.0 * y) / c)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.15e-38], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-144], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-83], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 2.4e+116], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1499999999999998e-38

   1. Initial program 79.0%

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

      1. associate-*l* 79.0%

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

      2. associate-*l* 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in x around inf 46.1%

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

      1. expm1-log1p-u 21.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 20.1%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 21.6%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 21.6%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 26.3%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 54.9%

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

   8. Simplified 54.9%

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

   if -3.1499999999999998e-38 < y < 1.19999999999999997e-144

   1. Initial program 87.0%

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

      1. associate-*l* 87.0%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 51.2%

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

   6. Simplified 51.2%

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

   if 1.19999999999999997e-144 < y < 3.05000000000000001e-83

   1. Initial program 88.0%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in b around inf 61.5%

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

   if 3.05000000000000001e-83 < y < 2.4e116

   1. Initial program 73.4%

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

      1. associate-/r* 73.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in b around 0 49.3%

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

      1. associate-/l* 49.4%

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

      2. associate-/r/ 51.0%

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

   9. Simplified 51.0%

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

   if 2.4e116 < y

   1. Initial program 68.4%

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

      1. associate-*l* 66.0%

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

      2. associate-*l* 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in x around inf 38.6%

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

      1. expm1-log1p-u 28.2%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)\right)} \]

      2. expm1-udef 26.0%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot x}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 37.8%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{c} \cdot \frac{x}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 37.8%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 46.2%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c} \cdot \frac{x}{z}\right)\right)} \]

      2. expm1-log1p 58.0%

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

   8. Simplified 58.0%

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

      1. associate-*r* 58.0%

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

      2. associate-*r/ 60.2%

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

      3. associate-*r/ 60.3%

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

   10. Applied egg-rr 60.3%

       \[\leadsto \color{blue}{\frac{\frac{9 \cdot y}{c} \cdot x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-38}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-144}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+116}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y}{c}}{z}\\ \end{array} \]

Alternative 11: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{-6} \lor \neg \left(z \leq 2.85 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.25e-6) (not (<= z 2.85e-27)))
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.25e-6) || !(z <= 2.85e-27)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((z <= (-3.25d-6)) .or. (.not. (z <= 2.85d-27))) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.25e-6) || !(z <= 2.85e-27)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.25e-6) or not (z <= 2.85e-27):
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.25e-6) || !(z <= 2.85e-27))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.25e-6) || ~((z <= 2.85e-27)))
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.25e-6], N[Not[LessEqual[z, 2.85e-27]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2499999999999998e-6 or 2.8499999999999998e-27 < z

   1. Initial program 69.2%

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

      1. associate-/r* 77.8%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 78.7%

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

      1. associate-*r* 78.7%

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

      2. *-commutative 78.7%

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

      3. *-commutative 78.7%

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

   6. Simplified 78.7%

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

   if -3.2499999999999998e-6 < z < 2.8499999999999998e-27

   1. Initial program 91.8%

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

      1. associate-*l* 91.8%

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

      2. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around 0 77.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{-6} \lor \neg \left(z \leq 2.85 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]

Alternative 12: 68.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+105}:\\ \;\;\;\;t_1 \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 -4.0))))
   (if (<= z -6e+105)
     (* t_1 (/ 1.0 c))
     (if (<= z 1.55e+23) (/ (+ b (* 9.0 (* x y))) (* c z)) (/ t_1 c)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -6e+105) {
		tmp = t_1 * (1.0 / c);
	} else if (z <= 1.55e+23) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = t_1 / c;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 = t * (a * (-4.0d0))
    if (z <= (-6d+105)) then
        tmp = t_1 * (1.0d0 / c)
    else if (z <= 1.55d+23) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = t_1 / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -6e+105) {
		tmp = t_1 * (1.0 / c);
	} else if (z <= 1.55e+23) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = t_1 / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -6e+105:
		tmp = t_1 * (1.0 / c)
	elif z <= 1.55e+23:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = t_1 / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -6e+105)
		tmp = Float64(t_1 * Float64(1.0 / c));
	elseif (z <= 1.55e+23)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(t_1 / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -6e+105)
		tmp = t_1 * (1.0 / c);
	elseif (z <= 1.55e+23)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = t_1 / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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 * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+105], N[(t$95$1 * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+23], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000001e105

   1. Initial program 57.3%

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

      1. associate-/r* 67.7%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

      3. *-commutative 67.7%

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

   6. Simplified 67.7%

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

      1. div-inv 67.7%

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

   8. Applied egg-rr 67.7%

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

   if -6.0000000000000001e105 < z < 1.54999999999999985e23

   1. Initial program 91.7%

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

      1. associate-*l* 91.6%

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

      2. associate-*l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in z around 0 73.3%

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

   if 1.54999999999999985e23 < z

   1. Initial program 66.7%

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

      1. associate-/r* 77.0%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around inf 62.5%

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

      1. associate-*r* 62.5%

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

      2. *-commutative 62.5%

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

      3. *-commutative 62.5%

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

   6. Simplified 62.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+105}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 13: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.2e+137)
   (/ b (* c z))
   (if (<= b 2.1e+82) (* -4.0 (* t (/ a c))) (/ (/ b z) c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+137) {
		tmp = b / (c * z);
	} else if (b <= 2.1e+82) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.2d+137)) then
        tmp = b / (c * z)
    else if (b <= 2.1d+82) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+137) {
		tmp = b / (c * z);
	} else if (b <= 2.1e+82) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.2e+137:
		tmp = b / (c * z)
	elif b <= 2.1e+82:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / z) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.2e+137)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= 2.1e+82)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.2e+137)
		tmp = b / (c * z);
	elseif (b <= 2.1e+82)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.2e+137], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+82], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999992e137

   1. Initial program 81.1%

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

      1. associate-*l* 81.2%

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

      2. associate-*l* 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in b around inf 58.5%

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

   if -1.19999999999999992e137 < b < 2.1e82

   1. Initial program 78.0%

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

      1. associate-/r* 77.1%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around 0 57.7%

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

      1. associate-*r* 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   7. Taylor expanded in b around 0 46.0%

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

      1. associate-/l* 47.3%

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

      2. associate-/r/ 50.0%

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

   9. Simplified 50.0%

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

   if 2.1e82 < b

   1. Initial program 84.5%

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

      1. associate-/r* 87.1%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 84.5%

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

      1. associate-*r* 84.5%

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

      2. *-commutative 84.5%

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

      3. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in b around inf 64.8%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14: 50.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.2e+137)
   (/ b (* c z))
   (if (<= b 3.5e+80) (* -4.0 (* t (/ a c))) (/ (/ 1.0 z) (/ c b)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+137) {
		tmp = b / (c * z);
	} else if (b <= 3.5e+80) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1.2d+137)) then
        tmp = b / (c * z)
    else if (b <= 3.5d+80) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (1.0d0 / z) / (c / b)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.2e+137) {
		tmp = b / (c * z);
	} else if (b <= 3.5e+80) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.2e+137:
		tmp = b / (c * z)
	elif b <= 3.5e+80:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (1.0 / z) / (c / b)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.2e+137)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= 3.5e+80)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.2e+137)
		tmp = b / (c * z);
	elseif (b <= 3.5e+80)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (1.0 / z) / (c / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.2e+137], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+80], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999992e137

   1. Initial program 81.1%

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

      1. associate-*l* 81.2%

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

      2. associate-*l* 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in b around inf 58.5%

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

   if -1.19999999999999992e137 < b < 3.49999999999999994e80

   1. Initial program 78.0%

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

      1. associate-/r* 77.1%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around 0 57.7%

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

      1. associate-*r* 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   7. Taylor expanded in b around 0 46.0%

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

      1. associate-/l* 47.3%

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

      2. associate-/r/ 50.0%

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

   9. Simplified 50.0%

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

   if 3.49999999999999994e80 < b

   1. Initial program 84.5%

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

      1. associate-*l* 84.5%

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

      2. associate-*l* 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 63.3%

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

      1. associate-/r* 63.4%

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

   6. Simplified 63.4%

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

      1. associate-/r* 63.3%

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

      2. div-inv 63.2%

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

   8. Applied egg-rr 63.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 63.3%

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

      2. frac-times 63.5%

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

      3. *-commutative 63.5%

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

      4. clear-num 63.4%

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

      5. un-div-inv 65.9%

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

   10. Applied egg-rr 65.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+80}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]

Alternative 15: 35.9% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

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

Fortran

NOTE: x and y 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 / (c * z)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

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

Derivation

1. Initial program 79.5%

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

   1. associate-*l* 79.0%

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

   2. associate-*l* 77.5%

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

3. Simplified 77.5%

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

4. Taylor expanded in b around inf 31.0%

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

5. Final simplification 31.0%

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

Developer target: 81.2% accurate, 0.2× 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 2023214 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

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