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

Percentage Accurate: 79.4% → 88.9%

Time: 16.3s

Alternatives: 22

Speedup: 0.7×

• 37.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{y} - x \cdot -9\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot t\_1}{z}}{c\_m}\\ t_3 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+211}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{y}{z} \cdot t\_1}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (- (/ b y) (* x -9.0)))
        (t_2 (/ (+ (* -4.0 (* t a)) (/ (* y t_1) z)) c_m))
        (t_3 (/ (+ b (- (* y (* x 9.0)) (* a (* (* z 4.0) t)))) (* c_m z))))
   (*
    c_s
    (if (<= t_3 (- INFINITY))
      t_2
      (if (<= t_3 -4e-61)
        t_3
        (if (<= t_3 0.0)
          t_2
          (if (<= t_3 5e+211)
            t_3
            (if (<= t_3 INFINITY)
              (/ (+ (* a (* t -4.0)) (* (/ y z) t_1)) c_m)
              (* a (/ (* t -4.0) c_m))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b / y) - (x * -9.0);
	double t_2 = ((-4.0 * (t * a)) + ((y * t_1) / z)) / c_m;
	double t_3 = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -4e-61) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 5e+211) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = ((a * (t * -4.0)) + ((y / z) * t_1)) / c_m;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b / y) - (x * -9.0);
	double t_2 = ((-4.0 * (t * a)) + ((y * t_1) / z)) / c_m;
	double t_3 = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= -4e-61) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 5e+211) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = ((a * (t * -4.0)) + ((y / z) * t_1)) / c_m;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b / y) - (x * -9.0)
	t_2 = ((-4.0 * (t * a)) + ((y * t_1) / z)) / c_m
	t_3 = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= -4e-61:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 5e+211:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = ((a * (t * -4.0)) + ((y / z) * t_1)) / c_m
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b / y) - Float64(x * -9.0))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(y * t_1) / z)) / c_m)
	t_3 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(Float64(z * 4.0) * t)))) / Float64(c_m * z))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -4e-61)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 5e+211)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(y / z) * t_1)) / c_m);
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b / y) - (x * -9.0);
	t_2 = ((-4.0 * (t * a)) + ((y * t_1) / z)) / c_m;
	t_3 = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= -4e-61)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 5e+211)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = ((a * (t * -4.0)) + ((y / z) * t_1)) / c_m;
	else
		tmp = a * ((t * -4.0) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b / y), $MachinePrecision] - N[(x * -9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -4e-61], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 5e+211], t$95$3, If[LessEqual[t$95$3, Infinity], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -inf.0 or -4.0000000000000002e-61 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 70.5%

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

      1. associate-+l- 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

      5. associate-+l- 71.6%

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

      6. associate-*l* 71.6%

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

      7. associate-*l* 72.8%

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

      8. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 57.2%

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

   6. Taylor expanded in z around -inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. *-commutative 75.2%

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

      4. associate-/l* 76.3%

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

      5. *-commutative 76.3%

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

      6. associate-/l* 73.2%

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

      7. mul-1-neg 73.2%

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

      8. unsub-neg 73.2%

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

      9. associate-*r/ 73.2%

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

      10. *-commutative 73.2%

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

      11. associate-/l* 73.2%

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

      12. associate-/r* 77.2%

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

   8. Simplified 77.2%

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

   9. Taylor expanded in c around 0 91.6%

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

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.0000000000000002e-61 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 4.9999999999999995e211

   1. Initial program 99.3%

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

   if 4.9999999999999995e211 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.9%

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

      1. associate-+l- 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r* 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-+l- 90.4%

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

      6. associate-*l* 90.4%

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

      7. associate-*l* 88.0%

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

      8. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in y around inf 77.4%

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

   6. Taylor expanded in z around -inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-/l* 72.6%

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

      5. *-commutative 72.6%

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

      6. associate-/l* 71.4%

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

      7. mul-1-neg 71.4%

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

      8. unsub-neg 71.4%

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

      9. associate-*r/ 71.4%

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

      10. *-commutative 71.4%

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

      11. associate-/l* 71.4%

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

      12. associate-/r* 67.7%

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

   8. Simplified 67.7%

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

   9. Taylor expanded in c around 0 89.1%

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

       1. *-commutative 89.1%

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

       2. associate-*l* 89.1%

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

       3. *-commutative 89.1%

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

       4. associate-/l* 87.8%

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

   11. Simplified 87.8%

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

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

   1. Initial program 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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 5.9%

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

      4. *-commutative 5.9%

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

      5. associate-+l- 5.9%

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

      6. associate-*l* 5.9%

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

      7. associate-*l* 5.9%

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

      8. *-commutative 5.9%

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

   3. Simplified 5.9%

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

   5. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-/l* 89.8%

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

      3. associate-*r* 89.8%

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

      4. associate-*l/ 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z} \leq -\infty:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z} \leq -4 \cdot 10^{-61}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z} \leq 5 \cdot 10^{+211}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{y}{z} \cdot \left(\frac{b}{y} - x \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* t a)) (/ (* y (- (/ b y) (* x -9.0))) z)) c_m)))
   (*
    c_s
    (if (<= z -1.36e+14)
      t_1
      (if (<= z 4.6e-169)
        (/ (+ b (- (* y (* x 9.0)) (* a (* (* z 4.0) t)))) (* c_m z))
        (if (<= z 2.45e+204) t_1 (* a (/ (* t -4.0) c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	double tmp;
	if (z <= -1.36e+14) {
		tmp = t_1;
	} else if (z <= 4.6e-169) {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	} else if (z <= 2.45e+204) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (t * a)) + ((y * ((b / y) - (x * (-9.0d0)))) / z)) / c_m
    if (z <= (-1.36d+14)) then
        tmp = t_1
    else if (z <= 4.6d-169) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * ((z * 4.0d0) * t)))) / (c_m * z)
    else if (z <= 2.45d+204) then
        tmp = t_1
    else
        tmp = a * ((t * (-4.0d0)) / c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	double tmp;
	if (z <= -1.36e+14) {
		tmp = t_1;
	} else if (z <= 4.6e-169) {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	} else if (z <= 2.45e+204) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m
	tmp = 0
	if z <= -1.36e+14:
		tmp = t_1
	elif z <= 4.6e-169:
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)
	elif z <= 2.45e+204:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(y * Float64(Float64(b / y) - Float64(x * -9.0))) / z)) / c_m)
	tmp = 0.0
	if (z <= -1.36e+14)
		tmp = t_1;
	elseif (z <= 4.6e-169)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(Float64(z * 4.0) * t)))) / Float64(c_m * z));
	elseif (z <= 2.45e+204)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	tmp = 0.0;
	if (z <= -1.36e+14)
		tmp = t_1;
	elseif (z <= 4.6e-169)
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	elseif (z <= 2.45e+204)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(b / y), $MachinePrecision] - N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.36e+14], t$95$1, If[LessEqual[z, 4.6e-169], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+204], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36e14 or 4.6000000000000002e-169 < z < 2.4499999999999999e204

   1. Initial program 70.1%

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

      1. associate-+l- 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*r* 70.2%

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

      4. *-commutative 70.2%

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

      5. associate-+l- 70.2%

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

      6. associate-*l* 70.2%

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

      7. associate-*l* 74.3%

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

      8. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 67.8%

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

   6. Taylor expanded in z around -inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. *-commutative 72.2%

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

      4. associate-/l* 73.5%

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

      5. *-commutative 73.5%

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

      6. associate-/l* 74.8%

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

      7. mul-1-neg 74.8%

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

      8. unsub-neg 74.8%

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

      9. associate-*r/ 74.9%

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

      10. *-commutative 74.9%

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

      11. associate-/l* 74.9%

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

      12. associate-/r* 79.0%

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

   8. Simplified 79.0%

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

   9. Taylor expanded in c around 0 85.5%

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

   if -1.36e14 < z < 4.6000000000000002e-169

   1. Initial program 96.0%

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

   if 2.4499999999999999e204 < z

   1. Initial program 42.2%

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

      1. associate-+l- 42.2%

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

      2. *-commutative 42.2%

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

      3. associate-*r* 34.2%

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

      4. *-commutative 34.2%

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

      5. associate-+l- 34.2%

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

      6. associate-*l* 34.2%

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

      7. associate-*l* 42.5%

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

      8. *-commutative 42.5%

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

   3. Simplified 42.5%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-/l* 92.2%

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

      3. associate-*r* 92.2%

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

      4. associate-*l/ 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+14}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-169}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+204}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{\frac{b}{y} - x \cdot -9}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= z -6.2e+88)
      t_1
      (if (<= z -2.8e-45)
        (* y (/ (- (/ b y) (* x -9.0)) (* c_m z)))
        (if (<= z -6.5e-92)
          (/ (- b (* 4.0 (* a (* z t)))) (* c_m z))
          (if (<= z 2.7e+39) (/ (+ b (* y (* x 9.0))) (* c_m z)) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	double tmp;
	if (z <= -6.2e+88) {
		tmp = t_1;
	} else if (z <= -2.8e-45) {
		tmp = y * (((b / y) - (x * -9.0)) / (c_m * z));
	} else if (z <= -6.5e-92) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 2.7e+39) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    if (z <= (-6.2d+88)) then
        tmp = t_1
    else if (z <= (-2.8d-45)) then
        tmp = y * (((b / y) - (x * (-9.0d0))) / (c_m * z))
    else if (z <= (-6.5d-92)) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else if (z <= 2.7d+39) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	double tmp;
	if (z <= -6.2e+88) {
		tmp = t_1;
	} else if (z <= -2.8e-45) {
		tmp = y * (((b / y) - (x * -9.0)) / (c_m * z));
	} else if (z <= -6.5e-92) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 2.7e+39) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m
	tmp = 0
	if z <= -6.2e+88:
		tmp = t_1
	elif z <= -2.8e-45:
		tmp = y * (((b / y) - (x * -9.0)) / (c_m * z))
	elif z <= -6.5e-92:
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z)
	elif z <= 2.7e+39:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (z <= -6.2e+88)
		tmp = t_1;
	elseif (z <= -2.8e-45)
		tmp = Float64(y * Float64(Float64(Float64(b / y) - Float64(x * -9.0)) / Float64(c_m * z)));
	elseif (z <= -6.5e-92)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	elseif (z <= 2.7e+39)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	tmp = 0.0;
	if (z <= -6.2e+88)
		tmp = t_1;
	elseif (z <= -2.8e-45)
		tmp = y * (((b / y) - (x * -9.0)) / (c_m * z));
	elseif (z <= -6.5e-92)
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	elseif (z <= 2.7e+39)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -6.2e+88], t$95$1, If[LessEqual[z, -2.8e-45], N[(y * N[(N[(N[(b / y), $MachinePrecision] - N[(x * -9.0), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-92], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+39], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2000000000000003e88 or 2.70000000000000003e39 < z

   1. Initial program 58.6%

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

      1. associate-+l- 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-+l- 58.8%

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

      6. associate-*l* 58.8%

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

      7. associate-*l* 63.5%

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

      8. *-commutative 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in y around inf 62.5%

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

   6. Taylor expanded in z around -inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

      3. *-commutative 70.9%

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

      4. associate-/l* 72.7%

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

      5. *-commutative 72.7%

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

      6. associate-/l* 72.6%

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

      7. mul-1-neg 72.6%

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

      8. unsub-neg 72.6%

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

      9. associate-*r/ 72.7%

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

      10. *-commutative 72.7%

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

      11. associate-/l* 72.7%

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

      12. associate-/r* 78.4%

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

   8. Simplified 78.4%

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

   9. Taylor expanded in c around 0 80.4%

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

   10. Taylor expanded in y around 0 80.9%

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

       1. associate-*r/ 80.9%

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

       2. mul-1-neg 80.9%

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

   12. Simplified 80.9%

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

   if -6.2000000000000003e88 < z < -2.8000000000000001e-45

   1. Initial program 86.4%

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

      1. associate-+l- 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-+l- 83.6%

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

      6. associate-*l* 83.6%

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

      7. associate-*l* 89.0%

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

      8. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around inf 67.6%

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

   6. Taylor expanded in z around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-/l* 71.8%

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

      5. *-commutative 71.8%

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

      6. associate-/l* 74.5%

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

      7. mul-1-neg 74.5%

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

      8. unsub-neg 74.5%

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

      9. associate-*r/ 74.4%

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

      10. *-commutative 74.4%

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

      11. associate-/l* 74.5%

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

      12. associate-/r* 78.0%

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

   8. Simplified 78.0%

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

   9. Taylor expanded in c around 0 81.4%

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

   10. Taylor expanded in a around 0 67.2%

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

       1. mul-1-neg 67.2%

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

       2. associate-/l* 67.0%

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

       3. distribute-lft-neg-in 67.0%

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

   12. Simplified 67.0%

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

   if -2.8000000000000001e-45 < z < -6.50000000000000035e-92

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. associate-*l* 99.6%

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

      7. associate-*l* 87.6%

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

      8. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if -6.50000000000000035e-92 < z < 2.70000000000000003e39

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-+l- 95.4%

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

      6. associate-*l* 95.4%

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

      7. associate-*l* 91.8%

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

      8. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around inf 82.8%

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

      1. associate-*r* 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{\frac{b}{y} - x \cdot -9}{c \cdot z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{y \cdot \left(\frac{b}{y} + x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)))
   (*
    c_s
    (if (<= z -3.85e+87)
      t_1
      (if (<= z -2.6e-43)
        (/ (* y (+ (/ b y) (* x 9.0))) (* c_m z))
        (if (<= z -4.2e-93)
          (/ (- b (* 4.0 (* a (* z t)))) (* c_m z))
          (if (<= z 4.5e+38) (/ (+ b (* y (* x 9.0))) (* c_m z)) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	double tmp;
	if (z <= -3.85e+87) {
		tmp = t_1;
	} else if (z <= -2.6e-43) {
		tmp = (y * ((b / y) + (x * 9.0))) / (c_m * z);
	} else if (z <= -4.2e-93) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 4.5e+38) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    if (z <= (-3.85d+87)) then
        tmp = t_1
    else if (z <= (-2.6d-43)) then
        tmp = (y * ((b / y) + (x * 9.0d0))) / (c_m * z)
    else if (z <= (-4.2d-93)) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else if (z <= 4.5d+38) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	double tmp;
	if (z <= -3.85e+87) {
		tmp = t_1;
	} else if (z <= -2.6e-43) {
		tmp = (y * ((b / y) + (x * 9.0))) / (c_m * z);
	} else if (z <= -4.2e-93) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= 4.5e+38) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m
	tmp = 0
	if z <= -3.85e+87:
		tmp = t_1
	elif z <= -2.6e-43:
		tmp = (y * ((b / y) + (x * 9.0))) / (c_m * z)
	elif z <= -4.2e-93:
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z)
	elif z <= 4.5e+38:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m)
	tmp = 0.0
	if (z <= -3.85e+87)
		tmp = t_1;
	elseif (z <= -2.6e-43)
		tmp = Float64(Float64(y * Float64(Float64(b / y) + Float64(x * 9.0))) / Float64(c_m * z));
	elseif (z <= -4.2e-93)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	elseif (z <= 4.5e+38)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c_m;
	tmp = 0.0;
	if (z <= -3.85e+87)
		tmp = t_1;
	elseif (z <= -2.6e-43)
		tmp = (y * ((b / y) + (x * 9.0))) / (c_m * z);
	elseif (z <= -4.2e-93)
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	elseif (z <= 4.5e+38)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -3.85e+87], t$95$1, If[LessEqual[z, -2.6e-43], N[(N[(y * N[(N[(b / y), $MachinePrecision] + N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-93], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+38], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -3.85000000000000015e87 or 4.4999999999999998e38 < z

   1. Initial program 58.6%

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

      1. associate-+l- 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

      5. associate-+l- 58.8%

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

      6. associate-*l* 58.8%

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

      7. associate-*l* 63.5%

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

      8. *-commutative 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in y around inf 62.5%

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

   6. Taylor expanded in z around -inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

      3. *-commutative 70.9%

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

      4. associate-/l* 72.7%

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

      5. *-commutative 72.7%

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

      6. associate-/l* 72.6%

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

      7. mul-1-neg 72.6%

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

      8. unsub-neg 72.6%

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

      9. associate-*r/ 72.7%

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

      10. *-commutative 72.7%

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

      11. associate-/l* 72.7%

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

      12. associate-/r* 78.4%

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

   8. Simplified 78.4%

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

   9. Taylor expanded in c around 0 80.4%

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

   10. Taylor expanded in y around 0 80.9%

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

       1. associate-*r/ 80.9%

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

       2. mul-1-neg 80.9%

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

   12. Simplified 80.9%

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

   if -3.85000000000000015e87 < z < -2.6e-43

   1. Initial program 86.4%

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

      1. associate-+l- 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-+l- 83.6%

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

      6. associate-*l* 83.6%

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

      7. associate-*l* 89.0%

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

      8. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in y around inf 67.2%

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

   if -2.6e-43 < z < -4.2000000000000002e-93

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. associate-*l* 99.6%

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

      7. associate-*l* 87.6%

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

      8. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if -4.2000000000000002e-93 < z < 4.4999999999999998e38

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-+l- 95.4%

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

      6. associate-*l* 95.4%

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

      7. associate-*l* 91.8%

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

      8. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around inf 82.8%

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

      1. associate-*r* 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+87}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{y \cdot \left(\frac{b}{y} + x \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+158} \lor \neg \left(z \leq 7.8 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3.9e+158) (not (<= z 7.8e+99)))
    (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)
    (/ (+ b (- (* y (* x 9.0)) (* a (* (* z 4.0) t)))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.9e+158) || !(z <= 7.8e+99)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-3.9d+158)) .or. (.not. (z <= 7.8d+99))) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * ((z * 4.0d0) * t)))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.9e+158) || !(z <= 7.8e+99)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -3.9e+158) or not (z <= 7.8e+99):
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3.9e+158) || !(z <= 7.8e+99))
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(Float64(z * 4.0) * t)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -3.9e+158) || ~((z <= 7.8e+99)))
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3.9e+158], N[Not[LessEqual[z, 7.8e+99]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e158 or 7.79999999999999989e99 < z

   1. Initial program 51.1%

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

      1. associate-+l- 51.1%

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

      2. *-commutative 51.1%

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

      3. associate-*r* 51.4%

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

      4. *-commutative 51.4%

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

      5. associate-+l- 51.4%

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

      6. associate-*l* 51.4%

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

      7. associate-*l* 57.5%

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

      8. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around inf 58.8%

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

   6. Taylor expanded in z around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-/l* 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-/l* 72.4%

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

      7. mul-1-neg 72.4%

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

      8. unsub-neg 72.4%

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

      9. associate-*r/ 72.5%

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

      10. *-commutative 72.5%

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

      11. associate-/l* 72.5%

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

      12. associate-/r* 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in c around 0 79.0%

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

   10. Taylor expanded in y around 0 82.1%

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

       1. associate-*r/ 82.1%

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

       2. mul-1-neg 82.1%

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

   12. Simplified 82.1%

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

   if -3.9e158 < z < 7.79999999999999989e99

   1. Initial program 91.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+158} \lor \neg \left(z \leq 7.8 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+152} \lor \neg \left(z \leq 5.5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3.3e+152) (not (<= z 5.5e+84)))
    (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)
    (/ (- b (- (* (* z 4.0) (* t a)) (* x (* 9.0 y)))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.3e+152) || !(z <= 5.5e+84)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-3.3d+152)) .or. (.not. (z <= 5.5d+84))) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    else
        tmp = (b - (((z * 4.0d0) * (t * a)) - (x * (9.0d0 * y)))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.3e+152) || !(z <= 5.5e+84)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -3.3e+152) or not (z <= 5.5e+84):
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m
	else:
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3.3e+152) || !(z <= 5.5e+84))
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m);
	else
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - Float64(x * Float64(9.0 * y)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -3.3e+152) || ~((z <= 5.5e+84)))
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	else
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3.3e+152], N[Not[LessEqual[z, 5.5e+84]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.3000000000000001e152 or 5.5000000000000004e84 < z

   1. Initial program 53.4%

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

      1. associate-+l- 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r* 53.7%

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

      4. *-commutative 53.7%

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

      5. associate-+l- 53.7%

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

      6. associate-*l* 53.7%

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

      7. associate-*l* 59.5%

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

      8. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in y around inf 59.6%

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

   6. Taylor expanded in z around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

      3. *-commutative 70.2%

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

      4. associate-/l* 72.5%

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

      5. *-commutative 72.5%

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

      6. associate-/l* 71.4%

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

      7. mul-1-neg 71.4%

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

      8. unsub-neg 71.4%

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

      9. associate-*r/ 71.5%

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

      10. *-commutative 71.5%

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

      11. associate-/l* 71.5%

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

      12. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

   9. Taylor expanded in c around 0 79.9%

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

   10. Taylor expanded in y around 0 83.0%

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

       1. associate-*r/ 83.0%

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

       2. mul-1-neg 83.0%

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

   12. Simplified 83.0%

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

   if -3.3000000000000001e152 < z < 5.5000000000000004e84

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r* 90.9%

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

      4. *-commutative 90.9%

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

      5. associate-+l- 90.9%

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

      6. associate-*l* 91.0%

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

      7. associate-*l* 89.3%

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

      8. *-commutative 89.3%

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

   3. Simplified 89.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+152} \lor \neg \left(z \leq 5.5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 4.8:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{y}{z} \cdot \left(\frac{\frac{b}{c\_m}}{y} - x \cdot \frac{-9}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 4.8)
    (/ (- b (- (* (* z 4.0) (* t a)) (* x (* 9.0 y)))) (* c_m z))
    (+
     (* -4.0 (* t (/ a c_m)))
     (* (/ y z) (- (/ (/ b c_m) y) (* x (/ -9.0 c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 4.8) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + ((y / z) * (((b / c_m) / y) - (x * (-9.0 / c_m))));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (c_m <= 4.8d0) then
        tmp = (b - (((z * 4.0d0) * (t * a)) - (x * (9.0d0 * y)))) / (c_m * z)
    else
        tmp = ((-4.0d0) * (t * (a / c_m))) + ((y / z) * (((b / c_m) / y) - (x * ((-9.0d0) / c_m))))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 4.8) {
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + ((y / z) * (((b / c_m) / y) - (x * (-9.0 / c_m))));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 4.8:
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z)
	else:
		tmp = (-4.0 * (t * (a / c_m))) + ((y / z) * (((b / c_m) / y) - (x * (-9.0 / c_m))))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 4.8)
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - Float64(x * Float64(9.0 * y)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + Float64(Float64(y / z) * Float64(Float64(Float64(b / c_m) / y) - Float64(x * Float64(-9.0 / c_m)))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 4.8)
		tmp = (b - (((z * 4.0) * (t * a)) - (x * (9.0 * y)))) / (c_m * z);
	else
		tmp = (-4.0 * (t * (a / c_m))) + ((y / z) * (((b / c_m) / y) - (x * (-9.0 / c_m))));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 4.8], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(N[(b / c$95$m), $MachinePrecision] / y), $MachinePrecision] - N[(x * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4.79999999999999982

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r* 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-+l- 85.2%

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

      6. associate-*l* 85.2%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   if 4.79999999999999982 < c

   1. Initial program 61.8%

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

      1. associate-+l- 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*r* 58.9%

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

      4. *-commutative 58.9%

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

      5. associate-+l- 58.9%

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

      6. associate-*l* 58.9%

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

      7. associate-*l* 62.1%

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

      8. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around inf 69.3%

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

   6. Taylor expanded in z around -inf 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-/l* 87.6%

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

      5. *-commutative 87.6%

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

      6. associate-/l* 82.3%

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

      7. mul-1-neg 82.3%

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

      8. unsub-neg 82.3%

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

      9. associate-*r/ 82.2%

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

      10. *-commutative 82.2%

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

      11. associate-/l* 82.2%

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

      12. associate-/r* 85.5%

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

   8. Simplified 85.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 4.8:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{y}{z} \cdot \left(\frac{\frac{b}{c}}{y} - x \cdot \frac{-9}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;a \leq 48000000000 \lor \neg \left(a \leq 1.55 \cdot 10^{+91}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c_m)))))
   (*
    c_s
    (if (<= a -3.1e-35)
      t_1
      (if (<= a 2.1e-34)
        (/ (/ b z) c_m)
        (if (or (<= a 48000000000.0) (not (<= a 1.55e+91)))
          t_1
          (/ (/ b c_m) z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (a <= -3.1e-35) {
		tmp = t_1;
	} else if (a <= 2.1e-34) {
		tmp = (b / z) / c_m;
	} else if ((a <= 48000000000.0) || !(a <= 1.55e+91)) {
		tmp = t_1;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c_m))
    if (a <= (-3.1d-35)) then
        tmp = t_1
    else if (a <= 2.1d-34) then
        tmp = (b / z) / c_m
    else if ((a <= 48000000000.0d0) .or. (.not. (a <= 1.55d+91))) then
        tmp = t_1
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (a <= -3.1e-35) {
		tmp = t_1;
	} else if (a <= 2.1e-34) {
		tmp = (b / z) / c_m;
	} else if ((a <= 48000000000.0) || !(a <= 1.55e+91)) {
		tmp = t_1;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * (t * (a / c_m))
	tmp = 0
	if a <= -3.1e-35:
		tmp = t_1
	elif a <= 2.1e-34:
		tmp = (b / z) / c_m
	elif (a <= 48000000000.0) or not (a <= 1.55e+91):
		tmp = t_1
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -3.1e-35)
		tmp = t_1;
	elseif (a <= 2.1e-34)
		tmp = Float64(Float64(b / z) / c_m);
	elseif ((a <= 48000000000.0) || !(a <= 1.55e+91))
		tmp = t_1;
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * (t * (a / c_m));
	tmp = 0.0;
	if (a <= -3.1e-35)
		tmp = t_1;
	elseif (a <= 2.1e-34)
		tmp = (b / z) / c_m;
	elseif ((a <= 48000000000.0) || ~((a <= 1.55e+91)))
		tmp = t_1;
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -3.1e-35], t$95$1, If[LessEqual[a, 2.1e-34], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[Or[LessEqual[a, 48000000000.0], N[Not[LessEqual[a, 1.55e+91]], $MachinePrecision]], t$95$1, N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if a < -3.10000000000000012e-35 or 2.1000000000000001e-34 < a < 4.8e10 or 1.54999999999999999e91 < a

   1. Initial program 78.6%

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

      1. associate-+l- 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 73.2%

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

      4. *-commutative 73.2%

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

      5. associate-+l- 73.2%

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

      6. associate-*l* 73.2%

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

      7. associate-*l* 75.6%

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

      8. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in z around 0 78.3%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 65.7%

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

   8. Simplified 65.7%

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

   if -3.10000000000000012e-35 < a < 2.1000000000000001e-34

   1. Initial program 81.3%

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

      1. associate-+l- 81.3%

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

      2. *-commutative 81.3%

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

      3. associate-*r* 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-+l- 86.2%

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

      6. associate-*l* 86.2%

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

      7. associate-*l* 86.2%

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

      8. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around inf 66.9%

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

   6. Taylor expanded in z around -inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-/l* 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-/l* 78.0%

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

      7. mul-1-neg 78.0%

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

      8. unsub-neg 78.0%

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

      9. associate-*r/ 78.0%

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

      10. *-commutative 78.0%

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

      11. associate-/l* 78.0%

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

      12. associate-/r* 83.9%

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

   8. Simplified 83.9%

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

   9. Taylor expanded in c around 0 89.4%

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

   10. Taylor expanded in b around inf 45.8%

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

   if 4.8e10 < a < 1.54999999999999999e91

   1. Initial program 65.4%

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

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r* 65.3%

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

      4. *-commutative 65.3%

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

      5. associate-+l- 65.3%

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

      6. associate-*l* 65.3%

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

      7. associate-*l* 56.2%

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

      8. *-commutative 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in b around inf 38.0%

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

      1. associate-/r* 46.2%

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

   7. Simplified 46.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 48000000000 \lor \neg \left(a \leq 1.55 \cdot 10^{+91}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c\_m}}{z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -2.35e+296)
    (/ (/ b c_m) z)
    (if (<= t -5.4e+93)
      (* a (/ (* t -4.0) c_m))
      (if (<= t -1.4e-107)
        (* 9.0 (/ (* x (/ y c_m)) z))
        (if (<= t 1.05e-65) (/ b (* c_m z)) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.4e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -1.4e-107) {
		tmp = 9.0 * ((x * (y / c_m)) / z);
	} else if (t <= 1.05e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-2.35d+296)) then
        tmp = (b / c_m) / z
    else if (t <= (-5.4d+93)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= (-1.4d-107)) then
        tmp = 9.0d0 * ((x * (y / c_m)) / z)
    else if (t <= 1.05d-65) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.4e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -1.4e-107) {
		tmp = 9.0 * ((x * (y / c_m)) / z);
	} else if (t <= 1.05e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -2.35e+296:
		tmp = (b / c_m) / z
	elif t <= -5.4e+93:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= -1.4e-107:
		tmp = 9.0 * ((x * (y / c_m)) / z)
	elif t <= 1.05e-65:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -2.35e+296)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t <= -5.4e+93)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= -1.4e-107)
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c_m)) / z));
	elseif (t <= 1.05e-65)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -2.35e+296)
		tmp = (b / c_m) / z;
	elseif (t <= -5.4e+93)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= -1.4e-107)
		tmp = 9.0 * ((x * (y / c_m)) / z);
	elseif (t <= 1.05e-65)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -2.35e+296], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.4e+93], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-107], N[(9.0 * N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-65], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e296

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 0.3%

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

      8. *-commutative 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   if -2.3499999999999999e296 < t < -5.3999999999999999e93

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 68.9%

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

      8. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.6%

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

      3. associate-*r* 65.6%

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

      4. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -5.3999999999999999e93 < t < -1.3999999999999999e-107

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*l* 90.8%

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

      8. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-/r* 59.2%

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

      2. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   if -1.3999999999999999e-107 < t < 1.05000000000000001e-65

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*r* 80.1%

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

      4. *-commutative 80.1%

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

      5. associate-+l- 80.1%

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

      6. associate-*l* 80.1%

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

      7. associate-*l* 87.0%

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

      8. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if 1.05000000000000001e-65 < t

   1. Initial program 73.9%

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

      1. associate-+l- 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

      6. associate-*l* 76.3%

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

      7. associate-*l* 73.9%

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

      8. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 71.6%

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

   6. Taylor expanded in a around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-/l* 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-108}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -2.35e+296)
    (/ (/ b c_m) z)
    (if (<= t -5.2e+93)
      (* a (/ (* t -4.0) c_m))
      (if (<= t -3.8e-108)
        (* 9.0 (/ (* x y) (* c_m z)))
        (if (<= t 6.4e-65) (/ b (* c_m z)) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.2e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -3.8e-108) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (t <= 6.4e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-2.35d+296)) then
        tmp = (b / c_m) / z
    else if (t <= (-5.2d+93)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= (-3.8d-108)) then
        tmp = 9.0d0 * ((x * y) / (c_m * z))
    else if (t <= 6.4d-65) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.2e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -3.8e-108) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (t <= 6.4e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -2.35e+296:
		tmp = (b / c_m) / z
	elif t <= -5.2e+93:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= -3.8e-108:
		tmp = 9.0 * ((x * y) / (c_m * z))
	elif t <= 6.4e-65:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -2.35e+296)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t <= -5.2e+93)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= -3.8e-108)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z)));
	elseif (t <= 6.4e-65)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -2.35e+296)
		tmp = (b / c_m) / z;
	elseif (t <= -5.2e+93)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= -3.8e-108)
		tmp = 9.0 * ((x * y) / (c_m * z));
	elseif (t <= 6.4e-65)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -2.35e+296], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.2e+93], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-108], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-65], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e296

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 0.3%

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

      8. *-commutative 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   if -2.3499999999999999e296 < t < -5.19999999999999999e93

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 68.9%

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

      8. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.6%

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

      3. associate-*r* 65.6%

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

      4. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -5.19999999999999999e93 < t < -3.79999999999999973e-108

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*l* 90.8%

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

      8. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 59.1%

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

   if -3.79999999999999973e-108 < t < 6.3999999999999998e-65

   1. Initial program 87.2%

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

      1. associate-+l- 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 80.3%

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

      4. *-commutative 80.3%

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

      5. associate-+l- 80.3%

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

      6. associate-*l* 80.3%

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

      7. associate-*l* 87.2%

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

      8. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if 6.3999999999999998e-65 < t

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. associate-*r* 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-+l- 76.0%

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

      6. associate-*l* 76.1%

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

      7. associate-*l* 73.6%

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

      8. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in z around 0 71.3%

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

   6. Taylor expanded in a around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-108}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c\_m}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -2.35e+296)
    (/ (/ b c_m) z)
    (if (<= t -5.4e+93)
      (* a (/ (* t -4.0) c_m))
      (if (<= t -4.5e-109)
        (* 9.0 (* (/ y z) (/ x c_m)))
        (if (<= t 6.5e-66) (/ b (* c_m z)) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.4e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -4.5e-109) {
		tmp = 9.0 * ((y / z) * (x / c_m));
	} else if (t <= 6.5e-66) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-2.35d+296)) then
        tmp = (b / c_m) / z
    else if (t <= (-5.4d+93)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= (-4.5d-109)) then
        tmp = 9.0d0 * ((y / z) * (x / c_m))
    else if (t <= 6.5d-66) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.4e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -4.5e-109) {
		tmp = 9.0 * ((y / z) * (x / c_m));
	} else if (t <= 6.5e-66) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -2.35e+296:
		tmp = (b / c_m) / z
	elif t <= -5.4e+93:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= -4.5e-109:
		tmp = 9.0 * ((y / z) * (x / c_m))
	elif t <= 6.5e-66:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -2.35e+296)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t <= -5.4e+93)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= -4.5e-109)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c_m)));
	elseif (t <= 6.5e-66)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -2.35e+296)
		tmp = (b / c_m) / z;
	elseif (t <= -5.4e+93)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= -4.5e-109)
		tmp = 9.0 * ((y / z) * (x / c_m));
	elseif (t <= 6.5e-66)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -2.35e+296], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.4e+93], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-109], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-66], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e296

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 0.3%

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

      8. *-commutative 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   if -2.3499999999999999e296 < t < -5.3999999999999999e93

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 68.9%

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

      8. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.6%

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

      3. associate-*r* 65.6%

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

      4. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -5.3999999999999999e93 < t < -4.5000000000000001e-109

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*l* 90.8%

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

      8. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. times-frac 54.7%

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

   7. Applied egg-rr 54.7%

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

   if -4.5000000000000001e-109 < t < 6.50000000000000024e-66

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*r* 80.1%

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

      4. *-commutative 80.1%

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

      5. associate-+l- 80.1%

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

      6. associate-*l* 80.1%

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

      7. associate-*l* 87.0%

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

      8. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if 6.50000000000000024e-66 < t

   1. Initial program 73.9%

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

      1. associate-+l- 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

      6. associate-*l* 76.3%

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

      7. associate-*l* 73.9%

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

      8. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 71.6%

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

   6. Taylor expanded in a around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-/l* 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -2.35e+296)
    (/ (/ b c_m) z)
    (if (<= t -5.2e+93)
      (* a (/ (* t -4.0) c_m))
      (if (<= t -2.1e-109)
        (* 9.0 (* x (/ (/ y c_m) z)))
        (if (<= t 6e-65) (/ b (* c_m z)) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.2e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -2.1e-109) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (t <= 6e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-2.35d+296)) then
        tmp = (b / c_m) / z
    else if (t <= (-5.2d+93)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= (-2.1d-109)) then
        tmp = 9.0d0 * (x * ((y / c_m) / z))
    else if (t <= 6d-65) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -5.2e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -2.1e-109) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else if (t <= 6e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -2.35e+296:
		tmp = (b / c_m) / z
	elif t <= -5.2e+93:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= -2.1e-109:
		tmp = 9.0 * (x * ((y / c_m) / z))
	elif t <= 6e-65:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -2.35e+296)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t <= -5.2e+93)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= -2.1e-109)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c_m) / z)));
	elseif (t <= 6e-65)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -2.35e+296)
		tmp = (b / c_m) / z;
	elseif (t <= -5.2e+93)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= -2.1e-109)
		tmp = 9.0 * (x * ((y / c_m) / z));
	elseif (t <= 6e-65)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -2.35e+296], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.2e+93], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-109], N[(9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-65], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e296

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 0.3%

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

      8. *-commutative 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   if -2.3499999999999999e296 < t < -5.19999999999999999e93

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 68.9%

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

      8. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.6%

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

      3. associate-*r* 65.6%

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

      4. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -5.19999999999999999e93 < t < -2.09999999999999996e-109

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*l* 90.8%

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

      8. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-/l* 52.4%

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

      2. associate-/r* 52.5%

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

   7. Simplified 52.5%

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

   if -2.09999999999999996e-109 < t < 5.99999999999999996e-65

   1. Initial program 87.2%

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

      1. associate-+l- 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 80.3%

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

      4. *-commutative 80.3%

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

      5. associate-+l- 80.3%

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

      6. associate-*l* 80.3%

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

      7. associate-*l* 87.2%

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

      8. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if 5.99999999999999996e-65 < t

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. associate-*r* 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-+l- 76.0%

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

      6. associate-*l* 76.1%

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

      7. associate-*l* 73.6%

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

      8. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in z around 0 71.3%

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

   6. Taylor expanded in a around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -2.35e+296)
    (/ (/ b c_m) z)
    (if (<= t -7e+93)
      (* a (/ (* t -4.0) c_m))
      (if (<= t -1.45e-107)
        (* 9.0 (* x (/ y (* c_m z))))
        (if (<= t 1.35e-65) (/ b (* c_m z)) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -7e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -1.45e-107) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (t <= 1.35e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (t <= (-2.35d+296)) then
        tmp = (b / c_m) / z
    else if (t <= (-7d+93)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= (-1.45d-107)) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (t <= 1.35d-65) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -2.35e+296) {
		tmp = (b / c_m) / z;
	} else if (t <= -7e+93) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= -1.45e-107) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (t <= 1.35e-65) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -2.35e+296:
		tmp = (b / c_m) / z
	elif t <= -7e+93:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= -1.45e-107:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif t <= 1.35e-65:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -2.35e+296)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t <= -7e+93)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= -1.45e-107)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (t <= 1.35e-65)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -2.35e+296)
		tmp = (b / c_m) / z;
	elseif (t <= -7e+93)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= -1.45e-107)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (t <= 1.35e-65)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -2.35e+296], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -7e+93], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.45e-107], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-65], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e296

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 0.3%

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

      8. *-commutative 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   if -2.3499999999999999e296 < t < -6.99999999999999996e93

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 68.9%

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

      8. *-commutative 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.6%

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

      3. associate-*r* 65.6%

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

      4. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   if -6.99999999999999996e93 < t < -1.4499999999999999e-107

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*l* 90.8%

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

      8. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. associate-/l* 52.4%

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

      2. *-commutative 52.4%

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

   7. Applied egg-rr 52.4%

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

   if -1.4499999999999999e-107 < t < 1.3499999999999999e-65

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*r* 80.1%

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

      4. *-commutative 80.1%

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

      5. associate-+l- 80.1%

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

      6. associate-*l* 80.1%

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

      7. associate-*l* 87.0%

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

      8. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if 1.3499999999999999e-65 < t

   1. Initial program 73.9%

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

      1. associate-+l- 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

      6. associate-*l* 76.3%

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

      7. associate-*l* 73.9%

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

      8. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 71.6%

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

   6. Taylor expanded in a around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. associate-/l* 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+93}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-107}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -3.35 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;a \leq 14000000000:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{b}{c\_m} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= a -3.35e-35)
    (* a (/ (* t -4.0) c_m))
    (if (<= a 2.8e-34)
      (/ (/ b z) c_m)
      (if (<= a 14000000000.0)
        (* a (* t (/ -4.0 c_m)))
        (if (<= a 3.5e+93)
          (* (/ b c_m) (/ 1.0 z))
          (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.35e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 2.8e-34) {
		tmp = (b / z) / c_m;
	} else if (a <= 14000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 3.5e+93) {
		tmp = (b / c_m) * (1.0 / z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (a <= (-3.35d-35)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (a <= 2.8d-34) then
        tmp = (b / z) / c_m
    else if (a <= 14000000000.0d0) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else if (a <= 3.5d+93) then
        tmp = (b / c_m) * (1.0d0 / z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.35e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 2.8e-34) {
		tmp = (b / z) / c_m;
	} else if (a <= 14000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 3.5e+93) {
		tmp = (b / c_m) * (1.0 / z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if a <= -3.35e-35:
		tmp = a * ((t * -4.0) / c_m)
	elif a <= 2.8e-34:
		tmp = (b / z) / c_m
	elif a <= 14000000000.0:
		tmp = a * (t * (-4.0 / c_m))
	elif a <= 3.5e+93:
		tmp = (b / c_m) * (1.0 / z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (a <= -3.35e-35)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (a <= 2.8e-34)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (a <= 14000000000.0)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	elseif (a <= 3.5e+93)
		tmp = Float64(Float64(b / c_m) * Float64(1.0 / z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (a <= -3.35e-35)
		tmp = a * ((t * -4.0) / c_m);
	elseif (a <= 2.8e-34)
		tmp = (b / z) / c_m;
	elseif (a <= 14000000000.0)
		tmp = a * (t * (-4.0 / c_m));
	elseif (a <= 3.5e+93)
		tmp = (b / c_m) * (1.0 / z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[a, -3.35e-35], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-34], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[a, 14000000000.0], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+93], N[(N[(b / c$95$m), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if a < -3.35e-35

   1. Initial program 76.5%

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

      1. associate-+l- 76.5%

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

      2. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 62.5%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 62.5%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. associate-*l/ 62.5%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -3.35e-35 < a < 2.79999999999999997e-34

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 79.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 79.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 79.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 78.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 78.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 83.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 83.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 89.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in b around inf 45.8%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if 2.79999999999999997e-34 < a < 1.4e10

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 60.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 62.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.7%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 62.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 62.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 62.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 62.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 43.4%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in t around inf 42.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. associate-*r/ 41.6%

          \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

       2. *-commutative 41.6%

          \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

       3. associate-*l* 41.6%

          \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

       4. *-commutative 41.6%

          \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

       5. associate-*r/ 41.6%

          \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

       6. *-commutative 41.6%

          \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

       7. associate-/l* 41.6%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot \frac{-4}{c}\right)} \]

   11. Simplified 41.6%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   if 1.4e10 < a < 3.49999999999999998e93

   1. Initial program 65.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 65.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 46.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. div-inv 46.2%

         \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   9. Applied egg-rr 46.2%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   if 3.49999999999999998e93 < a

   1. Initial program 82.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 80.2%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 69.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 69.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -3.35 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;a \leq 4000000000000:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= a -3.35e-35)
    (* a (/ (* t -4.0) c_m))
    (if (<= a 6.8e-35)
      (/ (/ b z) c_m)
      (if (<= a 4000000000000.0)
        (* a (* t (/ -4.0 c_m)))
        (if (<= a 1.55e+91) (/ (/ b c_m) z) (* -4.0 (* t (/ a c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.35e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 6.8e-35) {
		tmp = (b / z) / c_m;
	} else if (a <= 4000000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 1.55e+91) {
		tmp = (b / c_m) / z;
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (a <= (-3.35d-35)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (a <= 6.8d-35) then
        tmp = (b / z) / c_m
    else if (a <= 4000000000000.0d0) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else if (a <= 1.55d+91) then
        tmp = (b / c_m) / z
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.35e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 6.8e-35) {
		tmp = (b / z) / c_m;
	} else if (a <= 4000000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 1.55e+91) {
		tmp = (b / c_m) / z;
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if a <= -3.35e-35:
		tmp = a * ((t * -4.0) / c_m)
	elif a <= 6.8e-35:
		tmp = (b / z) / c_m
	elif a <= 4000000000000.0:
		tmp = a * (t * (-4.0 / c_m))
	elif a <= 1.55e+91:
		tmp = (b / c_m) / z
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (a <= -3.35e-35)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (a <= 6.8e-35)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (a <= 4000000000000.0)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	elseif (a <= 1.55e+91)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (a <= -3.35e-35)
		tmp = a * ((t * -4.0) / c_m);
	elseif (a <= 6.8e-35)
		tmp = (b / z) / c_m;
	elseif (a <= 4000000000000.0)
		tmp = a * (t * (-4.0 / c_m));
	elseif (a <= 1.55e+91)
		tmp = (b / c_m) / z;
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[a, -3.35e-35], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-35], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[a, 4000000000000.0], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+91], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if a < -3.35e-35

   1. Initial program 76.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 62.5%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 62.5%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. associate-*l/ 62.5%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -3.35e-35 < a < 6.8000000000000005e-35

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 79.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 79.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 79.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 78.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 78.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 83.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 83.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 89.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in b around inf 45.8%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if 6.8000000000000005e-35 < a < 4e12

   1. Initial program 68.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 68.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 68.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 68.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 68.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 68.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 69.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 68.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 68.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 68.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 68.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 68.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 52.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 52.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 52.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 52.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 52.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 52.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 52.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. associate-*r/ 51.4%

          \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

       2. *-commutative 51.4%

          \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

       3. associate-*l* 51.4%

          \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

       4. *-commutative 51.4%

          \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

       5. associate-*r/ 51.4%

          \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

       6. *-commutative 51.4%

          \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

       7. associate-/l* 51.4%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot \frac{-4}{c}\right)} \]

   11. Simplified 51.4%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   if 4e12 < a < 1.54999999999999999e91

   1. Initial program 71.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 61.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 61.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 50.6%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if 1.54999999999999999e91 < a

   1. Initial program 82.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 80.2%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 58.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 69.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 69.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{elif}\;a \leq 125000000000:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c_m)))))
   (*
    c_s
    (if (<= a -3.4e-35)
      t_1
      (if (<= a 6.2e-32)
        (/ (/ b z) c_m)
        (if (<= a 125000000000.0)
          (* a (* t (/ -4.0 c_m)))
          (if (<= a 1.55e+91) (/ (/ b c_m) z) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (a <= -3.4e-35) {
		tmp = t_1;
	} else if (a <= 6.2e-32) {
		tmp = (b / z) / c_m;
	} else if (a <= 125000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 1.55e+91) {
		tmp = (b / c_m) / z;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c_m))
    if (a <= (-3.4d-35)) then
        tmp = t_1
    else if (a <= 6.2d-32) then
        tmp = (b / z) / c_m
    else if (a <= 125000000000.0d0) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else if (a <= 1.55d+91) then
        tmp = (b / c_m) / z
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * (t * (a / c_m));
	double tmp;
	if (a <= -3.4e-35) {
		tmp = t_1;
	} else if (a <= 6.2e-32) {
		tmp = (b / z) / c_m;
	} else if (a <= 125000000000.0) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (a <= 1.55e+91) {
		tmp = (b / c_m) / z;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * (t * (a / c_m))
	tmp = 0
	if a <= -3.4e-35:
		tmp = t_1
	elif a <= 6.2e-32:
		tmp = (b / z) / c_m
	elif a <= 125000000000.0:
		tmp = a * (t * (-4.0 / c_m))
	elif a <= 1.55e+91:
		tmp = (b / c_m) / z
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -3.4e-35)
		tmp = t_1;
	elseif (a <= 6.2e-32)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (a <= 125000000000.0)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	elseif (a <= 1.55e+91)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * (t * (a / c_m));
	tmp = 0.0;
	if (a <= -3.4e-35)
		tmp = t_1;
	elseif (a <= 6.2e-32)
		tmp = (b / z) / c_m;
	elseif (a <= 125000000000.0)
		tmp = a * (t * (-4.0 / c_m));
	elseif (a <= 1.55e+91)
		tmp = (b / c_m) / z;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -3.4e-35], t$95$1, If[LessEqual[a, 6.2e-32], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[a, 125000000000.0], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+91], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if a < -3.4000000000000003e-35 or 1.54999999999999999e91 < a

   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

      1. associate-+l- 78.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 72.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 75.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 66.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 66.7%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -3.4000000000000003e-35 < a < 6.20000000000000021e-32

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 86.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 79.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 79.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 79.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 78.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 78.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 78.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 78.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 83.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 83.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 89.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in b around inf 45.8%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if 6.20000000000000021e-32 < a < 1.25e11

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 60.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 62.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.7%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 62.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 62.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 62.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 62.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 43.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 43.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 43.4%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in t around inf 42.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. associate-*r/ 41.6%

          \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

       2. *-commutative 41.6%

          \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

       3. associate-*l* 41.6%

          \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

       4. *-commutative 41.6%

          \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

       5. associate-*r/ 41.6%

          \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

       6. *-commutative 41.6%

          \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

       7. associate-/l* 41.6%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot \frac{-4}{c}\right)} \]

   11. Simplified 41.6%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   if 1.25e11 < a < 1.54999999999999999e91

   1. Initial program 65.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 65.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 65.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 46.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+31}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m \cdot z}\\ \mathbf{elif}\;x \leq 1500000:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{b}{c\_m \cdot y} - -9 \cdot \frac{x}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= x -3.8e+31)
    (+ (* -4.0 (/ (* t a) c_m)) (* 9.0 (/ (* x y) (* c_m z))))
    (if (<= x 1500000.0)
      (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)
      (* (/ y z) (- (/ b (* c_m y)) (* -9.0 (/ x c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (x <= -3.8e+31) {
		tmp = (-4.0 * ((t * a) / c_m)) + (9.0 * ((x * y) / (c_m * z)));
	} else if (x <= 1500000.0) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (y / z) * ((b / (c_m * y)) - (-9.0 * (x / c_m)));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (x <= (-3.8d+31)) then
        tmp = ((-4.0d0) * ((t * a) / c_m)) + (9.0d0 * ((x * y) / (c_m * z)))
    else if (x <= 1500000.0d0) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    else
        tmp = (y / z) * ((b / (c_m * y)) - ((-9.0d0) * (x / c_m)))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (x <= -3.8e+31) {
		tmp = (-4.0 * ((t * a) / c_m)) + (9.0 * ((x * y) / (c_m * z)));
	} else if (x <= 1500000.0) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = (y / z) * ((b / (c_m * y)) - (-9.0 * (x / c_m)));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if x <= -3.8e+31:
		tmp = (-4.0 * ((t * a) / c_m)) + (9.0 * ((x * y) / (c_m * z)))
	elif x <= 1500000.0:
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m
	else:
		tmp = (y / z) * ((b / (c_m * y)) - (-9.0 * (x / c_m)))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (x <= -3.8e+31)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c_m)) + Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z))));
	elseif (x <= 1500000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m);
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(b / Float64(c_m * y)) - Float64(-9.0 * Float64(x / c_m))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (x <= -3.8e+31)
		tmp = (-4.0 * ((t * a) / c_m)) + (9.0 * ((x * y) / (c_m * z)));
	elseif (x <= 1500000.0)
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	else
		tmp = (y / z) * ((b / (c_m * y)) - (-9.0 * (x / c_m)));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[x, -3.8e+31], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1500000.0], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(b / N[(c$95$m * y), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if x < -3.8000000000000001e31

   1. Initial program 74.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 75.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 74.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 70.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   6. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -3.8000000000000001e31 < x < 1.5e6

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 69.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 69.9%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 69.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 69.9%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 71.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 71.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 65.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 65.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 65.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 65.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 65.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 65.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 73.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 83.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in y around 0 74.4%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - -1 \cdot \frac{b}{z}}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 74.4%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \color{blue}{\frac{-1 \cdot b}{z}}}{c} \]

       2. mul-1-neg 74.4%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{-b}}{z}}{c} \]

   12. Simplified 74.4%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{-b}{z}}{c}} \]

   if 1.5e6 < x

   1. Initial program 79.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 78.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 75.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 75.7%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 75.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 75.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 77.3%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 77.3%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 74.5%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 74.5%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 74.5%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 74.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 74.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 74.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 73.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in t around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 67.9%

          \[\leadsto \color{blue}{-\frac{y \cdot \left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)}{z}} \]

       2. distribute-neg-frac2 67.9%

          \[\leadsto \color{blue}{\frac{y \cdot \left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)}{-z}} \]

       3. *-commutative 67.9%

          \[\leadsto \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right) \cdot y}}{-z} \]

       4. *-commutative 67.9%

          \[\leadsto \frac{\left(-9 \cdot \frac{x}{c} - \frac{b}{\color{blue}{y \cdot c}}\right) \cdot y}{-z} \]

       5. associate-*r/ 67.9%

          \[\leadsto \frac{\left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{y \cdot c}\right) \cdot y}{-z} \]

       6. *-commutative 67.9%

          \[\leadsto \frac{\left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{y \cdot c}\right) \cdot y}{-z} \]

       7. associate-*r/ 67.9%

          \[\leadsto \frac{\left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{y \cdot c}\right) \cdot y}{-z} \]

       8. associate-*r/ 66.4%

          \[\leadsto \color{blue}{\left(x \cdot \frac{-9}{c} - \frac{b}{y \cdot c}\right) \cdot \frac{y}{-z}} \]

       9. associate-*r/ 66.4%

          \[\leadsto \left(\color{blue}{\frac{x \cdot -9}{c}} - \frac{b}{y \cdot c}\right) \cdot \frac{y}{-z} \]

       10. *-commutative 66.4%

           \[\leadsto \left(\frac{\color{blue}{-9 \cdot x}}{c} - \frac{b}{y \cdot c}\right) \cdot \frac{y}{-z} \]

       11. associate-*r/ 66.3%

           \[\leadsto \left(\color{blue}{-9 \cdot \frac{x}{c}} - \frac{b}{y \cdot c}\right) \cdot \frac{y}{-z} \]

       12. *-commutative 66.3%

           \[\leadsto \left(-9 \cdot \frac{x}{c} - \frac{b}{\color{blue}{c \cdot y}}\right) \cdot \frac{y}{-z} \]

   11. Simplified 66.3%

       \[\leadsto \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{-z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+31}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;x \leq 1500000:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{b}{c \cdot y} - -9 \cdot \frac{x}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3.65e+59) (not (<= z 4.5e+38)))
    (/ (+ (* -4.0 (* t a)) (/ b z)) c_m)
    (/ (+ (* x (* 9.0 y)) b) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.65e+59) || !(z <= 4.5e+38)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-3.65d+59)) .or. (.not. (z <= 4.5d+38))) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c_m
    else
        tmp = ((x * (9.0d0 * y)) + b) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3.65e+59) || !(z <= 4.5e+38)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	} else {
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -3.65e+59) or not (z <= 4.5e+38):
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m
	else:
		tmp = ((x * (9.0 * y)) + b) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3.65e+59) || !(z <= 4.5e+38))
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c_m);
	else
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -3.65e+59) || ~((z <= 4.5e+38)))
		tmp = ((-4.0 * (t * a)) + (b / z)) / c_m;
	else
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3.65e+59], N[Not[LessEqual[z, 4.5e+38]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.6500000000000001e59 or 4.4999999999999998e38 < z

   1. Initial program 59.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 59.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 59.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 59.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 59.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 59.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 59.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 64.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 64.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 71.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 71.1%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 71.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 71.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 73.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 73.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 74.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 74.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 74.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 74.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 74.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 74.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 78.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 78.8%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 80.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in y around 0 79.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - -1 \cdot \frac{b}{z}}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 79.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \color{blue}{\frac{-1 \cdot b}{z}}}{c} \]

       2. mul-1-neg 79.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{-b}}{z}}{c} \]

   12. Simplified 79.2%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{-b}{z}}{c}} \]

   if -3.6500000000000001e59 < z < 4.4999999999999998e38

   1. Initial program 94.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 93.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 91.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 91.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 78.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 78.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 78.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 78.9%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+59} \lor \neg \left(z \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+174}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= a -3.4e-35)
    (* a (/ (* t -4.0) c_m))
    (if (<= a 3.4e+174)
      (/ (+ (* x (* 9.0 y)) b) (* c_m z))
      (* -4.0 (* t (/ a c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.4e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 3.4e+174) {
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (a <= (-3.4d-35)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (a <= 3.4d+174) then
        tmp = ((x * (9.0d0 * y)) + b) / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (a <= -3.4e-35) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 3.4e+174) {
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if a <= -3.4e-35:
		tmp = a * ((t * -4.0) / c_m)
	elif a <= 3.4e+174:
		tmp = ((x * (9.0 * y)) + b) / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (a <= -3.4e-35)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (a <= 3.4e+174)
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (a <= -3.4e-35)
		tmp = a * ((t * -4.0) / c_m);
	elseif (a <= 3.4e+174)
		tmp = ((x * (9.0 * y)) + b) / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[a, -3.4e-35], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+174], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < -3.4000000000000003e-35

   1. Initial program 76.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 70.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 62.5%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 62.5%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. associate-*l/ 62.5%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -3.4000000000000003e-35 < a < 3.4000000000000001e174

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 83.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 83.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.4%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 70.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 70.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 70.5%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 3.4000000000000001e174 < a

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 85.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 85.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 85.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 84.8%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 70.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 77.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 77.6%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+174}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\frac{b}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (* c_s (if (<= b -5.2e+234) (/ (/ b z) c_m) (/ (/ b c_m) z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5.2e+234) {
		tmp = (b / z) / c_m;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-5.2d+234)) then
        tmp = (b / z) / c_m
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -5.2e+234) {
		tmp = (b / z) / c_m;
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -5.2e+234:
		tmp = (b / z) / c_m
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -5.2e+234)
		tmp = Float64(Float64(b / z) / c_m);
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -5.2e+234)
		tmp = (b / z) / c_m;
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -5.2e+234], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000003e234

   1. Initial program 89.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 89.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 89.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 78.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 56.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 56.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 56.9%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 56.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 56.9%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 56.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 56.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 62.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 62.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 62.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 62.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 62.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 61.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 56.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 84.5%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in b around inf 79.1%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if -5.2000000000000003e234 < b

   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

      1. associate-+l- 78.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 79.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 30.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 32.4%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 34.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{\frac{b}{c\_m}}{z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ (/ b c_m) z)))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * ((b / c_m) / z);
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    code = c_s * ((b / c_m) / z)
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * ((b / c_m) / z);
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * ((b / c_m) / z)

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(Float64(b / c_m) / z))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * ((b / c_m) / z);
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 79.3%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 79.3%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 79.0%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 79.8%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 79.8%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 79.8%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 32.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. associate-/r* 33.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Simplified 33.9%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
8. Add Preprocessing

Alternative 22: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 79.3%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 79.3%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 79.0%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 79.8%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 79.8%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 79.8%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 32.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 32.8%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 32.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 32.8%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer target: 80.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (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)))