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

Percentage Accurate: 78.8% → 86.2%

Time: 15.1s

Alternatives: 12

Speedup: 0.5×

• 36.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 78.8% 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: 86.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 2.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{\mathsf{fma}\left(\frac{9}{z}, x \cdot \frac{y}{c\_m}, \frac{b}{c\_m \cdot z}\right)}{t} - \frac{a}{c\_m} \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 2.5e+74)
    (/ (+ (- (* x (* 9.0 y)) (* (* z 4.0) (* t a))) b) (* c_m z))
    (*
     t
     (-
      (/ (fma (/ 9.0 z) (* x (/ y c_m)) (/ b (* c_m z))) t)
      (* (/ a c_m) 4.0))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
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 <= 2.5e+74) {
		tmp = (((x * (9.0 * y)) - ((z * 4.0) * (t * a))) + b) / (c_m * z);
	} else {
		tmp = t * ((fma((9.0 / z), (x * (y / c_m)), (b / (c_m * z))) / t) - ((a / c_m) * 4.0));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 2.5e+74)
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(c_m * z));
	else
		tmp = Float64(t * Float64(Float64(fma(Float64(9.0 / z), Float64(x * Float64(y / c_m)), Float64(b / Float64(c_m * z))) / t) - Float64(Float64(a / c_m) * 4.0)));
	end
	return Float64(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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 2.5e+74], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(N[(9.0 / z), $MachinePrecision] * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(a / c$95$m), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 2.49999999999999982e74

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*r* 82.4%

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

      4. *-commutative 82.4%

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

      5. associate-+l- 82.4%

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

      6. associate-*l* 82.4%

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

      7. associate-*l* 86.0%

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

      8. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   if 2.49999999999999982e74 < c

   1. Initial program 70.9%

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

      1. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 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%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in t around -inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   7. Simplified 83.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{\mathsf{fma}\left(\frac{9}{z}, x \cdot \frac{y}{c}, \frac{b}{c \cdot z}\right)}{t} - \frac{a}{c} \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.9% accurate, 0.5× speedup

Math

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

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<=
       (/ (+ b (- (* y (* x 9.0)) (* a (* (* z 4.0) t)))) (* c_m z))
       INFINITY)
    (/ (+ (- (* x (* 9.0 y)) (* (* z 4.0) (* t a))) b) (* c_m z))
    (* a (/ (* t -4.0) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (((b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)) <= ((double) INFINITY)) {
		tmp = (((x * (9.0 * y)) - ((z * 4.0) * (t * a))) + b) / (c_m * z);
	} 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);
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 + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)) <= Double.POSITIVE_INFINITY) {
		tmp = (((x * (9.0 * y)) - ((z * 4.0) * (t * a))) + b) / (c_m * z);
	} 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)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if ((b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)) <= math.inf:
		tmp = (((x * (9.0 * y)) - ((z * 4.0) * (t * a))) + b) / (c_m * z)
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(Float64(z * 4.0) * t)))) / Float64(c_m * z)) <= Inf)
		tmp = Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(c_m * z));
	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);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (((b + ((y * (x * 9.0)) - (a * ((z * 4.0) * t)))) / (c_m * z)) <= Inf)
		tmp = (((x * (9.0 * y)) - ((z * 4.0) * (t * a))) + b) / (c_m * z);
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[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], Infinity], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-*r* 86.6%

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

      4. *-commutative 86.6%

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

      5. associate-+l- 86.6%

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

      6. associate-*l* 86.6%

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

      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

   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* 5.0%

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

      4. *-commutative 5.0%

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

      5. associate-+l- 5.0%

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

   3. Simplified 5.0%

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

   5. Taylor expanded in t around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 70.5%

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

      3. associate-*r* 70.5%

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

      4. *-commutative 70.5%

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

      5. *-commutative 70.5%

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

      6. associate-*l/ 70.5%

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

   7. Simplified 70.5%

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

4. Final simplification 87.5%

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

Alternative 3: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-162}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;b \leq 0.00285:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c\_m}{b}}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -2.1e+40)
    (/ (/ b c_m) z)
    (if (<= b -1e-162)
      (* 9.0 (* x (/ y (* c_m z))))
      (if (<= b 2.2e-215)
        (* -4.0 (/ (* t a) c_m))
        (if (<= b 0.00285)
          (* 9.0 (* x (/ (/ y c_m) z)))
          (/ 1.0 (* z (/ c_m b)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -2.1e+40) {
		tmp = (b / c_m) / z;
	} else if (b <= -1e-162) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= 2.2e-215) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (b <= 0.00285) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-2.1d+40)) then
        tmp = (b / c_m) / z
    else if (b <= (-1d-162)) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (b <= 2.2d-215) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (b <= 0.00285d0) then
        tmp = 9.0d0 * (x * ((y / c_m) / z))
    else
        tmp = 1.0d0 / (z * (c_m / b))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
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 <= -2.1e+40) {
		tmp = (b / c_m) / z;
	} else if (b <= -1e-162) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= 2.2e-215) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (b <= 0.00285) {
		tmp = 9.0 * (x * ((y / c_m) / z));
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -2.1e+40:
		tmp = (b / c_m) / z
	elif b <= -1e-162:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif b <= 2.2e-215:
		tmp = -4.0 * ((t * a) / c_m)
	elif b <= 0.00285:
		tmp = 9.0 * (x * ((y / c_m) / z))
	else:
		tmp = 1.0 / (z * (c_m / b))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -2.1e+40)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= -1e-162)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (b <= 2.2e-215)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (b <= 0.00285)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c_m) / z)));
	else
		tmp = Float64(1.0 / Float64(z * Float64(c_m / b)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -2.1e+40)
		tmp = (b / c_m) / z;
	elseif (b <= -1e-162)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (b <= 2.2e-215)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (b <= 0.00285)
		tmp = 9.0 * (x * ((y / c_m) / z));
	else
		tmp = 1.0 / (z * (c_m / b));
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -2.1e+40], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -1e-162], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-215], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00285], N[(9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(c$95$m / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if b < -2.1000000000000001e40

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-+l- 85.8%

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

      6. associate-*l* 85.8%

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

      7. associate-*l* 87.4%

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

      8. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in t around inf 84.0%

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

   6. Taylor expanded in b around inf 63.9%

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

      1. associate-/r* 66.1%

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

   8. Simplified 66.1%

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

   if -2.1000000000000001e40 < b < -9.99999999999999954e-163

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-+l- 71.7%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in x around inf 46.5%

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

      1. associate-/l* 51.3%

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

      2. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   if -9.99999999999999954e-163 < b < 2.19999999999999996e-215

   1. Initial program 84.6%

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

      1. associate-+l- 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*r* 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-+l- 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around inf 58.4%

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

   if 2.19999999999999996e-215 < b < 0.0028500000000000001

   1. Initial program 74.8%

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

      1. associate-+l- 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r* 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%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-/l* 59.7%

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

      3. associate-*l* 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*r/ 59.8%

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

      6. *-commutative 59.8%

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

      7. associate-/l* 59.3%

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

      8. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in x around 0 51.5%

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

      1. associate-/l* 59.7%

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

      2. associate-/r* 60.3%

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

   10. Simplified 60.3%

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

   if 0.0028500000000000001 < b

   1. Initial program 86.3%

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

      1. associate-+l- 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*r* 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-+l- 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in b around inf 63.4%

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

      1. *-commutative 63.4%

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

   7. Simplified 63.4%

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

      1. clear-num 63.5%

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

      2. inv-pow 63.5%

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

   9. Applied egg-rr 63.5%

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

       1. unpow-1 63.5%

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

       2. associate-/l* 64.8%

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

   11. Simplified 64.8%

       \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{c}{b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-162}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;b \leq 0.00285:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+156}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c\_m}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -4.7e+156)
    (* (* a -4.0) (/ t c_m))
    (if (<= t -2.6e+36)
      (/ (+ b (* t (* z (* a -4.0)))) (* c_m z))
      (if (<= t 1.35e-21)
        (/ (+ b (* y (* x 9.0))) (* c_m z))
        (* a (/ (* t -4.0) c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -4.7e+156) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= -2.6e+36) {
		tmp = (b + (t * (z * (a * -4.0)))) / (c_m * z);
	} else if (t <= 1.35e-21) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-4.7d+156)) then
        tmp = (a * (-4.0d0)) * (t / c_m)
    else if (t <= (-2.6d+36)) then
        tmp = (b + (t * (z * (a * (-4.0d0))))) / (c_m * z)
    else if (t <= 1.35d-21) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    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);
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 <= -4.7e+156) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= -2.6e+36) {
		tmp = (b + (t * (z * (a * -4.0)))) / (c_m * z);
	} else if (t <= 1.35e-21) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} 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)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -4.7e+156:
		tmp = (a * -4.0) * (t / c_m)
	elif t <= -2.6e+36:
		tmp = (b + (t * (z * (a * -4.0)))) / (c_m * z)
	elif t <= 1.35e-21:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -4.7e+156)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c_m));
	elseif (t <= -2.6e+36)
		tmp = Float64(Float64(b + Float64(t * Float64(z * Float64(a * -4.0)))) / Float64(c_m * z));
	elseif (t <= 1.35e-21)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	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);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -4.7e+156)
		tmp = (a * -4.0) * (t / c_m);
	elseif (t <= -2.6e+36)
		tmp = (b + (t * (z * (a * -4.0)))) / (c_m * z);
	elseif (t <= 1.35e-21)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -4.7e+156], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e+36], N[(N[(b + N[(t * N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-21], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -4.7e156

   1. Initial program 67.4%

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

      1. associate-+l- 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*r* 71.0%

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

      4. *-commutative 71.0%

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

      5. associate-+l- 71.0%

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

      6. associate-*l* 71.0%

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

      7. associate-*l* 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 t around inf 70.9%

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

   6. Taylor expanded in t around inf 64.5%

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

      1. associate-*r/ 70.7%

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

      2. associate-*r* 70.7%

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

   8. Simplified 70.7%

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

   if -4.7e156 < t < -2.6000000000000001e36

   1. Initial program 80.9%

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

      1. associate-+l- 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-*r* 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* 80.9%

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

      7. associate-*l* 70.9%

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

      8. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in t around inf 80.9%

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

   6. Taylor expanded in x around 0 69.9%

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

      1. associate-*r* 69.9%

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

   8. Simplified 69.9%

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

   if -2.6000000000000001e36 < t < 1.3500000000000001e-21

   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* 83.0%

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

      4. *-commutative 83.0%

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

      5. associate-+l- 83.0%

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

      6. associate-*l* 83.0%

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

      7. associate-*l* 88.6%

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

      8. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in z around inf 87.1%

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

   6. Taylor expanded in z around 0 74.5%

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

      1. associate-*r* 74.5%

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

   8. Simplified 74.5%

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

   if 1.3500000000000001e-21 < t

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in t around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-/l* 48.3%

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

      3. associate-*r* 48.3%

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

      4. *-commutative 48.3%

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

      5. *-commutative 48.3%

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

      6. associate-*l/ 48.3%

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

   7. Simplified 48.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+156}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+33} \lor \neg \left(t \leq 1.2 \cdot 10^{-100}\right):\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m} + \frac{b}{z \cdot \left(c\_m \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= t -4.9e+33) (not (<= t 1.2e-100)))
    (* a (+ (* -4.0 (/ t c_m)) (/ b (* z (* c_m a)))))
    (/ (+ b (* y (* x 9.0))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -4.9e+33) || !(t <= 1.2e-100)) {
		tmp = a * ((-4.0 * (t / c_m)) + (b / (z * (c_m * a))));
	} else {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-4.9d+33)) .or. (.not. (t <= 1.2d-100))) then
        tmp = a * (((-4.0d0) * (t / c_m)) + (b / (z * (c_m * a))))
    else
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
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 <= -4.9e+33) || !(t <= 1.2e-100)) {
		tmp = a * ((-4.0 * (t / c_m)) + (b / (z * (c_m * a))));
	} else {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (t <= -4.9e+33) or not (t <= 1.2e-100):
		tmp = a * ((-4.0 * (t / c_m)) + (b / (z * (c_m * a))))
	else:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((t <= -4.9e+33) || !(t <= 1.2e-100))
		tmp = Float64(a * Float64(Float64(-4.0 * Float64(t / c_m)) + Float64(b / Float64(z * Float64(c_m * a)))));
	else
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((t <= -4.9e+33) || ~((t <= 1.2e-100)))
		tmp = a * ((-4.0 * (t / c_m)) + (b / (z * (c_m * a))));
	else
		tmp = (b + (y * (x * 9.0))) / (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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[t, -4.9e+33], N[Not[LessEqual[t, 1.2e-100]], $MachinePrecision]], N[(a * N[(N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * N[(c$95$m * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -4.90000000000000014e33 or 1.2000000000000001e-100 < t

   1. Initial program 76.0%

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

      1. associate-+l- 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r* 78.9%

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

      4. *-commutative 78.9%

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

      5. associate-+l- 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in x around inf 66.2%

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

   6. Taylor expanded in a around inf 66.4%

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

   7. Taylor expanded in x around 0 67.1%

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

      1. associate-*r* 65.7%

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

   9. Simplified 65.7%

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

   if -4.90000000000000014e33 < t < 1.2000000000000001e-100

   1. Initial program 86.1%

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

      1. associate-+l- 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

      6. associate-*l* 81.8%

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

      7. associate-*l* 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 z around inf 85.9%

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

   6. Taylor expanded in z around 0 77.0%

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

      1. associate-*r* 76.9%

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

   8. Simplified 76.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+33} \lor \neg \left(t \leq 1.2 \cdot 10^{-100}\right):\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c} + \frac{b}{z \cdot \left(c \cdot a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + z \cdot \left(t \cdot \left(a \cdot -4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - \left(t \cdot a\right) \cdot 4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(z \cdot t\right)\right) \cdot 4}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -9e+38)
    (/ (+ b (* z (* t (* a -4.0)))) (* c_m z))
    (if (<= b 28500000.0)
      (/ (- (* 9.0 (/ (* x y) z)) (* (* t a) 4.0)) c_m)
      (/ (- b (* (* a (* z t)) 4.0)) (* c_m z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -9e+38) {
		tmp = (b + (z * (t * (a * -4.0)))) / (c_m * z);
	} else if (b <= 28500000.0) {
		tmp = ((9.0 * ((x * y) / z)) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = (b - ((a * (z * t)) * 4.0)) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-9d+38)) then
        tmp = (b + (z * (t * (a * (-4.0d0))))) / (c_m * z)
    else if (b <= 28500000.0d0) then
        tmp = ((9.0d0 * ((x * y) / z)) - ((t * a) * 4.0d0)) / c_m
    else
        tmp = (b - ((a * (z * t)) * 4.0d0)) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
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 <= -9e+38) {
		tmp = (b + (z * (t * (a * -4.0)))) / (c_m * z);
	} else if (b <= 28500000.0) {
		tmp = ((9.0 * ((x * y) / z)) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = (b - ((a * (z * t)) * 4.0)) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -9e+38:
		tmp = (b + (z * (t * (a * -4.0)))) / (c_m * z)
	elif b <= 28500000.0:
		tmp = ((9.0 * ((x * y) / z)) - ((t * a) * 4.0)) / c_m
	else:
		tmp = (b - ((a * (z * t)) * 4.0)) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -9e+38)
		tmp = Float64(Float64(b + Float64(z * Float64(t * Float64(a * -4.0)))) / Float64(c_m * z));
	elseif (b <= 28500000.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(Float64(t * a) * 4.0)) / c_m);
	else
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(z * t)) * 4.0)) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -9e+38)
		tmp = (b + (z * (t * (a * -4.0)))) / (c_m * z);
	elseif (b <= 28500000.0)
		tmp = ((9.0 * ((x * y) / z)) - ((t * a) * 4.0)) / c_m;
	else
		tmp = (b - ((a * (z * t)) * 4.0)) / (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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -9e+38], N[(N[(b + N[(z * N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 28500000.0], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b - N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -8.99999999999999961e38

   1. Initial program 84.1%

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

      1. associate-+l- 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-+l- 86.0%

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

      6. associate-*l* 86.0%

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

      7. associate-*l* 87.7%

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

      8. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around inf 85.9%

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

   6. Taylor expanded in x around 0 79.0%

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

      1. associate-*r* 79.0%

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

   8. Simplified 79.0%

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

   if -8.99999999999999961e38 < b < 2.85e7

   1. Initial program 77.0%

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

      1. associate-+l- 77.0%

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

      2. *-commutative 77.0%

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

      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* 80.9%

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

      8. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 80.2%

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

   6. Taylor expanded in b around 0 82.6%

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

   if 2.85e7 < b

   1. Initial program 86.3%

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

      1. associate-+l- 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*r* 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-+l- 81.3%

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

      6. associate-*l* 81.3%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around 0 78.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + z \cdot \left(t \cdot \left(a \cdot -4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - \left(t \cdot a\right) \cdot 4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(z \cdot t\right)\right) \cdot 4}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-163}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c\_m}{b}}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -1.02e+40)
    (/ (/ b c_m) z)
    (if (<= b -6.8e-163)
      (* 9.0 (* x (/ y (* c_m z))))
      (if (<= b 4e-13) (* -4.0 (/ (* t a) c_m)) (/ 1.0 (* z (/ c_m b))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -1.02e+40) {
		tmp = (b / c_m) / z;
	} else if (b <= -6.8e-163) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= 4e-13) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-1.02d+40)) then
        tmp = (b / c_m) / z
    else if (b <= (-6.8d-163)) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (b <= 4d-13) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = 1.0d0 / (z * (c_m / b))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
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 <= -1.02e+40) {
		tmp = (b / c_m) / z;
	} else if (b <= -6.8e-163) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (b <= 4e-13) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -1.02e+40:
		tmp = (b / c_m) / z
	elif b <= -6.8e-163:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif b <= 4e-13:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = 1.0 / (z * (c_m / b))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -1.02e+40)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= -6.8e-163)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (b <= 4e-13)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(1.0 / Float64(z * Float64(c_m / b)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -1.02e+40)
		tmp = (b / c_m) / z;
	elseif (b <= -6.8e-163)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (b <= 4e-13)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = 1.0 / (z * (c_m / b));
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -1.02e+40], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -6.8e-163], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-13], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(c$95$m / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if b < -1.02e40

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-+l- 85.8%

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

      6. associate-*l* 85.8%

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

      7. associate-*l* 87.4%

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

      8. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in t around inf 84.0%

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

   6. Taylor expanded in b around inf 63.9%

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

      1. associate-/r* 66.1%

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

   8. Simplified 66.1%

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

   if -1.02e40 < b < -6.80000000000000028e-163

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-+l- 71.7%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in x around inf 46.5%

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

      1. associate-/l* 51.3%

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

      2. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   if -6.80000000000000028e-163 < b < 4.0000000000000001e-13

   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* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in t around inf 53.5%

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

   if 4.0000000000000001e-13 < b

   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* 82.2%

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

      4. *-commutative 82.2%

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

      5. associate-+l- 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in b around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

      1. clear-num 63.6%

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

      2. inv-pow 63.6%

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

   9. Applied egg-rr 63.6%

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

       1. unpow-1 63.6%

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

       2. associate-/l* 64.9%

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

   11. Simplified 64.9%

       \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{c}{b}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-163}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c\_m}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -1.45e+77)
    (* (* a -4.0) (/ t c_m))
    (if (<= t 1.3e-22)
      (/ (+ b (* y (* x 9.0))) (* c_m z))
      (* a (/ (* t -4.0) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -1.45e+77) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= 1.3e-22) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-1.45d+77)) then
        tmp = (a * (-4.0d0)) * (t / c_m)
    else if (t <= 1.3d-22) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    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);
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 <= -1.45e+77) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= 1.3e-22) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} 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)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -1.45e+77:
		tmp = (a * -4.0) * (t / c_m)
	elif t <= 1.3e-22:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -1.45e+77)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c_m));
	elseif (t <= 1.3e-22)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	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);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -1.45e+77)
		tmp = (a * -4.0) * (t / c_m);
	elseif (t <= 1.3e-22)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -1.45e+77], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-22], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.4500000000000001e77

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-+l- 75.3%

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

      6. associate-*l* 75.3%

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

      7. associate-*l* 75.0%

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

      8. *-commutative 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in t around inf 75.2%

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

   6. Taylor expanded in t around inf 64.1%

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

      1. associate-*r/ 66.2%

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

      2. associate-*r* 66.2%

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

   8. Simplified 66.2%

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

   if -1.4500000000000001e77 < t < 1.3e-22

   1. Initial program 86.5%

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

      1. associate-+l- 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 82.5%

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

      4. *-commutative 82.5%

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

      5. associate-+l- 82.5%

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

      6. associate-*l* 82.5%

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

      7. associate-*l* 87.1%

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

      8. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in z around inf 85.7%

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

   6. Taylor expanded in z around 0 73.7%

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

      1. associate-*r* 73.7%

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

   8. Simplified 73.7%

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

   if 1.3e-22 < t

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in t around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-/l* 48.3%

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

      3. associate-*r* 48.3%

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

      4. *-commutative 48.3%

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

      5. *-commutative 48.3%

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

      6. associate-*l/ 48.3%

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

   7. Simplified 48.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c\_m}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -1.75e+77)
    (* (* a -4.0) (/ t c_m))
    (if (<= t 1.2e-21)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (* a (/ (* t -4.0) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -1.75e+77) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= 1.2e-21) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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 <= (-1.75d+77)) then
        tmp = (a * (-4.0d0)) * (t / c_m)
    else if (t <= 1.2d-21) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    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);
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 <= -1.75e+77) {
		tmp = (a * -4.0) * (t / c_m);
	} else if (t <= 1.2e-21) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} 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)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -1.75e+77:
		tmp = (a * -4.0) * (t / c_m)
	elif t <= 1.2e-21:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	else:
		tmp = a * ((t * -4.0) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -1.75e+77)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c_m));
	elseif (t <= 1.2e-21)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	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);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -1.75e+77)
		tmp = (a * -4.0) * (t / c_m);
	elseif (t <= 1.2e-21)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -1.75e+77], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-21], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.7500000000000001e77

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-+l- 75.3%

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

      6. associate-*l* 75.3%

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

      7. associate-*l* 75.0%

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

      8. *-commutative 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in t around inf 75.2%

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

   6. Taylor expanded in t around inf 64.1%

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

      1. associate-*r/ 66.2%

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

      2. associate-*r* 66.2%

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

   8. Simplified 66.2%

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

   if -1.7500000000000001e77 < t < 1.2e-21

   1. Initial program 86.5%

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

      1. associate-+l- 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 82.5%

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

      4. *-commutative 82.5%

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

      5. associate-+l- 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   if 1.2e-21 < t

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in t around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-/l* 48.3%

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

      3. associate-*r* 48.3%

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

      4. *-commutative 48.3%

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

      5. *-commutative 48.3%

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

      6. associate-*l/ 48.3%

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

   7. Simplified 48.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-28} \lor \neg \left(b \leq 3.7 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= b -4e-28) (not (<= b 3.7e-20)))
    (/ (/ b c_m) z)
    (* -4.0 (/ (* t a) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((b <= -4e-28) || !(b <= 3.7e-20)) {
		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)
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 <= (-4d-28)) .or. (.not. (b <= 3.7d-20))) 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);
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 <= -4e-28) || !(b <= 3.7e-20)) {
		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)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (b <= -4e-28) or not (b <= 3.7e-20):
		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)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((b <= -4e-28) || !(b <= 3.7e-20))
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((b <= -4e-28) || ~((b <= 3.7e-20)))
		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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[b, -4e-28], N[Not[LessEqual[b, 3.7e-20]], $MachinePrecision]], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if b < -3.99999999999999988e-28 or 3.7000000000000001e-20 < b

   1. Initial program 85.0%

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

      1. associate-+l- 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*r* 83.7%

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

      4. *-commutative 83.7%

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

      5. associate-+l- 83.7%

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

      6. associate-*l* 83.7%

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

      7. associate-*l* 84.2%

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

      8. *-commutative 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in t around inf 81.5%

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

   6. Taylor expanded in b around inf 60.2%

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

      1. associate-/r* 61.1%

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

   8. Simplified 61.1%

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

   if -3.99999999999999988e-28 < b < 3.7000000000000001e-20

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around inf 48.8%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-28} \lor \neg \left(b \leq 3.7 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c\_m}{b}}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -5.2e-28)
    (/ (/ b c_m) z)
    (if (<= b 7.5e-16) (* -4.0 (/ (* t a) c_m)) (/ 1.0 (* z (/ c_m b)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
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-28) {
		tmp = (b / c_m) / z;
	} else if (b <= 7.5e-16) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
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-28)) then
        tmp = (b / c_m) / z
    else if (b <= 7.5d-16) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = 1.0d0 / (z * (c_m / b))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
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-28) {
		tmp = (b / c_m) / z;
	} else if (b <= 7.5e-16) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 1.0 / (z * (c_m / b));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -5.2e-28:
		tmp = (b / c_m) / z
	elif b <= 7.5e-16:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = 1.0 / (z * (c_m / b))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -5.2e-28)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= 7.5e-16)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(1.0 / Float64(z * Float64(c_m / b)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -5.2e-28)
		tmp = (b / c_m) / z;
	elseif (b <= 7.5e-16)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = 1.0 / (z * (c_m / b));
	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]
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -5.2e-28], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 7.5e-16], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(c$95$m / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -5.2e-28

   1. Initial program 83.3%

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

      1. associate-+l- 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*r* 84.9%

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

      4. *-commutative 84.9%

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

      5. associate-+l- 84.9%

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

      6. associate-*l* 84.9%

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

      7. associate-*l* 86.1%

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

      8. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in t around inf 82.2%

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

   6. Taylor expanded in b around inf 57.4%

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

      1. associate-/r* 58.8%

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

   8. Simplified 58.8%

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

   if -5.2e-28 < b < 7.5e-16

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around inf 48.8%

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

   if 7.5e-16 < b

   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* 82.2%

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

      4. *-commutative 82.2%

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

      5. associate-+l- 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in b around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

      1. clear-num 63.6%

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

      2. inv-pow 63.6%

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

   9. Applied egg-rr 63.6%

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

       1. unpow-1 63.6%

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

       2. associate-/l* 64.9%

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

   11. Simplified 64.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
(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);
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)
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);
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)
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)
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);
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]
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 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* 80.3%

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

   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%

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

3. Simplified 80.3%

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

5. Taylor expanded in b around inf 37.0%

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

   1. *-commutative 37.0%

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

7. Simplified 37.0%

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

8. Final simplification 37.0%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer Target 1: 80.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

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