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

Percentage Accurate: 78.9% → 89.8%

Time: 14.1s

Alternatives: 14

Speedup: 0.8×

• 37.5% 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: 78.9% 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: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-188} \lor \neg \left(z \leq 1.05 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.9e-188) (not (<= z 1.05e-90)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.9e-188) || !(z <= 1.05e-90)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.9e-188) || !(z <= 1.05e-90))
		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(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.9e-188], N[Not[LessEqual[z, 1.05e-90]], $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[(y * N[(x * 9.0), $MachinePrecision]), $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 < -3.89999999999999977e-188 or 1.05e-90 < z

   1. Initial program 72.0%

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

      1. associate-/r* 78.2%

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

   3. Simplified 90.6%

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

   if -3.89999999999999977e-188 < z < 1.05e-90

   1. Initial program 99.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-188} \lor \neg \left(z \leq 1.05 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 2: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 0.00021:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\frac{9 \cdot \left(x \cdot y\right)}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 0.00021)
   (* (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) (/ 1.0 c))
   (+ (/ (/ b c) z) (fma (/ a (/ c t)) -4.0 (/ (/ (* 9.0 (* x y)) z) c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 0.00021) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) * (1.0 / c);
	} else {
		tmp = ((b / c) / z) + fma((a / (c / t)), -4.0, (((9.0 * (x * y)) / z) / c));
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 0.00021)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(Float64(b / c) / z) + fma(Float64(a / Float64(c / t)), -4.0, Float64(Float64(Float64(9.0 * Float64(x * y)) / z) / c)));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 0.00021], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision] + N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.1000000000000001e-4

   1. Initial program 82.5%

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

      1. associate-/r* 86.3%

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

   3. Simplified 91.8%

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

      1. div-inv 91.7%

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

      2. +-commutative 91.7%

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

      3. fma-def 93.2%

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

   5. Applied egg-rr 93.2%

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

   if 2.1000000000000001e-4 < c

   1. Initial program 67.9%

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

      1. associate-*l* 67.9%

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

      2. associate-*l* 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in x around 0 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-/r* 82.4%

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

      3. cancel-sign-sub-inv 82.4%

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

      4. metadata-eval 82.4%

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

      5. +-commutative 82.4%

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

      6. *-commutative 82.4%

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

      7. fma-def 82.4%

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

      8. associate-/l* 85.7%

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

      9. associate-*r/ 85.6%

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

      10. associate-*r* 85.7%

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

      11. *-commutative 85.7%

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

      12. *-commutative 85.7%

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

      13. associate-/r* 84.1%

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

      14. *-commutative 84.1%

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

      15. associate-*r* 84.1%

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

   6. Simplified 84.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 0.00021:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\frac{9 \cdot \left(x \cdot y\right)}{z}}{c}\right)\\ \end{array} \]

Alternative 3: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.35e+112)
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (if (<= z 1.7e+99)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
     (/ (fma 9.0 (/ y (/ z x)) (* -4.0 (* t a))) c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.35e+112) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (z <= 1.7e+99) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = fma(9.0, (y / (z / x)), (-4.0 * (t * a))) / c;
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.35e+112)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (z <= 1.7e+99)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(fma(9.0, Float64(y / Float64(z / x)), Float64(-4.0 * Float64(t * a))) / c);
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.35e+112], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.7e+99], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e112

   1. Initial program 48.0%

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

      1. associate-/r* 55.3%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 82.0%

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

   if -1.3500000000000001e112 < z < 1.69999999999999992e99

   1. Initial program 93.9%

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

   if 1.69999999999999992e99 < z

   1. Initial program 55.2%

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

      1. associate-/r* 65.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in b around 0 76.7%

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

      1. fma-def 76.7%

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

      2. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \end{array} \]

Alternative 4: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+170}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z} + t_1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a 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+111)
     (/ (+ t_1 (/ b z)) c)
     (if (<= z 6e+170)
       (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* c z))
       (/ (+ (/ (* 9.0 (* x y)) z) t_1) c)))))

C

assert(t < a);
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+111) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 6e+170) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	} else {
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a 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+111)) then
        tmp = (t_1 + (b / z)) / c
    else if (z <= 6d+170) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (c * z)
    else
        tmp = (((9.0d0 * (x * y)) / z) + t_1) / c
    end if
    code = tmp
end function

Java

assert t < a;
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+111) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 6e+170) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	} else {
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -6e+111:
		tmp = (t_1 + (b / z)) / c
	elif z <= 6e+170:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z)
	else:
		tmp = (((9.0 * (x * y)) / z) + t_1) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -6e+111)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (z <= 6e+170)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(x * y)) / z) + t_1) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -6e+111)
		tmp = (t_1 + (b / z)) / c;
	elseif (z <= 6e+170)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c * z);
	else
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a 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+111], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6e+170], 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], N[(N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e111

   1. Initial program 48.0%

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

      1. associate-/r* 55.3%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 82.0%

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

   if -6e111 < z < 5.99999999999999994e170

   1. Initial program 92.8%

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

      1. associate-*l* 92.8%

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

      2. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   if 5.99999999999999994e170 < z

   1. Initial program 47.0%

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

      1. associate-/r* 56.5%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around inf 76.8%

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

      1. associate-*r/ 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+170}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 5: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z} + t_1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a 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 -4.8e+111)
     (/ (+ t_1 (/ b z)) c)
     (if (<= z 6.8e+100)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
       (/ (+ (/ (* 9.0 (* x y)) z) t_1) c)))))

C

assert(t < a);
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 <= -4.8e+111) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 6.8e+100) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 <= (-4.8d+111)) then
        tmp = (t_1 + (b / z)) / c
    else if (z <= 6.8d+100) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else
        tmp = (((9.0d0 * (x * y)) / z) + t_1) / c
    end if
    code = tmp
end function

Java

assert t < a;
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 <= -4.8e+111) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 6.8e+100) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -4.8e+111:
		tmp = (t_1 + (b / z)) / c
	elif z <= 6.8e+100:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	else:
		tmp = (((9.0 * (x * y)) / z) + t_1) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -4.8e+111)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (z <= 6.8e+100)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(x * y)) / z) + t_1) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -4.8e+111)
		tmp = (t_1 + (b / z)) / c;
	elseif (z <= 6.8e+100)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	else
		tmp = (((9.0 * (x * y)) / z) + t_1) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a 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, -4.8e+111], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.8e+100], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000011e111

   1. Initial program 48.0%

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

      1. associate-/r* 55.3%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 82.0%

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

   if -4.80000000000000011e111 < z < 6.79999999999999988e100

   1. Initial program 93.9%

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

   if 6.79999999999999988e100 < z

   1. Initial program 55.2%

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

      1. associate-/r* 65.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 76.7%

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

      1. associate-*r/ 76.7%

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

   6. Simplified 76.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+100}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 6: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-189}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.12e-125)
   (/ (* a (* t -4.0)) c)
   (if (<= a 1.4e-248)
     (/ (/ b z) c)
     (if (<= a 3.3e-189)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (<= a 4.8e+65) (* b (/ 1.0 (* c z))) (* -4.0 (* t (/ a c))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.12e-125) {
		tmp = (a * (t * -4.0)) / c;
	} else if (a <= 1.4e-248) {
		tmp = (b / z) / c;
	} else if (a <= 3.3e-189) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (a <= 4.8e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a 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 (a <= (-1.12d-125)) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (a <= 1.4d-248) then
        tmp = (b / z) / c
    else if (a <= 3.3d-189) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (a <= 4.8d+65) then
        tmp = b * (1.0d0 / (c * z))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.12e-125) {
		tmp = (a * (t * -4.0)) / c;
	} else if (a <= 1.4e-248) {
		tmp = (b / z) / c;
	} else if (a <= 3.3e-189) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (a <= 4.8e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.12e-125:
		tmp = (a * (t * -4.0)) / c
	elif a <= 1.4e-248:
		tmp = (b / z) / c
	elif a <= 3.3e-189:
		tmp = 9.0 * ((y / c) * (x / z))
	elif a <= 4.8e+65:
		tmp = b * (1.0 / (c * z))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.12e-125)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (a <= 1.4e-248)
		tmp = Float64(Float64(b / z) / c);
	elseif (a <= 3.3e-189)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (a <= 4.8e+65)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.12e-125)
		tmp = (a * (t * -4.0)) / c;
	elseif (a <= 1.4e-248)
		tmp = (b / z) / c;
	elseif (a <= 3.3e-189)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (a <= 4.8e+65)
		tmp = b * (1.0 / (c * z));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.12e-125], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 1.4e-248], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 3.3e-189], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+65], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.11999999999999997e-125

   1. Initial program 79.4%

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

      1. associate-/r* 82.8%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-*l* 56.8%

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

   6. Simplified 56.8%

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

   if -1.11999999999999997e-125 < a < 1.40000000000000005e-248

   1. Initial program 74.0%

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

      1. associate-*l* 74.0%

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

      2. associate-*l* 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in b around inf 56.5%

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

      1. associate-/r* 49.9%

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

   6. Simplified 49.9%

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

   7. Taylor expanded in b around 0 56.5%

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

      1. associate-/l/ 55.0%

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

   9. Simplified 55.0%

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

   if 1.40000000000000005e-248 < a < 3.3000000000000001e-189

   1. Initial program 76.5%

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

      1. associate-*l* 76.5%

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

      2. associate-*l* 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around inf 60.2%

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

      1. times-frac 59.2%

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

   6. Simplified 59.2%

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

   if 3.3000000000000001e-189 < a < 4.8000000000000003e65

   1. Initial program 87.5%

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

      1. associate-*l* 87.5%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in b around inf 55.4%

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

      1. div-inv 57.2%

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

      2. *-commutative 57.2%

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

   6. Applied egg-rr 57.2%

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

   if 4.8000000000000003e65 < a

   1. Initial program 76.2%

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

      1. associate-/r* 75.1%

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

   3. Simplified 84.8%

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

      1. div-inv 84.7%

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

      2. +-commutative 84.7%

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

      3. fma-def 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. associate-/l* 64.4%

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

      2. associate-/r/ 71.0%

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

   8. Simplified 71.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-189}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 7: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-69} \lor \neg \left(z \leq 6.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.1e-69) (not (<= z 6.8e-88)))
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* c z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.1e-69) || !(z <= 6.8e-88)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: t and a 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 <= (-2.1d-69)) .or. (.not. (z <= 6.8d-88))) 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 t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.1e-69) || !(z <= 6.8e-88)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.1e-69) or not (z <= 6.8e-88):
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.1e-69) || !(z <= 6.8e-88))
		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

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.1e-69) || ~((z <= 6.8e-88)))
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.1e-69], N[Not[LessEqual[z, 6.8e-88]], $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 < -2.1e-69 or 6.79999999999999949e-88 < z

   1. Initial program 69.6%

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

      1. associate-/r* 75.1%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 78.6%

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

   if -2.1e-69 < z < 6.79999999999999949e-88

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around inf 84.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-69} \lor \neg \left(z \leq 6.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.6e-92)
   (* (* a -4.0) (/ t c))
   (if (<= a 2e+76) (/ (+ b (* 9.0 (* x y))) (* c z)) (* -4.0 (* t (/ a c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.6e-92) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 2e+76) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a 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 (a <= (-1.6d-92)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (a <= 2d+76) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.6e-92) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 2e+76) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.6e-92:
		tmp = (a * -4.0) * (t / c)
	elif a <= 2e+76:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.6e-92)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (a <= 2e+76)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.6e-92)
		tmp = (a * -4.0) * (t / c);
	elseif (a <= 2e+76)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.6e-92], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+76], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5999999999999998e-92

   1. Initial program 80.6%

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

      1. associate-*l* 80.6%

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

      2. associate-*l* 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in z around inf 60.3%

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

      1. associate-/l* 56.0%

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

      2. associate-*r/ 56.0%

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

      3. *-commutative 56.0%

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

   6. Simplified 56.0%

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

      1. div-inv 56.0%

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

   8. Applied egg-rr 56.0%

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

   9. Taylor expanded in c around 0 57.4%

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

   if -1.5999999999999998e-92 < a < 2.0000000000000001e76

   1. Initial program 79.6%

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

      1. associate-*l* 79.6%

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

      2. associate-*l* 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in x around inf 71.9%

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

   if 2.0000000000000001e76 < a

   1. Initial program 77.1%

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

      1. associate-/r* 74.2%

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

   3. Simplified 84.3%

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

      1. div-inv 84.2%

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

      2. +-commutative 84.2%

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

      3. fma-def 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in t around inf 58.2%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 9: 50.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-125} \lor \neg \left(a \leq 1.65 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -3.9e-125) (not (<= a 1.65e+65)))
   (* -4.0 (* t (/ a c)))
   (/ b (* c z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.9e-125) || !(a <= 1.65e+65)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Fortran

NOTE: t and a 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 ((a <= (-3.9d-125)) .or. (.not. (a <= 1.65d+65))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.9e-125) || !(a <= 1.65e+65)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -3.9e-125) or not (a <= 1.65e+65):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (c * z)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -3.9e-125) || !(a <= 1.65e+65))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -3.9e-125) || ~((a <= 1.65e+65)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -3.9e-125], N[Not[LessEqual[a, 1.65e+65]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.89999999999999982e-125 or 1.65000000000000012e65 < a

   1. Initial program 78.2%

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

      1. associate-/r* 79.8%

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

   3. Simplified 87.7%

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

      1. div-inv 87.6%

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

      2. +-commutative 87.6%

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

      3. fma-def 89.7%

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

   5. Applied egg-rr 89.7%

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

   6. Taylor expanded in t around inf 56.7%

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

      1. associate-/l* 57.3%

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

      2. associate-/r/ 59.9%

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

   8. Simplified 59.9%

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

   if -3.89999999999999982e-125 < a < 1.65000000000000012e65

   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* 81.1%

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

      2. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in b around inf 52.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-125} \lor \neg \left(a \leq 1.65 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 10: 50.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125} \lor \neg \left(a \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -4.5e-125) (not (<= a 1.6e+65)))
   (* -4.0 (* t (/ a c)))
   (* b (/ 1.0 (* c z)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e-125) || !(a <= 1.6e+65)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * (1.0 / (c * z));
	}
	return tmp;
}

Fortran

NOTE: t and a 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 ((a <= (-4.5d-125)) .or. (.not. (a <= 1.6d+65))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b * (1.0d0 / (c * z))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.5e-125) || !(a <= 1.6e+65)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * (1.0 / (c * z));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -4.5e-125) or not (a <= 1.6e+65):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b * (1.0 / (c * z))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -4.5e-125) || !(a <= 1.6e+65))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -4.5e-125) || ~((a <= 1.6e+65)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b * (1.0 / (c * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -4.5e-125], N[Not[LessEqual[a, 1.6e+65]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.50000000000000012e-125 or 1.60000000000000003e65 < a

   1. Initial program 78.2%

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

      1. associate-/r* 79.8%

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

   3. Simplified 87.7%

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

      1. div-inv 87.6%

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

      2. +-commutative 87.6%

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

      3. fma-def 89.7%

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

   5. Applied egg-rr 89.7%

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

   6. Taylor expanded in t around inf 56.7%

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

      1. associate-/l* 57.3%

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

      2. associate-/r/ 59.9%

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

   8. Simplified 59.9%

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

   if -4.50000000000000012e-125 < a < 1.60000000000000003e65

   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* 81.1%

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

      2. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in b around inf 52.6%

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

      1. div-inv 53.5%

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

      2. *-commutative 53.5%

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

   6. Applied egg-rr 53.5%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125} \lor \neg \left(a \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \end{array} \]

Alternative 11: 50.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -4.5e-125)
   (* t (* a (/ -4.0 c)))
   (if (<= a 5e+65) (* b (/ 1.0 (* c z))) (* -4.0 (* t (/ a c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -4.5e-125) {
		tmp = t * (a * (-4.0 / c));
	} else if (a <= 5e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a 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 (a <= (-4.5d-125)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (a <= 5d+65) then
        tmp = b * (1.0d0 / (c * z))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -4.5e-125) {
		tmp = t * (a * (-4.0 / c));
	} else if (a <= 5e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -4.5e-125:
		tmp = t * (a * (-4.0 / c))
	elif a <= 5e+65:
		tmp = b * (1.0 / (c * z))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -4.5e-125)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (a <= 5e+65)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -4.5e-125)
		tmp = t * (a * (-4.0 / c));
	elseif (a <= 5e+65)
		tmp = b * (1.0 / (c * z));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -4.5e-125], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+65], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.50000000000000012e-125

   1. Initial program 79.4%

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

      1. associate-/r* 82.8%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around 0 79.9%

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

   5. Taylor expanded in b around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 71.6%

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

      3. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around inf 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*r* 56.8%

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

      3. associate-*r/ 54.2%

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

      4. *-lft-identity 54.2%

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

      5. *-commutative 54.2%

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

      6. associate-*r/ 54.1%

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

      7. *-commutative 54.1%

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

      8. *-commutative 54.1%

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

      9. associate-*r* 54.1%

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

      10. associate-*r* 54.3%

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

      11. associate-*r* 52.9%

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

      12. associate-*r/ 52.9%

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

      13. metadata-eval 52.9%

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

   10. Simplified 52.9%

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

   if -4.50000000000000012e-125 < a < 4.99999999999999973e65

   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* 81.1%

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

      2. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in b around inf 52.6%

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

      1. div-inv 53.5%

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

      2. *-commutative 53.5%

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

   6. Applied egg-rr 53.5%

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

   if 4.99999999999999973e65 < a

   1. Initial program 76.2%

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

      1. associate-/r* 75.1%

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

   3. Simplified 84.8%

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

      1. div-inv 84.7%

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

      2. +-commutative 84.7%

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

      3. fma-def 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. associate-/l* 64.4%

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

      2. associate-/r/ 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 12: 50.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -4.5e-125)
   (/ (* a (* t -4.0)) c)
   (if (<= a 2.8e+65) (* b (/ 1.0 (* c z))) (* -4.0 (* t (/ a c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -4.5e-125) {
		tmp = (a * (t * -4.0)) / c;
	} else if (a <= 2.8e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a 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 (a <= (-4.5d-125)) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (a <= 2.8d+65) then
        tmp = b * (1.0d0 / (c * z))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -4.5e-125) {
		tmp = (a * (t * -4.0)) / c;
	} else if (a <= 2.8e+65) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -4.5e-125:
		tmp = (a * (t * -4.0)) / c
	elif a <= 2.8e+65:
		tmp = b * (1.0 / (c * z))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -4.5e-125)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (a <= 2.8e+65)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -4.5e-125)
		tmp = (a * (t * -4.0)) / c;
	elseif (a <= 2.8e+65)
		tmp = b * (1.0 / (c * z));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -4.5e-125], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 2.8e+65], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.50000000000000012e-125

   1. Initial program 79.4%

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

      1. associate-/r* 82.8%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-*l* 56.8%

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

   6. Simplified 56.8%

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

   if -4.50000000000000012e-125 < a < 2.7999999999999999e65

   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* 81.1%

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

      2. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in b around inf 52.6%

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

      1. div-inv 53.5%

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

      2. *-commutative 53.5%

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

   6. Applied egg-rr 53.5%

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

   if 2.7999999999999999e65 < a

   1. Initial program 76.2%

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

      1. associate-/r* 75.1%

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

   3. Simplified 84.8%

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

      1. div-inv 84.7%

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

      2. +-commutative 84.7%

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

      3. fma-def 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. associate-/l* 64.4%

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

      2. associate-/r/ 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13: 34.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.58 \cdot 10^{+60}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 1.58e+60) (/ b (* c z)) (/ (/ b c) z)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 1.58e+60) {
		tmp = b / (c * z);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 <= 1.58d+60) then
        tmp = b / (c * z)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 1.58e+60) {
		tmp = b / (c * z);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= 1.58e+60:
		tmp = b / (c * z)
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= 1.58e+60)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= 1.58e+60)
		tmp = b / (c * z);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 1.58e+60], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.58e60

   1. Initial program 85.1%

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

      1. associate-*l* 85.1%

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

      2. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in b around inf 49.4%

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

   if 1.58e60 < z

   1. Initial program 58.9%

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

      1. associate-*l* 58.9%

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

      2. associate-*l* 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in b around inf 14.7%

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

      1. associate-/r* 29.7%

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

   6. Simplified 29.7%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.58 \cdot 10^{+60}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 34.4% accurate, 3.8× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: t and a 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 79.4%

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

   1. associate-*l* 79.4%

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

   2. associate-*l* 78.8%

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

3. Simplified 78.8%

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

4. Taylor expanded in b around inf 41.8%

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

5. Final simplification 41.8%

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

Developer target: 80.6% 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 2023195 
(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)))