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

Percentage Accurate: 79.5% → 94.2%

Time: 17.2s

Alternatives: 19

Speedup: 0.8×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% 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: 94.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+29} \lor \neg \left(z \leq 1.9 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z} + \frac{y}{z} \cdot \left(9 \cdot x\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.55e+29) (not (<= z 1.9e-37)))
   (/ (fma (* -4.0 a) t (+ (/ b z) (* (/ y z) (* 9.0 x)))) c)
   (/ (fma x (* 9.0 y) (+ b (* t (* a (* z -4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.55e+29) || !(z <= 1.9e-37)) {
		tmp = fma((-4.0 * a), t, ((b / z) + ((y / z) * (9.0 * x)))) / c;
	} else {
		tmp = fma(x, (9.0 * y), (b + (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.55e+29) || !(z <= 1.9e-37))
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(Float64(b / z) + Float64(Float64(y / z) * Float64(9.0 * x)))) / c);
	else
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.55e+29], N[Not[LessEqual[z, 1.9e-37]], $MachinePrecision]], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(b / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.55e29 or 1.9000000000000002e-37 < z

   1. Initial program 63.2%

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

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in x around 0 74.5%

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

      1. cancel-sign-sub-inv 74.5%

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

      2. metadata-eval 74.5%

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

      3. +-commutative 74.5%

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

      4. *-commutative 74.5%

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

      5. fma-def 74.5%

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

      6. associate-/l* 75.7%

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

      7. associate-/r/ 76.2%

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

      8. fma-def 76.2%

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

      9. times-frac 83.8%

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

      10. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in c around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. div-inv 84.8%

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

      3. fma-def 84.8%

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

      4. associate-*r/ 84.8%

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

      5. associate-*r* 84.8%

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

   9. Applied egg-rr 84.8%

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

       1. associate-*r* 84.8%

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

       2. fma-def 84.8%

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

       3. fma-udef 84.8%

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

       4. div-inv 84.8%

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

       5. associate-*r/ 88.9%

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

   11. Applied egg-rr 88.9%

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

   if -2.55e29 < z < 1.9000000000000002e-37

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate-*l* 97.2%

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

      3. fma-neg 98.0%

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

      4. neg-sub0 98.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      5. associate-+l- 98.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      6. neg-sub0 98.0%

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

      7. +-commutative 98.0%

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

      8. distribute-rgt-neg-out 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 97.2%

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

      11. distribute-rgt-neg-in 97.2%

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

      12. *-commutative 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-rgt-neg-in 97.2%

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

      15. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+29} \lor \neg \left(z \leq 1.9 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z} + \frac{y}{z} \cdot \left(9 \cdot x\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29} \lor \neg \left(z \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.2e+29) (not (<= z 5e-37)))
   (/ (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* x y) z)))) c)
   (/ (fma x (* 9.0 y) (+ b (* t (* a (* z -4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.2e+29) || !(z <= 5e-37)) {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	} else {
		tmp = fma(x, (9.0 * y), (b + (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.2e+29) || !(z <= 5e-37))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z)))) / c);
	else
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.2e+29], N[Not[LessEqual[z, 5e-37]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e29 or 4.9999999999999997e-37 < z

   1. Initial program 63.2%

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

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in x around 0 74.5%

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

      1. cancel-sign-sub-inv 74.5%

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

      2. metadata-eval 74.5%

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

      3. +-commutative 74.5%

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

      4. *-commutative 74.5%

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

      5. fma-def 74.5%

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

      6. associate-/l* 75.7%

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

      7. associate-/r/ 76.2%

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

      8. fma-def 76.2%

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

      9. times-frac 83.8%

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

      10. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in c around 0 84.8%

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

   if -1.2e29 < z < 4.9999999999999997e-37

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate-*l* 97.2%

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

      3. fma-neg 98.0%

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

      4. neg-sub0 98.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

      5. associate-+l- 98.0%

         \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

      6. neg-sub0 98.0%

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

      7. +-commutative 98.0%

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

      8. distribute-rgt-neg-out 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 97.2%

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

      11. distribute-rgt-neg-in 97.2%

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

      12. *-commutative 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-rgt-neg-in 97.2%

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

      15. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29} \lor \neg \left(z \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+255}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+255)))
     (* 9.0 (* (/ y z) (/ x c)))
     (/ (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* x y) z)))) c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+255)) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+255)) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+255):
		tmp = 9.0 * ((y / z) * (x / c))
	else:
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+255))
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z)))) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+255)))
		tmp = 9.0 * ((y / z) * (x / c));
	else
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+255]], $MachinePrecision]], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x 9) y) < -inf.0 or 1.99999999999999998e255 < (*.f64 (*.f64 x 9) y)

   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* 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-+l- 67.5%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in x around inf 67.6%

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

      1. times-frac 94.5%

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

   6. Simplified 94.5%

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

   if -inf.0 < (*.f64 (*.f64 x 9) y) < 1.99999999999999998e255

   1. Initial program 80.4%

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

      1. associate-+l- 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-+l- 77.4%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in x around 0 81.3%

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

      1. cancel-sign-sub-inv 81.3%

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

      2. metadata-eval 81.3%

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

      3. +-commutative 81.3%

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

      4. *-commutative 81.3%

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

      5. fma-def 81.3%

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

      6. associate-/l* 82.5%

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

      7. associate-/r/ 83.3%

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

      8. fma-def 83.3%

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

      9. times-frac 84.5%

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

      10. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in c around 0 88.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -\infty \lor \neg \left(y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+255}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \end{array} \]

Alternative 4: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+139}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.35e+139)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (if (<= t -4.1e+105)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= t -5.5e+85)
       (+ (* -4.0 (/ (* a t) c)) (* 9.0 (/ (* x y) (* z c))))
       (if (<= t 1.35e-23)
         (/ (- (/ b z) (* x (* (/ y z) -9.0))) c)
         (* -4.0 (/ a (/ c t))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.35e+139) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (t <= -4.1e+105) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t <= -5.5e+85) {
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((x * y) / (z * c)));
	} else if (t <= 1.35e-23) {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.35d+139)) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else if (t <= (-4.1d+105)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (t <= (-5.5d+85)) then
        tmp = ((-4.0d0) * ((a * t) / c)) + (9.0d0 * ((x * y) / (z * c)))
    else if (t <= 1.35d-23) then
        tmp = ((b / z) - (x * ((y / z) * (-9.0d0)))) / c
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.35e+139) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (t <= -4.1e+105) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t <= -5.5e+85) {
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((x * y) / (z * c)));
	} else if (t <= 1.35e-23) {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.35e+139:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	elif t <= -4.1e+105:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif t <= -5.5e+85:
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((x * y) / (z * c)))
	elif t <= 1.35e-23:
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.35e+139)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (t <= -4.1e+105)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t <= -5.5e+85)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c))));
	elseif (t <= 1.35e-23)
		tmp = Float64(Float64(Float64(b / z) - Float64(x * Float64(Float64(y / z) * -9.0))) / c);
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.35e+139)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	elseif (t <= -4.1e+105)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (t <= -5.5e+85)
		tmp = (-4.0 * ((a * t) / c)) + (9.0 * ((x * y) / (z * c)));
	elseif (t <= 1.35e-23)
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.35e+139], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -4.1e+105], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e+85], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-23], N[(N[(N[(b / z), $MachinePrecision] - N[(x * N[(N[(y / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.3499999999999999e139

   1. Initial program 83.2%

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

      1. associate-+l- 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*r* 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-+l- 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 87.4%

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

      1. cancel-sign-sub-inv 87.4%

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

      2. metadata-eval 87.4%

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

      3. +-commutative 87.4%

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

      4. *-commutative 87.4%

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

      5. fma-def 87.4%

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

      6. associate-/l* 79.0%

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

      7. associate-/r/ 83.4%

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

      8. fma-def 83.4%

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

      9. times-frac 87.7%

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

      10. *-commutative 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in c around 0 91.6%

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

   8. Taylor expanded in b around 0 88.0%

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

   if -1.3499999999999999e139 < t < -4.1000000000000002e105

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 87.5%

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

   if -4.1000000000000002e105 < t < -5.50000000000000008e85

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-+l- 99.7%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.7%

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

      1. cancel-sign-sub-inv 99.7%

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

      2. metadata-eval 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

      6. associate-/l* 99.7%

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

      7. associate-/r/ 99.7%

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

      8. fma-def 99.7%

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

      9. times-frac 99.7%

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

      10. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in b around 0 99.7%

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

   if -5.50000000000000008e85 < t < 1.34999999999999992e-23

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 76.7%

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

      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 80.6%

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

   4. Taylor expanded in x around 0 77.8%

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

      1. cancel-sign-sub-inv 77.8%

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

      2. metadata-eval 77.8%

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

      3. +-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. fma-def 77.8%

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

      6. associate-/l* 74.6%

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

      7. associate-/r/ 74.0%

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

      8. fma-def 74.0%

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

      9. times-frac 82.2%

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

      10. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in a around 0 60.5%

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

      1. fma-def 60.5%

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

      2. times-frac 68.6%

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

      3. associate-/r* 66.8%

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

   9. Simplified 66.8%

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

   10. Taylor expanded in c around -inf 68.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \frac{x \cdot y}{z} + -1 \cdot \frac{b}{z}}{c}} \]

   12. Simplified 70.7%

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

   if 1.34999999999999992e-23 < t

   1. Initial program 64.3%

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

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*r* 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-+l- 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 44.9%

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

      1. *-commutative 44.9%

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

      2. associate-/l* 61.5%

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

   6. Simplified 61.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+139}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 5: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+58} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.6e+58) (not (<= z 1e-37)))
   (/ (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* x y) z)))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.6e+58) || !(z <= 1e-37)) {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2.6d+58)) .or. (.not. (z <= 1d-37))) then
        tmp = (((-4.0d0) * (a * t)) + ((b / z) + (9.0d0 * ((x * y) / z)))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.6e+58) || !(z <= 1e-37)) {
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.6e+58) or not (z <= 1e-37):
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.6e+58) || !(z <= 1e-37))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z)))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.6e+58) || ~((z <= 1e-37)))
		tmp = ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z)))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.6e+58], N[Not[LessEqual[z, 1e-37]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999988e58 or 1.00000000000000007e-37 < z

   1. Initial program 62.4%

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

      1. associate-+l- 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 59.5%

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

      4. *-commutative 59.5%

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

      5. associate-+l- 59.5%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in x around 0 74.4%

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

      1. cancel-sign-sub-inv 74.4%

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

      2. metadata-eval 74.4%

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

      3. +-commutative 74.4%

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

      4. *-commutative 74.4%

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

      5. fma-def 74.4%

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

      6. associate-/l* 75.0%

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

      7. associate-/r/ 76.2%

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

      8. fma-def 76.2%

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

      9. times-frac 83.6%

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

      10. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in c around 0 85.3%

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

   if -2.59999999999999988e58 < z < 1.00000000000000007e-37

   1. Initial program 95.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+58} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 6: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y z) (/ x c)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -2.3e+119)
     t_2
     (if (<= t -1.35e+45)
       t_1
       (if (<= t -6.8e-228)
         (/ (/ b z) c)
         (if (<= t -7.2e-259)
           t_1
           (if (<= t -2.9e-301)
             (/ b (* z c))
             (if (<= t 3.8e-32) t_1 t_2))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.3e+119) {
		tmp = t_2;
	} else if (t <= -1.35e+45) {
		tmp = t_1;
	} else if (t <= -6.8e-228) {
		tmp = (b / z) / c;
	} else if (t <= -7.2e-259) {
		tmp = t_1;
	} else if (t <= -2.9e-301) {
		tmp = b / (z * c);
	} else if (t <= 3.8e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-2.3d+119)) then
        tmp = t_2
    else if (t <= (-1.35d+45)) then
        tmp = t_1
    else if (t <= (-6.8d-228)) then
        tmp = (b / z) / c
    else if (t <= (-7.2d-259)) then
        tmp = t_1
    else if (t <= (-2.9d-301)) then
        tmp = b / (z * c)
    else if (t <= 3.8d-32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.3e+119) {
		tmp = t_2;
	} else if (t <= -1.35e+45) {
		tmp = t_1;
	} else if (t <= -6.8e-228) {
		tmp = (b / z) / c;
	} else if (t <= -7.2e-259) {
		tmp = t_1;
	} else if (t <= -2.9e-301) {
		tmp = b / (z * c);
	} else if (t <= 3.8e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / z) * (x / c))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -2.3e+119:
		tmp = t_2
	elif t <= -1.35e+45:
		tmp = t_1
	elif t <= -6.8e-228:
		tmp = (b / z) / c
	elif t <= -7.2e-259:
		tmp = t_1
	elif t <= -2.9e-301:
		tmp = b / (z * c)
	elif t <= 3.8e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -2.3e+119)
		tmp = t_2;
	elseif (t <= -1.35e+45)
		tmp = t_1;
	elseif (t <= -6.8e-228)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -7.2e-259)
		tmp = t_1;
	elseif (t <= -2.9e-301)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 3.8e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / z) * (x / c));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -2.3e+119)
		tmp = t_2;
	elseif (t <= -1.35e+45)
		tmp = t_1;
	elseif (t <= -6.8e-228)
		tmp = (b / z) / c;
	elseif (t <= -7.2e-259)
		tmp = t_1;
	elseif (t <= -2.9e-301)
		tmp = b / (z * c);
	elseif (t <= 3.8e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+119], t$95$2, If[LessEqual[t, -1.35e+45], t$95$1, If[LessEqual[t, -6.8e-228], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -7.2e-259], t$95$1, If[LessEqual[t, -2.9e-301], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-32], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3000000000000001e119 or 3.80000000000000008e-32 < t

   1. Initial program 71.4%

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

      1. associate-+l- 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*r* 73.4%

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

      4. *-commutative 73.4%

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

      5. associate-+l- 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 60.8%

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

   6. Simplified 60.8%

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

   if -2.3000000000000001e119 < t < -1.34999999999999992e45 or -6.79999999999999981e-228 < t < -7.1999999999999996e-259 or -2.89999999999999984e-301 < t < 3.80000000000000008e-32

   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* 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-+l- 81.0%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in x around inf 45.2%

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

      1. times-frac 49.4%

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

   6. Simplified 49.4%

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

   if -1.34999999999999992e45 < t < -6.79999999999999981e-228

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in x around 0 73.5%

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

      1. cancel-sign-sub-inv 73.5%

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

      2. metadata-eval 73.5%

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

      3. +-commutative 73.5%

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

      4. *-commutative 73.5%

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

      5. fma-def 73.5%

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

      6. associate-/l* 70.5%

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

      7. associate-/r/ 69.1%

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

      8. fma-def 69.1%

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

      9. times-frac 78.4%

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

      10. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in c around 0 86.0%

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

   8. Taylor expanded in b around inf 45.4%

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

   if -7.1999999999999996e-259 < t < -2.89999999999999984e-301

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-+l- 73.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-259}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 7: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y z) (/ x c)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -8.5e+138)
     t_2
     (if (<= t -1.6e+46)
       (* 9.0 (/ (* x y) (* z c)))
       (if (<= t -1.65e-227)
         (/ (/ b z) c)
         (if (<= t -4.6e-259)
           t_1
           (if (<= t -3.1e-301) (/ b (* z c)) (if (<= t 5e-26) t_1 t_2))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_2;
	} else if (t <= -1.6e+46) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (t <= -1.65e-227) {
		tmp = (b / z) / c;
	} else if (t <= -4.6e-259) {
		tmp = t_1;
	} else if (t <= -3.1e-301) {
		tmp = b / (z * c);
	} else if (t <= 5e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-8.5d+138)) then
        tmp = t_2
    else if (t <= (-1.6d+46)) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (t <= (-1.65d-227)) then
        tmp = (b / z) / c
    else if (t <= (-4.6d-259)) then
        tmp = t_1
    else if (t <= (-3.1d-301)) then
        tmp = b / (z * c)
    else if (t <= 5d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_2;
	} else if (t <= -1.6e+46) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (t <= -1.65e-227) {
		tmp = (b / z) / c;
	} else if (t <= -4.6e-259) {
		tmp = t_1;
	} else if (t <= -3.1e-301) {
		tmp = b / (z * c);
	} else if (t <= 5e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / z) * (x / c))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -8.5e+138:
		tmp = t_2
	elif t <= -1.6e+46:
		tmp = 9.0 * ((x * y) / (z * c))
	elif t <= -1.65e-227:
		tmp = (b / z) / c
	elif t <= -4.6e-259:
		tmp = t_1
	elif t <= -3.1e-301:
		tmp = b / (z * c)
	elif t <= 5e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -8.5e+138)
		tmp = t_2;
	elseif (t <= -1.6e+46)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (t <= -1.65e-227)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -4.6e-259)
		tmp = t_1;
	elseif (t <= -3.1e-301)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 5e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / z) * (x / c));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -8.5e+138)
		tmp = t_2;
	elseif (t <= -1.6e+46)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (t <= -1.65e-227)
		tmp = (b / z) / c;
	elseif (t <= -4.6e-259)
		tmp = t_1;
	elseif (t <= -3.1e-301)
		tmp = b / (z * c);
	elseif (t <= 5e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+138], t$95$2, If[LessEqual[t, -1.6e+46], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e-227], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -4.6e-259], t$95$1, If[LessEqual[t, -3.1e-301], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-26], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.5000000000000006e138 or 5.00000000000000019e-26 < t

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if -8.5000000000000006e138 < t < -1.5999999999999999e46

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 43.1%

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

   if -1.5999999999999999e46 < t < -1.65e-227

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in x around 0 73.5%

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

      1. cancel-sign-sub-inv 73.5%

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

      2. metadata-eval 73.5%

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

      3. +-commutative 73.5%

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

      4. *-commutative 73.5%

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

      5. fma-def 73.5%

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

      6. associate-/l* 70.5%

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

      7. associate-/r/ 69.1%

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

      8. fma-def 69.1%

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

      9. times-frac 78.4%

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

      10. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in c around 0 86.0%

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

   8. Taylor expanded in b around inf 45.4%

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

   if -1.65e-227 < t < -4.5999999999999999e-259 or -3.10000000000000014e-301 < t < 5.00000000000000019e-26

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around inf 44.4%

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

      1. times-frac 49.7%

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

   6. Simplified 49.7%

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

   if -4.5999999999999999e-259 < t < -3.10000000000000014e-301

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-+l- 73.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-259}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 8: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-226}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y z) (/ x c)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -2.1e+139)
     t_2
     (if (<= t -1.3e+45)
       (* (/ x (/ c y)) (/ 9.0 z))
       (if (<= t -4.6e-226)
         (/ (/ b z) c)
         (if (<= t -5e-256)
           t_1
           (if (<= t -1.75e-300)
             (/ b (* z c))
             (if (<= t 4.9e-26) t_1 t_2))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_2;
	} else if (t <= -1.3e+45) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -4.6e-226) {
		tmp = (b / z) / c;
	} else if (t <= -5e-256) {
		tmp = t_1;
	} else if (t <= -1.75e-300) {
		tmp = b / (z * c);
	} else if (t <= 4.9e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-2.1d+139)) then
        tmp = t_2
    else if (t <= (-1.3d+45)) then
        tmp = (x / (c / y)) * (9.0d0 / z)
    else if (t <= (-4.6d-226)) then
        tmp = (b / z) / c
    else if (t <= (-5d-256)) then
        tmp = t_1
    else if (t <= (-1.75d-300)) then
        tmp = b / (z * c)
    else if (t <= 4.9d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.1e+139) {
		tmp = t_2;
	} else if (t <= -1.3e+45) {
		tmp = (x / (c / y)) * (9.0 / z);
	} else if (t <= -4.6e-226) {
		tmp = (b / z) / c;
	} else if (t <= -5e-256) {
		tmp = t_1;
	} else if (t <= -1.75e-300) {
		tmp = b / (z * c);
	} else if (t <= 4.9e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / z) * (x / c))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -2.1e+139:
		tmp = t_2
	elif t <= -1.3e+45:
		tmp = (x / (c / y)) * (9.0 / z)
	elif t <= -4.6e-226:
		tmp = (b / z) / c
	elif t <= -5e-256:
		tmp = t_1
	elif t <= -1.75e-300:
		tmp = b / (z * c)
	elif t <= 4.9e-26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -2.1e+139)
		tmp = t_2;
	elseif (t <= -1.3e+45)
		tmp = Float64(Float64(x / Float64(c / y)) * Float64(9.0 / z));
	elseif (t <= -4.6e-226)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -5e-256)
		tmp = t_1;
	elseif (t <= -1.75e-300)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 4.9e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / z) * (x / c));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -2.1e+139)
		tmp = t_2;
	elseif (t <= -1.3e+45)
		tmp = (x / (c / y)) * (9.0 / z);
	elseif (t <= -4.6e-226)
		tmp = (b / z) / c;
	elseif (t <= -5e-256)
		tmp = t_1;
	elseif (t <= -1.75e-300)
		tmp = b / (z * c);
	elseif (t <= 4.9e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+139], t$95$2, If[LessEqual[t, -1.3e+45], N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-226], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -5e-256], t$95$1, If[LessEqual[t, -1.75e-300], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-26], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.0999999999999999e139 or 4.8999999999999999e-26 < t

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if -2.0999999999999999e139 < t < -1.30000000000000004e45

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. times-frac 43.0%

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

      4. associate-/l* 43.1%

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

   6. Simplified 43.1%

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

   if -1.30000000000000004e45 < t < -4.6000000000000001e-226

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-+l- 73.8%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in x around 0 73.5%

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

      1. cancel-sign-sub-inv 73.5%

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

      2. metadata-eval 73.5%

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

      3. +-commutative 73.5%

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

      4. *-commutative 73.5%

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

      5. fma-def 73.5%

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

      6. associate-/l* 70.5%

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

      7. associate-/r/ 69.1%

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

      8. fma-def 69.1%

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

      9. times-frac 78.4%

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

      10. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in c around 0 86.0%

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

   8. Taylor expanded in b around inf 45.4%

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

   if -4.6000000000000001e-226 < t < -5e-256 or -1.7500000000000001e-300 < t < 4.8999999999999999e-26

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around inf 44.4%

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

      1. times-frac 49.7%

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

   6. Simplified 49.7%

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

   if -5e-256 < t < -1.7500000000000001e-300

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-+l- 73.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{\frac{c}{y}} \cdot \frac{9}{z}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-226}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-256}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 9: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+106}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)))
   (if (<= t -8.5e+138)
     t_1
     (if (<= t -1.25e+106)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (if (<= t -5e+84)
         t_1
         (if (<= t 2.1e-30)
           (/ (- (/ b z) (* x (* (/ y z) -9.0))) c)
           (* -4.0 (/ a (/ c t)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_1;
	} else if (t <= -1.25e+106) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t <= -5e+84) {
		tmp = t_1;
	} else if (t <= 2.1e-30) {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    if (t <= (-8.5d+138)) then
        tmp = t_1
    else if (t <= (-1.25d+106)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (t <= (-5d+84)) then
        tmp = t_1
    else if (t <= 2.1d-30) then
        tmp = ((b / z) - (x * ((y / z) * (-9.0d0)))) / c
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (t <= -8.5e+138) {
		tmp = t_1;
	} else if (t <= -1.25e+106) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (t <= -5e+84) {
		tmp = t_1;
	} else if (t <= 2.1e-30) {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	tmp = 0
	if t <= -8.5e+138:
		tmp = t_1
	elif t <= -1.25e+106:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif t <= -5e+84:
		tmp = t_1
	elif t <= 2.1e-30:
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c)
	tmp = 0.0
	if (t <= -8.5e+138)
		tmp = t_1;
	elseif (t <= -1.25e+106)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (t <= -5e+84)
		tmp = t_1;
	elseif (t <= 2.1e-30)
		tmp = Float64(Float64(Float64(b / z) - Float64(x * Float64(Float64(y / z) * -9.0))) / c);
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	tmp = 0.0;
	if (t <= -8.5e+138)
		tmp = t_1;
	elseif (t <= -1.25e+106)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (t <= -5e+84)
		tmp = t_1;
	elseif (t <= 2.1e-30)
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -8.5e+138], t$95$1, If[LessEqual[t, -1.25e+106], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e+84], t$95$1, If[LessEqual[t, 2.1e-30], N[(N[(N[(b / z), $MachinePrecision] - N[(x * N[(N[(y / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.5000000000000006e138 or -1.25e106 < t < -5.0000000000000001e84

   1. Initial program 86.0%

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

      1. associate-+l- 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*r* 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-+l- 89.5%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in x around 0 89.5%

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

      1. cancel-sign-sub-inv 89.5%

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

      2. metadata-eval 89.5%

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

      3. +-commutative 89.5%

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

      4. *-commutative 89.5%

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

      5. fma-def 89.5%

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

      6. associate-/l* 82.6%

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

      7. associate-/r/ 86.2%

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

      8. fma-def 86.2%

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

      9. times-frac 89.7%

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

      10. *-commutative 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in c around 0 89.8%

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

   8. Taylor expanded in b around 0 86.8%

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

   if -8.5000000000000006e138 < t < -1.25e106

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 87.5%

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

   if -5.0000000000000001e84 < t < 2.1000000000000002e-30

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 76.4%

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

      4. *-commutative 76.4%

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

      5. associate-+l- 76.4%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in x around 0 77.5%

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

      1. cancel-sign-sub-inv 77.5%

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

      2. metadata-eval 77.5%

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

      3. +-commutative 77.5%

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

      4. *-commutative 77.5%

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

      5. fma-def 77.5%

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

      6. associate-/l* 74.3%

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

      7. associate-/r/ 73.7%

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

      8. fma-def 73.7%

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

      9. times-frac 82.0%

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

      10. *-commutative 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in a around 0 60.0%

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

      1. fma-def 60.0%

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

      2. times-frac 68.1%

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

      3. associate-/r* 67.0%

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

   9. Simplified 67.0%

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

   10. Taylor expanded in c around -inf 67.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \frac{x \cdot y}{z} + -1 \cdot \frac{b}{z}}{c}} \]

   12. Simplified 70.3%

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

   if 2.1000000000000002e-30 < t

   1. Initial program 65.3%

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

      1. associate-+l- 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r* 66.8%

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

      4. *-commutative 66.8%

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

      5. associate-+l- 66.8%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in z around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-/l* 59.8%

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

   6. Simplified 59.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+106}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 10: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+138} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -8.8e+138) (not (<= t 7.2e-22)))
   (* -4.0 (/ a (/ c t)))
   (/ (- (/ b z) (* x (* (/ y z) -9.0))) c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -8.8e+138) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-8.8d+138)) .or. (.not. (t <= 7.2d-22))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = ((b / z) - (x * ((y / z) * (-9.0d0)))) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -8.8e+138) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -8.8e+138) or not (t <= 7.2e-22):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -8.8e+138) || !(t <= 7.2e-22))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(x * Float64(Float64(y / z) * -9.0))) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -8.8e+138) || ~((t <= 7.2e-22)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = ((b / z) - (x * ((y / z) * -9.0))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -8.8e+138], N[Not[LessEqual[t, 7.2e-22]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(x * N[(N[(y / z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8000000000000003e138 or 7.1999999999999996e-22 < t

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if -8.8000000000000003e138 < t < 7.1999999999999996e-22

   1. Initial program 83.9%

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

      1. associate-+l- 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-+l- 78.6%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. metadata-eval 79.5%

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

      3. +-commutative 79.5%

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

      4. *-commutative 79.5%

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

      5. fma-def 79.5%

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

      6. associate-/l* 76.6%

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

      7. associate-/r/ 76.0%

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

      8. fma-def 76.0%

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

      9. times-frac 83.0%

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

      10. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in a around 0 61.8%

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

      1. fma-def 61.8%

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

      2. times-frac 68.7%

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

      3. associate-/r* 67.0%

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

   9. Simplified 67.0%

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

   10. Taylor expanded in c around -inf 67.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{-9 \cdot \frac{x \cdot y}{z} + -1 \cdot \frac{b}{z}}{c}} \]

   12. Simplified 70.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+138} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - x \cdot \left(\frac{y}{z} \cdot -9\right)}{c}\\ \end{array} \]

Alternative 11: 50.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+38} \lor \neg \left(t \leq 1.7 \cdot 10^{-84}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -8e+131)
     t_1
     (if (<= t -2.2e+103)
       (/ b (* z c))
       (if (or (<= t -3.8e+38) (not (<= t 1.7e-84))) t_1 (/ (/ b z) c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -8e+131) {
		tmp = t_1;
	} else if (t <= -2.2e+103) {
		tmp = b / (z * c);
	} else if ((t <= -3.8e+38) || !(t <= 1.7e-84)) {
		tmp = t_1;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-8d+131)) then
        tmp = t_1
    else if (t <= (-2.2d+103)) then
        tmp = b / (z * c)
    else if ((t <= (-3.8d+38)) .or. (.not. (t <= 1.7d-84))) then
        tmp = t_1
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -8e+131) {
		tmp = t_1;
	} else if (t <= -2.2e+103) {
		tmp = b / (z * c);
	} else if ((t <= -3.8e+38) || !(t <= 1.7e-84)) {
		tmp = t_1;
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -8e+131:
		tmp = t_1
	elif t <= -2.2e+103:
		tmp = b / (z * c)
	elif (t <= -3.8e+38) or not (t <= 1.7e-84):
		tmp = t_1
	else:
		tmp = (b / z) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -8e+131)
		tmp = t_1;
	elseif (t <= -2.2e+103)
		tmp = Float64(b / Float64(z * c));
	elseif ((t <= -3.8e+38) || !(t <= 1.7e-84))
		tmp = t_1;
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -8e+131)
		tmp = t_1;
	elseif (t <= -2.2e+103)
		tmp = b / (z * c);
	elseif ((t <= -3.8e+38) || ~((t <= 1.7e-84)))
		tmp = t_1;
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+131], t$95$1, If[LessEqual[t, -2.2e+103], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.8e+38], N[Not[LessEqual[t, 1.7e-84]], $MachinePrecision]], t$95$1, N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.9999999999999993e131 or -2.19999999999999992e103 < t < -3.7999999999999998e38 or 1.7000000000000001e-84 < t

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-+l- 74.1%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in z around inf 44.8%

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

      1. *-commutative 44.8%

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

      2. associate-/l* 56.9%

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

   6. Simplified 56.9%

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

   if -7.9999999999999993e131 < t < -2.19999999999999992e103

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -3.7999999999999998e38 < t < 1.7000000000000001e-84

   1. Initial program 83.5%

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

      1. associate-+l- 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. associate-+l- 76.6%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. +-commutative 79.3%

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

      4. *-commutative 79.3%

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

      5. fma-def 79.3%

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

      6. associate-/l* 74.1%

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

      7. associate-/r/ 74.0%

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

      8. fma-def 74.0%

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

      9. times-frac 82.4%

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

      10. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in c around 0 89.0%

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

   8. Taylor expanded in b around inf 45.3%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+38} \lor \neg \left(t \leq 1.7 \cdot 10^{-84}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 12: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{+36} \lor \neg \left(t \leq 7.8 \cdot 10^{-84}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -7.5e+131)
     t_1
     (if (<= t -5.2e+102)
       (/ b (* z c))
       (if (or (<= t -8.8e+36) (not (<= t 7.8e-84)))
         t_1
         (* (/ b z) (/ 1.0 c)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -5.2e+102) {
		tmp = b / (z * c);
	} else if ((t <= -8.8e+36) || !(t <= 7.8e-84)) {
		tmp = t_1;
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-7.5d+131)) then
        tmp = t_1
    else if (t <= (-5.2d+102)) then
        tmp = b / (z * c)
    else if ((t <= (-8.8d+36)) .or. (.not. (t <= 7.8d-84))) then
        tmp = t_1
    else
        tmp = (b / z) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -7.5e+131) {
		tmp = t_1;
	} else if (t <= -5.2e+102) {
		tmp = b / (z * c);
	} else if ((t <= -8.8e+36) || !(t <= 7.8e-84)) {
		tmp = t_1;
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -7.5e+131:
		tmp = t_1
	elif t <= -5.2e+102:
		tmp = b / (z * c)
	elif (t <= -8.8e+36) or not (t <= 7.8e-84):
		tmp = t_1
	else:
		tmp = (b / z) * (1.0 / c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -5.2e+102)
		tmp = Float64(b / Float64(z * c));
	elseif ((t <= -8.8e+36) || !(t <= 7.8e-84))
		tmp = t_1;
	else
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -7.5e+131)
		tmp = t_1;
	elseif (t <= -5.2e+102)
		tmp = b / (z * c);
	elseif ((t <= -8.8e+36) || ~((t <= 7.8e-84)))
		tmp = t_1;
	else
		tmp = (b / z) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+131], t$95$1, If[LessEqual[t, -5.2e+102], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -8.8e+36], N[Not[LessEqual[t, 7.8e-84]], $MachinePrecision]], t$95$1, N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999995e131 or -5.20000000000000013e102 < t < -8.80000000000000002e36 or 7.80000000000000045e-84 < t

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-+l- 74.1%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in z around inf 44.8%

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

      1. *-commutative 44.8%

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

      2. associate-/l* 56.9%

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

   6. Simplified 56.9%

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

   if -7.4999999999999995e131 < t < -5.20000000000000013e102

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around inf 58.3%

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

      1. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -8.80000000000000002e36 < t < 7.80000000000000045e-84

   1. Initial program 83.5%

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

      1. associate-+l- 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. associate-+l- 76.6%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. +-commutative 79.3%

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

      4. *-commutative 79.3%

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

      5. fma-def 79.3%

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

      6. associate-/l* 74.1%

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

      7. associate-/r/ 74.0%

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

      8. fma-def 74.0%

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

      9. times-frac 82.4%

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

      10. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in c around 0 89.0%

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

   8. Taylor expanded in b around inf 45.3%

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

      1. div-inv 45.3%

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

   10. Applied egg-rr 45.3%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{+36} \lor \neg \left(t \leq 7.8 \cdot 10^{-84}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \]

Alternative 13: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.6e+139) (not (<= t 7.2e-22)))
   (* -4.0 (/ a (/ c t)))
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.6e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.6d+139)) .or. (.not. (t <= 7.2d-22))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.6e+139) || !(t <= 7.2e-22)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.6e+139) or not (t <= 7.2e-22):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.6e+139) || !(t <= 7.2e-22))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.6e+139) || ~((t <= 7.2e-22)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.6e+139], N[Not[LessEqual[t, 7.2e-22]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000022e139 or 7.1999999999999996e-22 < t

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if -2.60000000000000022e139 < t < 7.1999999999999996e-22

   1. Initial program 83.9%

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

      1. associate-+l- 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-+l- 78.6%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around inf 67.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+139} \lor \neg \left(t \leq 7.2 \cdot 10^{-22}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 14: 47.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.9 \cdot 10^{-66} \lor \neg \left(a \leq 1.2 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -7.9e-66) (not (<= a 1.2e-54)))
   (* -4.0 (/ (* a t) c))
   (/ b (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -7.9e-66) || !(a <= 1.2e-54)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-7.9d-66)) .or. (.not. (a <= 1.2d-54))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -7.9e-66) || !(a <= 1.2e-54)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -7.9e-66) or not (a <= 1.2e-54):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -7.9e-66) || !(a <= 1.2e-54))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -7.9e-66) || ~((a <= 1.2e-54)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -7.9e-66], N[Not[LessEqual[a, 1.2e-54]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.90000000000000026e-66 or 1.20000000000000007e-54 < a

   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* 70.3%

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

      4. *-commutative 70.3%

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

      5. associate-+l- 70.3%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around inf 47.3%

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

   if -7.90000000000000026e-66 < a < 1.20000000000000007e-54

   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* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   6. Simplified 51.5%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.9 \cdot 10^{-66} \lor \neg \left(a \leq 1.2 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15: 47.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-66} \lor \neg \left(a \leq 7.7 \cdot 10^{-59}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -2.05e-66) (not (<= a 7.7e-59)))
   (* -4.0 (/ (* a t) c))
   (* b (/ 1.0 (* z c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.05e-66) || !(a <= 7.7e-59)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-2.05d-66)) .or. (.not. (a <= 7.7d-59))) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b * (1.0d0 / (z * c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.05e-66) || !(a <= 7.7e-59)) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -2.05e-66) or not (a <= 7.7e-59):
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -2.05e-66) || !(a <= 7.7e-59))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -2.05e-66) || ~((a <= 7.7e-59)))
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b * (1.0 / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -2.05e-66], N[Not[LessEqual[a, 7.7e-59]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.04999999999999999e-66 or 7.7e-59 < a

   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* 70.3%

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

      4. *-commutative 70.3%

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

      5. associate-+l- 70.3%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around inf 47.3%

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

   if -2.04999999999999999e-66 < a < 7.7e-59

   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* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   6. Simplified 51.5%

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

      1. div-inv 52.4%

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

      2. *-commutative 52.4%

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

   8. Applied egg-rr 52.4%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-66} \lor \neg \left(a \leq 7.7 \cdot 10^{-59}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 16: 49.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-72}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -2.3e-72)
   (* -4.0 (/ (* a t) c))
   (if (<= a 3.5e-55) (* b (/ 1.0 (* z c))) (* t (/ -4.0 (/ c a))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.3e-72) {
		tmp = -4.0 * ((a * t) / c);
	} else if (a <= 3.5e-55) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-2.3d-72)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (a <= 3.5d-55) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t * ((-4.0d0) / (c / a))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.3e-72) {
		tmp = -4.0 * ((a * t) / c);
	} else if (a <= 3.5e-55) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.3e-72:
		tmp = -4.0 * ((a * t) / c)
	elif a <= 3.5e-55:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t * (-4.0 / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.3e-72)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (a <= 3.5e-55)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(t * Float64(-4.0 / Float64(c / a)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.3e-72)
		tmp = -4.0 * ((a * t) / c);
	elseif (a <= 3.5e-55)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t * (-4.0 / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.3e-72], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-55], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.29999999999999995e-72

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-+l- 77.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 46.4%

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

   if -2.29999999999999995e-72 < a < 3.50000000000000025e-55

   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* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   6. Simplified 51.5%

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

      1. div-inv 52.4%

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

      2. *-commutative 52.4%

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

   8. Applied egg-rr 52.4%

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

   if 3.50000000000000025e-55 < a

   1. Initial program 66.9%

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

      1. associate-+l- 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r* 63.1%

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

      4. *-commutative 63.1%

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

      5. associate-+l- 63.1%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in x around 0 69.5%

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

      1. cancel-sign-sub-inv 69.5%

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

      2. metadata-eval 69.5%

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

      3. +-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. fma-def 69.5%

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

      6. associate-/l* 76.9%

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

      7. associate-/r/ 74.5%

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

      8. fma-def 74.5%

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

      9. times-frac 84.2%

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

      10. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in c around 0 77.4%

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

   8. Taylor expanded in a around inf 48.2%

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

      1. associate-/l* 55.5%

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

      2. associate-*r/ 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-/r/ 54.4%

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

      5. *-commutative 54.4%

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

      6. *-commutative 54.4%

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

      7. associate-/l* 54.4%

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

   10. Simplified 54.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-72}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \]

Alternative 17: 49.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-67}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -6.5e-67)
   (* -4.0 (/ (* a t) c))
   (if (<= a 1.7e-53) (* b (/ 1.0 (* z c))) (* -4.0 (* t (/ a c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6.5e-67) {
		tmp = -4.0 * ((a * t) / c);
	} else if (a <= 1.7e-53) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-6.5d-67)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (a <= 1.7d-53) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -6.5e-67) {
		tmp = -4.0 * ((a * t) / c);
	} else if (a <= 1.7e-53) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -6.5e-67:
		tmp = -4.0 * ((a * t) / c)
	elif a <= 1.7e-53:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -6.5e-67)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (a <= 1.7e-53)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -6.5e-67)
		tmp = -4.0 * ((a * t) / c);
	elseif (a <= 1.7e-53)
		tmp = b * (1.0 / (z * c));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -6.5e-67], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-53], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.4999999999999997e-67

   1. Initial program 84.8%

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

      1. associate-+l- 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-+l- 77.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 46.4%

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

   if -6.4999999999999997e-67 < a < 1.7e-53

   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* 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-+l- 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   6. Simplified 51.5%

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

      1. div-inv 52.4%

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

      2. *-commutative 52.4%

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

   8. Applied egg-rr 52.4%

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

   if 1.7e-53 < a

   1. Initial program 66.9%

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

      1. associate-+l- 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r* 63.1%

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

      4. *-commutative 63.1%

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

      5. associate-+l- 63.1%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-/l* 55.5%

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

      3. associate-/r/ 54.4%

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

   6. Simplified 54.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-67}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 18: 36.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 20000000000000:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 20000000000000.0) (/ b (* z c)) (/ (/ b z) c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 20000000000000.0) {
		tmp = b / (z * c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= 20000000000000.0d0) then
        tmp = b / (z * c)
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 20000000000000.0) {
		tmp = b / (z * c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= 20000000000000.0:
		tmp = b / (z * c)
	else:
		tmp = (b / z) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= 20000000000000.0)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= 20000000000000.0)
		tmp = b / (z * c);
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 20000000000000.0], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2e13

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 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%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in b around inf 40.4%

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

      1. *-commutative 40.4%

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

   6. Simplified 40.4%

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

   if 2e13 < z

   1. Initial program 58.2%

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

      1. associate-+l- 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*r* 58.2%

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

      4. *-commutative 58.2%

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

      5. associate-+l- 58.2%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around 0 67.7%

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

      1. cancel-sign-sub-inv 67.7%

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

      2. metadata-eval 67.7%

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

      3. +-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. fma-def 67.7%

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

      6. associate-/l* 66.3%

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

      7. associate-/r/ 71.8%

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

      8. fma-def 71.8%

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

      9. times-frac 83.9%

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

      10. *-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in c around 0 83.8%

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

   8. Taylor expanded in b around inf 27.7%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 20000000000000:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 19: 35.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. associate-+l- 78.6%

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

   2. *-commutative 78.6%

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

   3. associate-*r* 76.0%

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

   4. *-commutative 76.0%

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

   5. associate-+l- 76.0%

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

3. Simplified 78.2%

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

4. Taylor expanded in b around inf 35.0%

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

   1. *-commutative 35.0%

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

6. Simplified 35.0%

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

7. Final simplification 35.0%

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

Developer target: 80.1% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

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

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