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

Percentage Accurate: 79.3% → 88.5%

Time: 17.2s

Alternatives: 13

Speedup: 0.8×

• 38.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.3% 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: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+48} \lor \neg \left(c \leq 2.2 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= c -3.7e+48) (not (<= c 2.2e-49)))
   (fma (/ a (/ c t)) -4.0 (fma 9.0 (* (/ x c) (/ y z)) (/ b (* c z))))
   (/ (+ (* x (* 9.0 y)) (- b (* (* z 4.0) (* a t)))) (* 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 ((c <= -3.7e+48) || !(c <= 2.2e-49)) {
		tmp = fma((a / (c / t)), -4.0, fma(9.0, ((x / c) * (y / z)), (b / (c * z))));
	} else {
		tmp = ((x * (9.0 * y)) + (b - ((z * 4.0) * (a * t)))) / (c * z);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -3.7e+48) || !(c <= 2.2e-49))
		tmp = fma(Float64(a / Float64(c / t)), -4.0, fma(9.0, Float64(Float64(x / c) * Float64(y / z)), Float64(b / Float64(c * z))));
	else
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + Float64(b - Float64(Float64(z * 4.0) * Float64(a * t)))) / 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[c, -3.7e+48], N[Not[LessEqual[c, 2.2e-49]], $MachinePrecision]], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(b - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.6999999999999999e48 or 2.1999999999999999e-49 < c

   1. Initial program 69.0%

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

   2. Taylor expanded in x around 0 80.6%

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

      1. cancel-sign-sub-inv 80.6%

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

      2. metadata-eval 80.6%

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

      3. +-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. fma-def 80.6%

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

      6. associate-/l* 83.1%

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

      7. fma-def 83.1%

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

      8. times-frac 88.0%

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

      9. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   if -3.6999999999999999e48 < c < 2.1999999999999999e-49

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. associate-*l* 96.1%

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

      3. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+48} \lor \neg \left(c \leq 2.2 \cdot 10^{-49}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-310}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c z))))
   (if (<= t_1 -4e-310)
     t_1
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (* a t)) (/ b z)) c)
       (if (<= t_1 INFINITY) t_1 (* (/ a (/ c t)) -4.0))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -4e-310) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

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 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -4e-310) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z)
	tmp = 0
	if t_1 <= -4e-310:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a / (c / t)) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -4e-310)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	tmp = 0.0;
	if (t_1 <= -4e-310)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a / (c / t)) * -4.0;
	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[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-310], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -3.999999999999988e-310 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 91.7%

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

   if -3.999999999999988e-310 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 36.6%

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

      1. associate-/r* 99.4%

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

      2. associate-+l- 99.4%

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

      3. associate-*r* 99.5%

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

      4. associate-*r* 99.6%

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

      5. div-inv 99.6%

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

      6. associate--r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. associate-*l* 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in x around 0 91.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 8.0%

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

      1. add-cube-cbrt 8.0%

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

      2. times-frac 16.6%

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

      3. pow2 16.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 16.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 16.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 16.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 48.8%

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

      1. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 3: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c z))))
   (if (<= t_1 -4e-310)
     (/ (+ (* x (* 9.0 y)) (- b (* (* z 4.0) (* a t)))) (* c z))
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (* a t)) (/ b z)) c)
       (if (<= t_1 INFINITY) t_1 (* (/ a (/ c t)) -4.0))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -4e-310) {
		tmp = ((x * (9.0 * y)) + (b - ((z * 4.0) * (a * t)))) / (c * z);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

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 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -4e-310) {
		tmp = ((x * (9.0 * y)) + (b - ((z * 4.0) * (a * t)))) / (c * z);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z)
	tmp = 0
	if t_1 <= -4e-310:
		tmp = ((x * (9.0 * y)) + (b - ((z * 4.0) * (a * t)))) / (c * z)
	elif t_1 <= 0.0:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a / (c / t)) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -4e-310)
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + Float64(b - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(c * z));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	tmp = 0.0;
	if (t_1 <= -4e-310)
		tmp = ((x * (9.0 * y)) + (b - ((z * 4.0) * (a * t)))) / (c * z);
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a / (c / t)) * -4.0;
	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[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-310], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(b - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -3.999999999999988e-310

   1. Initial program 93.2%

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

      1. associate-+l- 93.2%

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

      2. associate-*l* 93.2%

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

      3. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   if -3.999999999999988e-310 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 36.6%

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

      1. associate-/r* 99.4%

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

      2. associate-+l- 99.4%

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

      3. associate-*r* 99.5%

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

      4. associate-*r* 99.6%

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

      5. div-inv 99.6%

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

      6. associate--r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. associate-*l* 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in x around 0 91.2%

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

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

   1. Initial program 90.1%

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

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

   1. Initial program 0.0%

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

   3. Simplified 8.0%

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

      1. add-cube-cbrt 8.0%

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

      2. times-frac 16.6%

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

      3. pow2 16.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 16.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 16.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 16.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 48.8%

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

      1. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 4: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+51} \lor \neg \left(z \leq 3.2 \cdot 10^{-99}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 -1.9e+51) (not (<= z 3.2e-99)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (+ b (- (* y (* 9.0 x)) (* 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 <= -1.9e+51) || !(z <= 3.2e-99)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 ((z <= (-1.9d+51)) .or. (.not. (z <= 3.2d-99))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) * (1.0d0 / c)
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (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 ((z <= -1.9e+51) || !(z <= 3.2e-99)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.9e+51) or not (z <= 3.2e-99):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c)
	else:
		tmp = (b + ((y * (9.0 * x)) - (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 <= -1.9e+51) || !(z <= 3.2e-99))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / 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 ((z <= -1.9e+51) || ~((z <= 3.2e-99)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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[z, -1.9e+51], N[Not[LessEqual[z, 3.2e-99]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $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 < -1.8999999999999999e51 or 3.2000000000000001e-99 < z

   1. Initial program 66.0%

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

      1. associate-/r* 76.6%

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

      2. associate-+l- 76.6%

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

      3. associate-*r* 76.6%

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

      4. associate-*r* 80.5%

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

      5. div-inv 80.5%

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

      6. associate--r- 80.5%

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

      7. fma-neg 80.6%

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

      8. associate-*r* 76.8%

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

      9. distribute-rgt-neg-in 76.8%

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

      10. associate-*l* 76.8%

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

   3. Applied egg-rr 76.8%

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

   4. Taylor expanded in x around 0 87.3%

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

   if -1.8999999999999999e51 < z < 3.2000000000000001e-99

   1. Initial program 97.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+51} \lor \neg \left(z \leq 3.2 \cdot 10^{-99}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 5: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := b + x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{t_2}{c}}{z}\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -112000000000:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{c \cdot z}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a t))) (t_2 (+ b (* x (* 9.0 y)))))
   (if (<= b -1e+66)
     (/ (/ t_2 c) z)
     (if (<= b -8.6e+20)
       (/ (+ t_1 (/ b z)) c)
       (if (<= b -112000000000.0)
         (* 9.0 (/ (* x y) (* c z)))
         (if (<= b 3.1e+127)
           (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
           (/ t_2 (* c z))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double t_2 = b + (x * (9.0 * y));
	double tmp;
	if (b <= -1e+66) {
		tmp = (t_2 / c) / z;
	} else if (b <= -8.6e+20) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -112000000000.0) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (b <= 3.1e+127) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = t_2 / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    t_2 = b + (x * (9.0d0 * y))
    if (b <= (-1d+66)) then
        tmp = (t_2 / c) / z
    else if (b <= (-8.6d+20)) then
        tmp = (t_1 + (b / z)) / c
    else if (b <= (-112000000000.0d0)) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (b <= 3.1d+127) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = t_2 / (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 t_1 = -4.0 * (a * t);
	double t_2 = b + (x * (9.0 * y));
	double tmp;
	if (b <= -1e+66) {
		tmp = (t_2 / c) / z;
	} else if (b <= -8.6e+20) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= -112000000000.0) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (b <= 3.1e+127) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = t_2 / (c * z);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	t_2 = b + (x * (9.0 * y))
	tmp = 0
	if b <= -1e+66:
		tmp = (t_2 / c) / z
	elif b <= -8.6e+20:
		tmp = (t_1 + (b / z)) / c
	elif b <= -112000000000.0:
		tmp = 9.0 * ((x * y) / (c * z))
	elif b <= 3.1e+127:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = t_2 / (c * z)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	t_2 = Float64(b + Float64(x * Float64(9.0 * y)))
	tmp = 0.0
	if (b <= -1e+66)
		tmp = Float64(Float64(t_2 / c) / z);
	elseif (b <= -8.6e+20)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (b <= -112000000000.0)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (b <= 3.1e+127)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(t_2 / 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)
	t_1 = -4.0 * (a * t);
	t_2 = b + (x * (9.0 * y));
	tmp = 0.0;
	if (b <= -1e+66)
		tmp = (t_2 / c) / z;
	elseif (b <= -8.6e+20)
		tmp = (t_1 + (b / z)) / c;
	elseif (b <= -112000000000.0)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (b <= 3.1e+127)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = t_2 / (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_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+66], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -8.6e+20], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, -112000000000.0], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+127], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(t$95$2 / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.99999999999999945e65

   1. Initial program 87.4%

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

   3. Simplified 89.2%

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

      1. add-cube-cbrt 88.4%

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

      2. times-frac 87.0%

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

      3. pow2 87.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 87.0%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 87.0%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around 0 77.7%

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

      1. associate-/r* 78.8%

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

      2. associate-*r* 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*r* 78.8%

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

      5. *-commutative 78.8%

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

   8. Simplified 78.8%

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

   if -9.99999999999999945e65 < b < -8.6e20

   1. Initial program 63.6%

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

      1. associate-/r* 81.6%

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

      2. associate-+l- 81.6%

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

      3. associate-*r* 81.6%

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

      4. associate-*r* 81.6%

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

      5. div-inv 81.3%

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

      6. associate--r- 81.3%

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

      7. fma-neg 81.6%

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

      8. associate-*r* 81.6%

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

      9. distribute-rgt-neg-in 81.6%

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

      10. associate-*l* 81.6%

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

   3. Applied egg-rr 81.6%

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

   4. Taylor expanded in x around 0 81.4%

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

   5. Taylor expanded in x around 0 81.8%

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

   if -8.6e20 < b < -1.12e11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -1.12e11 < b < 3.1000000000000002e127

   1. Initial program 81.5%

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

      1. associate-/r* 85.4%

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

      2. associate-+l- 85.4%

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

      3. associate-*r* 85.4%

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

      4. associate-*r* 87.4%

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

      5. div-inv 87.5%

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

      6. associate--r- 87.5%

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

      7. fma-neg 87.5%

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

      8. associate-*r* 85.5%

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

      9. distribute-rgt-neg-in 85.5%

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

      10. associate-*l* 85.5%

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

   3. Applied egg-rr 85.5%

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

   4. Taylor expanded in x around 0 89.4%

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

   5. Taylor expanded in b around 0 82.1%

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

   if 3.1000000000000002e127 < b

   1. Initial program 80.7%

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

   2. Taylor expanded in x around inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r* 80.4%

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

   4. Simplified 80.4%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{c}}{z}\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -112000000000:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \end{array} \]

Alternative 6: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-70}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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 -3.9e-177)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 2.5e-182)
     (/ (/ b c) z)
     (if (<= a 8.2e-70)
       (* 9.0 (* x (/ y (* c z))))
       (if (<= a 6.8e+38) (/ b (* c z)) (* -4.0 (/ t (/ c a))))))))

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-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 2.5e-182) {
		tmp = (b / c) / z;
	} else if (a <= 8.2e-70) {
		tmp = 9.0 * (x * (y / (c * z)));
	} else if (a <= 6.8e+38) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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-177)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 2.5d-182) then
        tmp = (b / c) / z
    else if (a <= 8.2d-70) then
        tmp = 9.0d0 * (x * (y / (c * z)))
    else if (a <= 6.8d+38) then
        tmp = b / (c * z)
    else
        tmp = (-4.0d0) * (t / (c / a))
    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-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 2.5e-182) {
		tmp = (b / c) / z;
	} else if (a <= 8.2e-70) {
		tmp = 9.0 * (x * (y / (c * z)));
	} else if (a <= 6.8e+38) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.9e-177:
		tmp = (a / (c / t)) * -4.0
	elif a <= 2.5e-182:
		tmp = (b / c) / z
	elif a <= 8.2e-70:
		tmp = 9.0 * (x * (y / (c * z)))
	elif a <= 6.8e+38:
		tmp = b / (c * z)
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.9e-177)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 2.5e-182)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 8.2e-70)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c * z))));
	elseif (a <= 6.8e+38)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	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-177)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 2.5e-182)
		tmp = (b / c) / z;
	elseif (a <= 8.2e-70)
		tmp = 9.0 * (x * (y / (c * z)));
	elseif (a <= 6.8e+38)
		tmp = b / (c * z);
	else
		tmp = -4.0 * (t / (c / a));
	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, -3.9e-177], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 2.5e-182], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 8.2e-70], N[(9.0 * N[(x * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+38], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.90000000000000014e-177

   1. Initial program 76.1%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.7%

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

      2. times-frac 74.6%

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

      3. pow2 74.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 51.2%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -3.90000000000000014e-177 < a < 2.50000000000000012e-182

   1. Initial program 86.1%

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

   2. Taylor expanded in b around inf 57.5%

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

      1. associate-/r* 58.9%

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

   4. Simplified 58.9%

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

   if 2.50000000000000012e-182 < a < 8.19999999999999955e-70

   1. Initial program 82.1%

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

      1. associate-/r* 78.8%

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

      2. associate-+l- 78.8%

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

      3. associate-*r* 78.9%

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

      4. associate-*r* 92.1%

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

      5. div-inv 92.0%

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

      6. associate--r- 92.0%

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

      7. fma-neg 92.0%

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

      8. associate-*r* 78.8%

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

      9. distribute-rgt-neg-in 78.8%

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

      10. associate-*l* 78.8%

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

   3. Applied egg-rr 78.8%

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

   4. Taylor expanded in x around 0 92.1%

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

   5. Taylor expanded in x around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-*r/ 72.3%

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

   7. Simplified 72.3%

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

   if 8.19999999999999955e-70 < a < 6.79999999999999992e38

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf 46.6%

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

      1. *-commutative 46.6%

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

   4. Simplified 46.6%

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

   if 6.79999999999999992e38 < a

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   4. Simplified 55.9%

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

      1. *-commutative 55.9%

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

      2. *-un-lft-identity 55.9%

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

      3. times-frac 66.3%

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

   6. Applied egg-rr 66.3%

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

      1. /-rgt-identity 66.3%

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

      2. clear-num 66.3%

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

      3. un-div-inv 66.2%

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

   8. Applied egg-rr 66.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-70}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 7: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+39}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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 -3.9e-177)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 1.6e-182)
     (/ (/ b c) z)
     (if (<= a 1.35e-70)
       (* 9.0 (* (/ x c) (/ y z)))
       (if (<= a 1.22e+39) (/ b (* c z)) (* -4.0 (/ t (/ c a))))))))

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-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.6e-182) {
		tmp = (b / c) / z;
	} else if (a <= 1.35e-70) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 1.22e+39) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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-177)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 1.6d-182) then
        tmp = (b / c) / z
    else if (a <= 1.35d-70) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (a <= 1.22d+39) then
        tmp = b / (c * z)
    else
        tmp = (-4.0d0) * (t / (c / a))
    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-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.6e-182) {
		tmp = (b / c) / z;
	} else if (a <= 1.35e-70) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 1.22e+39) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.9e-177:
		tmp = (a / (c / t)) * -4.0
	elif a <= 1.6e-182:
		tmp = (b / c) / z
	elif a <= 1.35e-70:
		tmp = 9.0 * ((x / c) * (y / z))
	elif a <= 1.22e+39:
		tmp = b / (c * z)
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.9e-177)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 1.6e-182)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 1.35e-70)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (a <= 1.22e+39)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	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-177)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 1.6e-182)
		tmp = (b / c) / z;
	elseif (a <= 1.35e-70)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (a <= 1.22e+39)
		tmp = b / (c * z);
	else
		tmp = -4.0 * (t / (c / a));
	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, -3.9e-177], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 1.6e-182], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.35e-70], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e+39], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.90000000000000014e-177

   1. Initial program 76.1%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.7%

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

      2. times-frac 74.6%

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

      3. pow2 74.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 51.2%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -3.90000000000000014e-177 < a < 1.60000000000000001e-182

   1. Initial program 86.1%

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

   2. Taylor expanded in b around inf 57.5%

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

      1. associate-/r* 58.9%

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

   4. Simplified 58.9%

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

   if 1.60000000000000001e-182 < a < 1.3500000000000001e-70

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 72.3%

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

      1. times-frac 76.3%

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

   4. Simplified 76.3%

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

   if 1.3500000000000001e-70 < a < 1.22e39

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf 46.6%

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

      1. *-commutative 46.6%

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

   4. Simplified 46.6%

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

   if 1.22e39 < a

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   4. Simplified 55.9%

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

      1. *-commutative 55.9%

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

      2. *-un-lft-identity 55.9%

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

      3. times-frac 66.3%

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

   6. Applied egg-rr 66.3%

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

      1. /-rgt-identity 66.3%

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

      2. clear-num 66.3%

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

      3. un-div-inv 66.2%

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

   8. Applied egg-rr 66.2%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-70}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+39}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 8: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-178}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-71}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+39}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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 -3.2e-178)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 1.75e-182)
     (/ (/ b c) z)
     (if (<= a 8.5e-71)
       (* 9.0 (* (/ x z) (/ y c)))
       (if (<= a 1.06e+39) (/ b (* c z)) (* -4.0 (/ t (/ c a))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.2e-178) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.75e-182) {
		tmp = (b / c) / z;
	} else if (a <= 8.5e-71) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 1.06e+39) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 <= (-3.2d-178)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 1.75d-182) then
        tmp = (b / c) / z
    else if (a <= 8.5d-71) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (a <= 1.06d+39) then
        tmp = b / (c * z)
    else
        tmp = (-4.0d0) * (t / (c / a))
    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 <= -3.2e-178) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.75e-182) {
		tmp = (b / c) / z;
	} else if (a <= 8.5e-71) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 1.06e+39) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.2e-178:
		tmp = (a / (c / t)) * -4.0
	elif a <= 1.75e-182:
		tmp = (b / c) / z
	elif a <= 8.5e-71:
		tmp = 9.0 * ((x / z) * (y / c))
	elif a <= 1.06e+39:
		tmp = b / (c * z)
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.2e-178)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 1.75e-182)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 8.5e-71)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (a <= 1.06e+39)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	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 <= -3.2e-178)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 1.75e-182)
		tmp = (b / c) / z;
	elseif (a <= 8.5e-71)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (a <= 1.06e+39)
		tmp = b / (c * z);
	else
		tmp = -4.0 * (t / (c / a));
	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, -3.2e-178], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 1.75e-182], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 8.5e-71], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+39], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.2000000000000001e-178

   1. Initial program 76.1%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.7%

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

      2. times-frac 74.6%

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

      3. pow2 74.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 51.2%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -3.2000000000000001e-178 < a < 1.74999999999999992e-182

   1. Initial program 86.1%

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

   2. Taylor expanded in b around inf 57.5%

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

      1. associate-/r* 58.9%

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

   4. Simplified 58.9%

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

   if 1.74999999999999992e-182 < a < 8.49999999999999988e-71

   1. Initial program 82.1%

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

   3. Simplified 91.4%

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

      1. add-cube-cbrt 90.8%

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

      2. times-frac 90.8%

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

      3. pow2 90.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 90.8%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 90.8%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 90.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in x around inf 72.3%

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

      1. associate-*r/ 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r/ 72.3%

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

      4. times-frac 72.0%

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

   8. Simplified 72.0%

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

   if 8.49999999999999988e-71 < a < 1.06000000000000005e39

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf 46.6%

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

      1. *-commutative 46.6%

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

   4. Simplified 46.6%

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

   if 1.06000000000000005e39 < a

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   4. Simplified 55.9%

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

      1. *-commutative 55.9%

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

      2. *-un-lft-identity 55.9%

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

      3. times-frac 66.3%

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

   6. Applied egg-rr 66.3%

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

      1. /-rgt-identity 66.3%

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

      2. clear-num 66.3%

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

      3. un-div-inv 66.2%

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

   8. Applied egg-rr 66.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-178}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-71}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+39}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 9: 64.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+128} \lor \neg \left(x \leq 5.2 \cdot 10^{-70}\right):\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 (or (<= x -9.6e+128) (not (<= x 5.2e-70)))
   (* 9.0 (* (/ x z) (/ y c)))
   (/ (+ (* -4.0 (* a t)) (/ b 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 ((x <= -9.6e+128) || !(x <= 5.2e-70)) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / 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 ((x <= (-9.6d+128)) .or. (.not. (x <= 5.2d-70))) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / 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 ((x <= -9.6e+128) || !(x <= 5.2e-70)) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x <= -9.6e+128) or not (x <= 5.2e-70):
		tmp = 9.0 * ((x / z) * (y / c))
	else:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((x <= -9.6e+128) || !(x <= 5.2e-70))
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / 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 ((x <= -9.6e+128) || ~((x <= 5.2e-70)))
		tmp = 9.0 * ((x / z) * (y / c));
	else
		tmp = ((-4.0 * (a * t)) + (b / z)) / 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[Or[LessEqual[x, -9.6e+128], N[Not[LessEqual[x, 5.2e-70]], $MachinePrecision]], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.6000000000000007e128 or 5.20000000000000004e-70 < x

   1. Initial program 78.5%

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

   3. Simplified 76.0%

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

      1. add-cube-cbrt 75.5%

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

      2. times-frac 78.6%

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

      3. pow2 78.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 78.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 78.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in x around inf 50.1%

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

      1. associate-*r/ 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-*r/ 50.1%

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

      4. times-frac 55.7%

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

   8. Simplified 55.7%

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

   if -9.6000000000000007e128 < x < 5.20000000000000004e-70

   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-/r* 81.6%

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

      2. associate-+l- 81.6%

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

      3. associate-*r* 81.6%

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

      4. associate-*r* 82.4%

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

      5. div-inv 82.4%

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

      6. associate--r- 82.4%

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

      7. fma-neg 82.4%

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

      8. associate-*r* 81.6%

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

      9. distribute-rgt-neg-in 81.6%

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

      10. associate-*l* 81.6%

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

   3. Applied egg-rr 81.6%

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

   4. Taylor expanded in x around 0 86.0%

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

   5. Taylor expanded in x around 0 75.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+128} \lor \neg \left(x \leq 5.2 \cdot 10^{-70}\right):\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 10: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-100} \lor \neg \left(z \leq 4.6 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 -7.8e-100) (not (<= z 4.6e-97)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* x (* 9.0 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 <= -7.8e-100) || !(z <= 4.6e-97)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (x * (9.0 * 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 <= (-7.8d-100)) .or. (.not. (z <= 4.6d-97))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (x * (9.0d0 * 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 <= -7.8e-100) || !(z <= 4.6e-97)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (x * (9.0 * y))) / (c * z);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7.8e-100) or not (z <= 4.6e-97):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (x * (9.0 * 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 <= -7.8e-100) || !(z <= 4.6e-97))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * 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 <= -7.8e-100) || ~((z <= 4.6e-97)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (x * (9.0 * 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, -7.8e-100], N[Not[LessEqual[z, 4.6e-97]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999955e-100 or 4.59999999999999988e-97 < z

   1. Initial program 69.7%

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

      1. associate-/r* 78.7%

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

      2. associate-+l- 78.7%

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

      3. associate-*r* 78.8%

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

      4. associate-*r* 82.1%

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

      5. div-inv 82.1%

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

      6. associate--r- 82.1%

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

      7. fma-neg 82.2%

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

      8. associate-*r* 78.9%

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

      9. distribute-rgt-neg-in 78.9%

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

      10. associate-*l* 78.9%

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

   3. Applied egg-rr 78.9%

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

   4. Taylor expanded in x around 0 87.9%

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

   5. Taylor expanded in x around 0 72.0%

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

   if -7.79999999999999955e-100 < z < 4.59999999999999988e-97

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 84.8%

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

      1. associate-*r* 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r* 84.8%

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

   4. Simplified 84.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-100} \lor \neg \left(z \leq 4.6 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \end{array} \]

Alternative 11: 50.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+71} \lor \neg \left(b \leq 5.5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (<= b -1.8e+71) (not (<= b 5.5e+130)))
   (/ b (* c z))
   (* (/ a (/ c t)) -4.0)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.8e+71) || !(b <= 5.5e+130)) {
		tmp = b / (c * z);
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	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 ((b <= (-1.8d+71)) .or. (.not. (b <= 5.5d+130))) then
        tmp = b / (c * z)
    else
        tmp = (a / (c / t)) * (-4.0d0)
    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 ((b <= -1.8e+71) || !(b <= 5.5e+130)) {
		tmp = b / (c * z);
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.8e+71) or not (b <= 5.5e+130):
		tmp = b / (c * z)
	else:
		tmp = (a / (c / t)) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.8e+71) || !(b <= 5.5e+130))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	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 ((b <= -1.8e+71) || ~((b <= 5.5e+130)))
		tmp = b / (c * z);
	else
		tmp = (a / (c / t)) * -4.0;
	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[b, -1.8e+71], N[Not[LessEqual[b, 5.5e+130]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e71 or 5.4999999999999997e130 < b

   1. Initial program 84.3%

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

   2. Taylor expanded in b around inf 66.0%

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

      1. *-commutative 66.0%

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

   4. Simplified 66.0%

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

   if -1.8e71 < b < 5.4999999999999997e130

   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

   3. Simplified 77.5%

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

      1. add-cube-cbrt 76.8%

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

      2. times-frac 81.3%

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

      3. pow2 81.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 81.3%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 81.3%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 51.9%

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

      1. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+71} \lor \neg \left(b \leq 5.5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 12: 51.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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 -3.4e-177)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 7.5e+38) (* b (/ 1.0 (* c z))) (* -4.0 (/ t (/ c a))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.4e-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 7.5e+38) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 <= (-3.4d-177)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 7.5d+38) then
        tmp = b * (1.0d0 / (c * z))
    else
        tmp = (-4.0d0) * (t / (c / a))
    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 <= -3.4e-177) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 7.5e+38) {
		tmp = b * (1.0 / (c * z));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.4e-177:
		tmp = (a / (c / t)) * -4.0
	elif a <= 7.5e+38:
		tmp = b * (1.0 / (c * z))
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.4e-177)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 7.5e+38)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	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 <= -3.4e-177)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 7.5e+38)
		tmp = b * (1.0 / (c * z));
	else
		tmp = -4.0 * (t / (c / a));
	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, -3.4e-177], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 7.5e+38], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4000000000000001e-177

   1. Initial program 76.1%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.7%

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

      2. times-frac 74.6%

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

      3. pow2 74.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}\right)}^{2}}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      4. +-commutative 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right) + b}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

      5. fma-def 74.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)}\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{c} \]

   5. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}\right)}^{2}}{z} \cdot \frac{\sqrt[3]{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}{c}} \]

   6. Taylor expanded in t around inf 51.2%

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

      1. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -3.4000000000000001e-177 < a < 7.4999999999999999e38

   1. Initial program 86.3%

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

   2. Taylor expanded in b around inf 50.2%

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

      1. *-commutative 50.2%

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

   4. Simplified 50.2%

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

      1. div-inv 50.9%

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

   6. Applied egg-rr 50.9%

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

   if 7.4999999999999999e38 < a

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   4. Simplified 55.9%

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

      1. *-commutative 55.9%

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

      2. *-un-lft-identity 55.9%

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

      3. times-frac 66.3%

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

   6. Applied egg-rr 66.3%

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

      1. /-rgt-identity 66.3%

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

      2. clear-num 66.3%

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

      3. un-div-inv 66.2%

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

   8. Applied egg-rr 66.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 13: 35.2% 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 81.8%

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

2. Taylor expanded in b around inf 36.5%

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

   1. *-commutative 36.5%

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

4. Simplified 36.5%

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

5. Final simplification 36.5%

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

Developer target: 80.9% 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 2023298 
(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)))