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

Percentage Accurate: 79.3% → 93.0%

Time: 15.4s

Alternatives: 15

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: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{-88} \lor \neg \left(c \leq 1.35 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) + \frac{\frac{b}{c} - \frac{x}{\frac{c}{y}} \cdot -9}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.85e-88) (not (<= c 1.35e+69)))
   (+ (* t (* (/ a c) -4.0)) (/ (- (/ b c) (* (/ x (/ c y)) -9.0)) z))
   (/ (+ (* -4.0 (* t a)) (/ (- b (* -9.0 (* x y))) z)) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.85e-88) || !(c <= 1.35e+69)) {
		tmp = (t * ((a / c) * -4.0)) + (((b / c) - ((x / (c / y)) * -9.0)) / z);
	} else {
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 ((c <= (-1.85d-88)) .or. (.not. (c <= 1.35d+69))) then
        tmp = (t * ((a / c) * (-4.0d0))) + (((b / c) - ((x / (c / y)) * (-9.0d0))) / z)
    else
        tmp = (((-4.0d0) * (t * a)) + ((b - ((-9.0d0) * (x * y))) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.85e-88) || !(c <= 1.35e+69)) {
		tmp = (t * ((a / c) * -4.0)) + (((b / c) - ((x / (c / y)) * -9.0)) / z);
	} else {
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -1.85e-88) or not (c <= 1.35e+69):
		tmp = (t * ((a / c) * -4.0)) + (((b / c) - ((x / (c / y)) * -9.0)) / z)
	else:
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.85e-88) || !(c <= 1.35e+69))
		tmp = Float64(Float64(t * Float64(Float64(a / c) * -4.0)) + Float64(Float64(Float64(b / c) - Float64(Float64(x / Float64(c / y)) * -9.0)) / z));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b - Float64(-9.0 * Float64(x * y))) / z)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -1.85e-88) || ~((c <= 1.35e+69)))
		tmp = (t * ((a / c) * -4.0)) + (((b / c) - ((x / (c / y)) * -9.0)) / z);
	else
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.85e-88], N[Not[LessEqual[c, 1.35e+69]], $MachinePrecision]], N[(N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8499999999999999e-88 or 1.3499999999999999e69 < c

   1. Initial program 71.1%

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

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*r* 70.3%

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

      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 69.8%

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

   4. Taylor expanded in x around 0 77.0%

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

      1. cancel-sign-sub-inv 77.0%

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

      2. metadata-eval 77.0%

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

      3. +-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. fma-def 77.0%

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

      6. associate-/l* 83.4%

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

      7. associate-*r/ 83.4%

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

      8. associate-*r* 83.4%

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

      9. *-commutative 83.4%

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

      10. associate-*r* 83.4%

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

      11. *-commutative 83.4%

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

      12. times-frac 87.8%

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

      13. fma-def 87.8%

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

      14. associate-/l* 87.2%

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

      15. associate-/r* 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in z around -inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

      3. associate-*l/ 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

      6. associate-*l* 91.0%

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

      7. mul-1-neg 91.0%

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

      8. unsub-neg 91.0%

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

      9. *-commutative 91.0%

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

      10. associate-/l* 94.9%

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

   9. Simplified 94.9%

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

   if -1.8499999999999999e-88 < c < 1.3499999999999999e69

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-*r* 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-+l- 87.9%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around 0 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. metadata-eval 78.9%

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

      3. +-commutative 78.9%

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

      4. *-commutative 78.9%

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

      5. fma-def 78.9%

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

      6. associate-/l* 75.4%

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

      7. associate-*r/ 75.4%

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

      8. associate-*r* 75.4%

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

      9. *-commutative 75.4%

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

      10. associate-*r* 75.4%

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

      11. *-commutative 75.4%

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

      12. times-frac 74.4%

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

      13. fma-def 76.2%

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

      14. associate-/l* 76.2%

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

      15. associate-/r* 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around -inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-*l/ 76.6%

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

      4. *-commutative 76.6%

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

      5. *-commutative 76.6%

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

      6. associate-*l* 76.6%

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

      7. mul-1-neg 76.6%

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

      8. unsub-neg 76.6%

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

      9. *-commutative 76.6%

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

      10. associate-/l* 75.7%

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

   9. Simplified 75.7%

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

   10. Taylor expanded in c around 0 93.6%

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

       1. associate--l+ 93.6%

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

       2. associate-*r/ 93.6%

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

       3. sub-div 96.3%

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

   12. Applied egg-rr 96.3%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.85 \cdot 10^{-88} \lor \neg \left(c \leq 1.35 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) + \frac{\frac{b}{c} - \frac{x}{\frac{c}{y}} \cdot -9}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) - -9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z)))
        (t_2 (/ (+ (* -4.0 (* t a)) (/ (- b (* -9.0 (* x y))) z)) c)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-213)
       t_1
       (if (<= t_1 INFINITY)
         t_2
         (- (* t (* (/ a c) -4.0)) (* -9.0 (* (/ x c) (/ y z)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	double t_2 = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-213) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	}
	return tmp;
}

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	double t_2 = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -2e-213) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	t_2 = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -2e-213:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b - Float64(-9.0 * Float64(x * y))) / z)) / c)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-213)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * Float64(Float64(a / c) * -4.0)) - Float64(-9.0 * Float64(Float64(x / c) * Float64(y / z))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	t_2 = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -2e-213)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-213], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0 or -1.9999999999999999e-213 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r* 85.2%

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

      4. *-commutative 85.2%

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

      5. associate-+l- 85.2%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around 0 79.2%

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

      1. cancel-sign-sub-inv 79.2%

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

      2. metadata-eval 79.2%

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

      3. +-commutative 79.2%

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

      4. *-commutative 79.2%

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

      5. fma-def 79.2%

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

      6. associate-/l* 78.7%

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

      7. associate-*r/ 78.7%

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

      8. associate-*r* 78.7%

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

      9. *-commutative 78.7%

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

      10. associate-*r* 78.7%

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

      11. *-commutative 78.7%

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

      12. times-frac 80.7%

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

      13. fma-def 81.8%

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

      14. associate-/l* 81.8%

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

      15. associate-/r* 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in z around -inf 87.6%

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

      1. mul-1-neg 87.6%

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

      2. unsub-neg 87.6%

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

      3. associate-*l/ 86.4%

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

      4. *-commutative 86.4%

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

      5. *-commutative 86.4%

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

      6. associate-*l* 86.4%

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

      7. mul-1-neg 86.4%

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

      8. unsub-neg 86.4%

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

      9. *-commutative 86.4%

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

      10. associate-/l* 86.4%

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

   9. Simplified 86.4%

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

   10. Taylor expanded in c around 0 91.1%

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

       1. associate--l+ 91.1%

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

       2. associate-*r/ 91.1%

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

       3. sub-div 93.4%

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

   12. Applied egg-rr 93.4%

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

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.9999999999999999e-213

   1. Initial program 99.5%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 10.1%

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

      4. *-commutative 10.1%

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

      5. associate-+l- 10.1%

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

   3. Simplified 10.1%

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

   4. Taylor expanded in x around 0 40.7%

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

      1. cancel-sign-sub-inv 40.7%

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

      2. metadata-eval 40.7%

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

      3. +-commutative 40.7%

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

      4. *-commutative 40.7%

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

      5. fma-def 40.7%

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

      6. associate-/l* 53.9%

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

      7. associate-*r/ 53.9%

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

      8. associate-*r* 53.9%

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

      9. *-commutative 53.9%

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

      10. associate-*r* 53.9%

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

      11. *-commutative 53.9%

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

      12. times-frac 85.5%

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

      13. fma-def 85.5%

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

      14. associate-/l* 85.5%

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

      15. associate-/r* 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in z around -inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. unsub-neg 41.8%

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

      3. associate-*l/ 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

      6. associate-*l* 60.3%

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

      7. mul-1-neg 60.3%

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

      8. unsub-neg 60.3%

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

      9. *-commutative 60.3%

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

      10. associate-/l* 84.1%

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

   9. Simplified 84.1%

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

   10. Taylor expanded in x around inf 59.2%

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

       1. times-frac 90.8%

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

   12. Simplified 90.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -\infty:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -2 \cdot 10^{-213}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) - -9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 3: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{c}{y} \cdot \frac{z}{9}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+235}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* x 9.0))))
   (if (<= t_1 -5e+201)
     (/ x (* (/ c y) (/ z 9.0)))
     (if (<= t_1 2e+235)
       (/ (+ (* -4.0 (* t a)) (/ (- b (* -9.0 (* x y))) z)) c)
       (* 9.0 (* (/ x c) (/ y z)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+201) {
		tmp = x / ((c / y) * (z / 9.0));
	} else if (t_1 <= 2e+235) {
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	} else {
		tmp = 9.0 * ((x / c) * (y / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 = y * (x * 9.0d0)
    if (t_1 <= (-5d+201)) then
        tmp = x / ((c / y) * (z / 9.0d0))
    else if (t_1 <= 2d+235) then
        tmp = (((-4.0d0) * (t * a)) + ((b - ((-9.0d0) * (x * y))) / z)) / c
    else
        tmp = 9.0d0 * ((x / c) * (y / z))
    end if
    code = tmp
end function

Java

assert x < y;
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 * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+201) {
		tmp = x / ((c / y) * (z / 9.0));
	} else if (t_1 <= 2e+235) {
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	} else {
		tmp = 9.0 * ((x / c) * (y / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -5e+201:
		tmp = x / ((c / y) * (z / 9.0))
	elif t_1 <= 2e+235:
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c
	else:
		tmp = 9.0 * ((x / c) * (y / z))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+201)
		tmp = Float64(x / Float64(Float64(c / y) * Float64(z / 9.0)));
	elseif (t_1 <= 2e+235)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b - Float64(-9.0 * Float64(x * y))) / z)) / c);
	else
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -5e+201)
		tmp = x / ((c / y) * (z / 9.0));
	elseif (t_1 <= 2e+235)
		tmp = ((-4.0 * (t * a)) + ((b - (-9.0 * (x * y))) / z)) / c;
	else
		tmp = 9.0 * ((x / c) * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+201], N[(x / N[(N[(c / y), $MachinePrecision] * N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+235], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -4.9999999999999995e201

   1. Initial program 76.3%

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

      1. associate-+l- 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-+l- 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around inf 76.6%

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

      1. associate-*r/ 76.5%

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

      2. *-commutative 76.5%

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

   6. Simplified 76.5%

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

      1. times-frac 74.1%

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

   8. Applied egg-rr 74.1%

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

      1. clear-num 74.1%

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

      2. associate-/l* 81.9%

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

      3. frac-times 93.3%

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

      4. *-un-lft-identity 93.3%

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

   10. Applied egg-rr 93.3%

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

   if -4.9999999999999995e201 < (*.f64 (*.f64 x 9) y) < 2.0000000000000001e235

   1. Initial program 81.9%

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

      1. associate-+l- 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*r* 79.8%

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

      4. *-commutative 79.8%

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

      5. associate-+l- 79.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in x around 0 84.5%

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

      1. cancel-sign-sub-inv 84.5%

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

      2. metadata-eval 84.5%

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

      3. +-commutative 84.5%

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

      4. *-commutative 84.5%

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

      5. fma-def 84.5%

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

      6. associate-/l* 88.3%

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

      7. associate-*r/ 88.3%

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

      8. associate-*r* 88.4%

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

      9. *-commutative 88.4%

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

      10. associate-*r* 88.3%

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

      11. *-commutative 88.3%

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

      12. times-frac 83.6%

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

      13. fma-def 84.7%

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

      14. associate-/l* 84.2%

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

      15. associate-/r* 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in z around -inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

      3. associate-*l/ 92.5%

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

      4. *-commutative 92.5%

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

      5. *-commutative 92.5%

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

      6. associate-*l* 92.5%

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

      7. mul-1-neg 92.5%

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

      8. unsub-neg 92.5%

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

      9. *-commutative 92.5%

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

      10. associate-/l* 90.6%

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

   9. Simplified 90.6%

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

   10. Taylor expanded in c around 0 89.2%

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

       1. associate--l+ 89.2%

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

       2. associate-*r/ 89.1%

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

       3. sub-div 89.7%

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

   12. Applied egg-rr 89.7%

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

   if 2.0000000000000001e235 < (*.f64 (*.f64 x 9) y)

   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* 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-+l- 61.7%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in x around inf 61.8%

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

      1. times-frac 89.5%

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

   6. Applied egg-rr 89.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\frac{c}{y} \cdot \frac{z}{9}}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+235}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - -9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+151}:\\ \;\;\;\;\frac{t_1 - -9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* t a))) (t_2 (/ (+ t_1 (/ b z)) c)))
   (if (<= z -2.8e+67)
     t_2
     (if (<= z 5.6e-71)
       (* (/ 1.0 z) (/ (+ b (* y (* x 9.0))) c))
       (if (<= z 6.9e+151) (/ (- t_1 (* -9.0 (/ (* x y) z))) c) t_2)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * a);
	double t_2 = (t_1 + (b / z)) / c;
	double tmp;
	if (z <= -2.8e+67) {
		tmp = t_2;
	} else if (z <= 5.6e-71) {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	} else if (z <= 6.9e+151) {
		tmp = (t_1 - (-9.0 * ((x * y) / z))) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = (t_1 + (b / z)) / c
    if (z <= (-2.8d+67)) then
        tmp = t_2
    else if (z <= 5.6d-71) then
        tmp = (1.0d0 / z) * ((b + (y * (x * 9.0d0))) / c)
    else if (z <= 6.9d+151) then
        tmp = (t_1 - ((-9.0d0) * ((x * y) / z))) / c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
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 * (t * a);
	double t_2 = (t_1 + (b / z)) / c;
	double tmp;
	if (z <= -2.8e+67) {
		tmp = t_2;
	} else if (z <= 5.6e-71) {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	} else if (z <= 6.9e+151) {
		tmp = (t_1 - (-9.0 * ((x * y) / z))) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * a)
	t_2 = (t_1 + (b / z)) / c
	tmp = 0
	if z <= -2.8e+67:
		tmp = t_2
	elif z <= 5.6e-71:
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c)
	elif z <= 6.9e+151:
		tmp = (t_1 - (-9.0 * ((x * y) / z))) / c
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(Float64(t_1 + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.8e+67)
		tmp = t_2;
	elseif (z <= 5.6e-71)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c));
	elseif (z <= 6.9e+151)
		tmp = Float64(Float64(t_1 - Float64(-9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * a);
	t_2 = (t_1 + (b / z)) / c;
	tmp = 0.0;
	if (z <= -2.8e+67)
		tmp = t_2;
	elseif (z <= 5.6e-71)
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	elseif (z <= 6.9e+151)
		tmp = (t_1 - (-9.0 * ((x * y) / z))) / c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.8e+67], t$95$2, If[LessEqual[z, 5.6e-71], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.9e+151], N[(N[(t$95$1 - N[(-9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999998e67 or 6.90000000000000025e151 < z

   1. Initial program 56.9%

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

      1. associate-+l- 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-*r* 54.6%

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

      4. *-commutative 54.6%

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

      5. associate-+l- 54.6%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in x around 0 76.2%

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

      1. cancel-sign-sub-inv 76.2%

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

      2. metadata-eval 76.2%

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

      3. +-commutative 76.2%

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

      4. *-commutative 76.2%

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

      5. fma-def 76.2%

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

      6. associate-/l* 77.3%

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

      7. associate-*r/ 77.3%

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

      8. associate-*r* 77.2%

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

      9. *-commutative 77.2%

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

      10. associate-*r* 77.2%

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

      11. *-commutative 77.2%

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

      12. times-frac 89.4%

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

      13. fma-def 89.4%

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

      14. associate-/l* 89.4%

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

      15. associate-/r* 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in z around -inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

      3. associate-*l/ 79.8%

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

      4. *-commutative 79.8%

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

      5. *-commutative 79.8%

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

      6. associate-*l* 79.8%

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

      7. mul-1-neg 79.8%

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

      8. unsub-neg 79.8%

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

      9. *-commutative 79.8%

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

      10. associate-/l* 87.0%

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

   9. Simplified 87.0%

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

   10. Taylor expanded in c around 0 83.5%

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

   11. Taylor expanded in x around 0 74.1%

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

   if -2.7999999999999998e67 < z < 5.60000000000000001e-71

   1. Initial program 95.1%

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

      1. associate-+l- 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*r* 94.4%

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

      4. *-commutative 94.4%

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

      5. associate-+l- 94.4%

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

   3. Simplified 92.0%

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

      1. *-un-lft-identity 92.0%

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

      2. times-frac 93.4%

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

      3. associate-+l- 93.4%

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

      4. associate-*r* 96.5%

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

      5. associate-+l- 96.5%

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

      6. associate-*l* 96.6%

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

      7. associate-*r* 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in x around inf 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*r* 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*l* 82.9%

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

   8. Simplified 82.9%

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

   if 5.60000000000000001e-71 < z < 6.90000000000000025e151

   1. Initial program 78.4%

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

      1. associate-+l- 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*r* 81.1%

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

      4. *-commutative 81.1%

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

      5. associate-+l- 81.1%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around 0 81.0%

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

      1. cancel-sign-sub-inv 81.0%

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

      2. metadata-eval 81.0%

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

      3. +-commutative 81.0%

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

      4. *-commutative 81.0%

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

      5. fma-def 81.0%

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

      6. associate-/l* 78.4%

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

      7. associate-*r/ 78.3%

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

      8. associate-*r* 78.4%

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

      9. *-commutative 78.4%

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

      10. associate-*r* 78.3%

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

      11. *-commutative 78.3%

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

      12. times-frac 87.4%

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

      13. fma-def 87.4%

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

      14. associate-/l* 85.5%

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

      15. associate-/r* 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in z around -inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-*l/ 81.1%

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

      4. *-commutative 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-*l* 81.1%

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

      7. mul-1-neg 81.1%

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

      8. unsub-neg 81.1%

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

      9. *-commutative 81.1%

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

      10. associate-/l* 81.2%

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

   9. Simplified 81.2%

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

   10. Taylor expanded in c around 0 88.2%

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

   11. Taylor expanded in b around 0 80.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+151}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) - -9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+67} \lor \neg \left(z \leq 1.1 \cdot 10^{-101}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) - -9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -1e+67) (not (<= z 1.1e-101)))
   (- (* t (* (/ a c) -4.0)) (* -9.0 (* (/ x c) (/ y z))))
   (* (/ 1.0 z) (/ (+ b (* y (* x 9.0))) c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e+67) || !(z <= 1.1e-101)) {
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	} else {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1d+67)) .or. (.not. (z <= 1.1d-101))) then
        tmp = (t * ((a / c) * (-4.0d0))) - ((-9.0d0) * ((x / c) * (y / z)))
    else
        tmp = (1.0d0 / z) * ((b + (y * (x * 9.0d0))) / c)
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -1e+67) || !(z <= 1.1e-101)) {
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	} else {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1e+67) or not (z <= 1.1e-101):
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)))
	else:
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e+67) || !(z <= 1.1e-101))
		tmp = Float64(Float64(t * Float64(Float64(a / c) * -4.0)) - Float64(-9.0 * Float64(Float64(x / c) * Float64(y / z))));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1e+67) || ~((z <= 1.1e-101)))
		tmp = (t * ((a / c) * -4.0)) - (-9.0 * ((x / c) * (y / z)));
	else
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -1e+67], N[Not[LessEqual[z, 1.1e-101]], $MachinePrecision]], N[(N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999983e66 or 1.0999999999999999e-101 < z

   1. Initial program 64.8%

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

      1. associate-+l- 64.8%

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

      2. *-commutative 64.8%

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

      3. associate-*r* 64.1%

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

      4. *-commutative 64.1%

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

      5. associate-+l- 64.1%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in x around 0 77.6%

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

      1. cancel-sign-sub-inv 77.6%

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

      2. metadata-eval 77.6%

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

      3. +-commutative 77.6%

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

      4. *-commutative 77.6%

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

      5. fma-def 77.6%

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

      6. associate-/l* 78.2%

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

      7. associate-*r/ 78.2%

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

      8. associate-*r* 78.2%

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

      9. *-commutative 78.2%

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

      10. associate-*r* 78.1%

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

      11. *-commutative 78.1%

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

      12. times-frac 89.4%

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

      13. fma-def 89.4%

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

      14. associate-/l* 88.9%

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

      15. associate-/r* 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around -inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. associate-*l/ 80.7%

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

      4. *-commutative 80.7%

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

      5. *-commutative 80.7%

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

      6. associate-*l* 80.7%

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

      7. mul-1-neg 80.7%

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

      8. unsub-neg 80.7%

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

      9. *-commutative 80.7%

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

      10. associate-/l* 86.1%

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

   9. Simplified 86.1%

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

   10. Taylor expanded in x around inf 68.8%

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

       1. times-frac 76.6%

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

   12. Simplified 76.6%

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

   if -9.99999999999999983e66 < z < 1.0999999999999999e-101

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*r* 94.8%

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

      4. *-commutative 94.8%

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

      5. associate-+l- 94.8%

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

   3. Simplified 93.1%

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

      1. *-un-lft-identity 93.1%

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

      2. times-frac 94.6%

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

      3. associate-+l- 94.6%

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

      4. associate-*r* 97.1%

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

      5. associate-+l- 97.1%

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

      6. associate-*l* 97.2%

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

      7. associate-*r* 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in x around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r* 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-*l* 84.2%

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

   8. Simplified 84.2%

      \[\leadsto \frac{1}{z} \cdot \frac{\color{blue}{y \cdot \left(9 \cdot x\right)} + b}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+67} \lor \neg \left(z \leq 1.1 \cdot 10^{-101}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right) - -9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \end{array} \]

Alternative 6: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{b + \left(x \cdot y\right) \cdot 9}{c \cdot z}\\ \mathbf{elif}\;z \leq 10^{+130} \lor \neg \left(z \leq 8.5 \cdot 10^{+150}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* t a)) (/ b z)) c)))
   (if (<= z -2.35e+66)
     t_1
     (if (<= z 6.2e-14)
       (/ (+ b (* (* x y) 9.0)) (* c z))
       (if (or (<= z 1e+130) (not (<= z 8.5e+150)))
         t_1
         (* 9.0 (* (/ x z) (/ y c))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c;
	double tmp;
	if (z <= -2.35e+66) {
		tmp = t_1;
	} else if (z <= 6.2e-14) {
		tmp = (b + ((x * y) * 9.0)) / (c * z);
	} else if ((z <= 1e+130) || !(z <= 8.5e+150)) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) * (t * a)) + (b / z)) / c
    if (z <= (-2.35d+66)) then
        tmp = t_1
    else if (z <= 6.2d-14) then
        tmp = (b + ((x * y) * 9.0d0)) / (c * z)
    else if ((z <= 1d+130) .or. (.not. (z <= 8.5d+150))) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((x / z) * (y / c))
    end if
    code = tmp
end function

Java

assert x < y;
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 * (t * a)) + (b / z)) / c;
	double tmp;
	if (z <= -2.35e+66) {
		tmp = t_1;
	} else if (z <= 6.2e-14) {
		tmp = (b + ((x * y) * 9.0)) / (c * z);
	} else if ((z <= 1e+130) || !(z <= 8.5e+150)) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c
	tmp = 0
	if z <= -2.35e+66:
		tmp = t_1
	elif z <= 6.2e-14:
		tmp = (b + ((x * y) * 9.0)) / (c * z)
	elif (z <= 1e+130) or not (z <= 8.5e+150):
		tmp = t_1
	else:
		tmp = 9.0 * ((x / z) * (y / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.35e+66)
		tmp = t_1;
	elseif (z <= 6.2e-14)
		tmp = Float64(Float64(b + Float64(Float64(x * y) * 9.0)) / Float64(c * z));
	elseif ((z <= 1e+130) || !(z <= 8.5e+150))
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -2.35e+66)
		tmp = t_1;
	elseif (z <= 6.2e-14)
		tmp = (b + ((x * y) * 9.0)) / (c * z);
	elseif ((z <= 1e+130) || ~((z <= 8.5e+150)))
		tmp = t_1;
	else
		tmp = 9.0 * ((x / z) * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.35e+66], t$95$1, If[LessEqual[z, 6.2e-14], N[(N[(b + N[(N[(x * y), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1e+130], N[Not[LessEqual[z, 8.5e+150]], $MachinePrecision]], t$95$1, N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3500000000000001e66 or 6.20000000000000009e-14 < z < 1.0000000000000001e130 or 8.4999999999999999e150 < z

   1. Initial program 62.1%

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

      1. associate-+l- 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-*r* 60.4%

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

      4. *-commutative 60.4%

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

      5. associate-+l- 60.4%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in x around 0 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. metadata-eval 78.9%

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

      3. +-commutative 78.9%

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

      4. *-commutative 78.9%

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

      5. fma-def 78.9%

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

      6. associate-/l* 79.7%

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

      7. associate-*r/ 79.7%

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

      8. associate-*r* 79.7%

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

      9. *-commutative 79.7%

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

      10. associate-*r* 79.7%

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

      11. *-commutative 79.7%

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

      12. times-frac 89.3%

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

      13. fma-def 89.3%

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

      14. associate-/l* 89.3%

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

      15. associate-/r* 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in z around -inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. associate-*l/ 81.8%

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

      4. *-commutative 81.8%

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

      5. *-commutative 81.8%

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

      6. associate-*l* 81.8%

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

      7. mul-1-neg 81.8%

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

      8. unsub-neg 81.8%

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

      9. *-commutative 81.8%

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

      10. associate-/l* 87.4%

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

   9. Simplified 87.4%

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

   10. Taylor expanded in c around 0 86.3%

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

   11. Taylor expanded in x around 0 73.6%

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

   if -2.3500000000000001e66 < z < 6.20000000000000009e-14

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-+l- 95.4%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 81.6%

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

   if 1.0000000000000001e130 < z < 8.4999999999999999e150

   1. Initial program 31.5%

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

      1. associate-+l- 31.5%

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

      2. *-commutative 31.5%

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

      3. associate-*r* 45.8%

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

      4. *-commutative 45.8%

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

      5. associate-+l- 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in x around inf 45.8%

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

      1. div-inv 45.5%

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

      2. *-commutative 45.5%

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

   6. Applied egg-rr 45.5%

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

      1. associate-*r/ 45.8%

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

      2. *-rgt-identity 45.8%

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

      3. times-frac 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+66}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{b + \left(x \cdot y\right) \cdot 9}{c \cdot z}\\ \mathbf{elif}\;z \leq 10^{+130} \lor \neg \left(z \leq 8.5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 7: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+130} \lor \neg \left(z \leq 8.5 \cdot 10^{+150}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* t a)) (/ b z)) c)))
   (if (<= z -3.2e+68)
     t_1
     (if (<= z 4000000.0)
       (* (/ 1.0 z) (/ (+ b (* y (* x 9.0))) c))
       (if (or (<= z 8.8e+130) (not (<= z 8.5e+150)))
         t_1
         (* 9.0 (* (/ x z) (/ y c))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (t * a)) + (b / z)) / c;
	double tmp;
	if (z <= -3.2e+68) {
		tmp = t_1;
	} else if (z <= 4000000.0) {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	} else if ((z <= 8.8e+130) || !(z <= 8.5e+150)) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) * (t * a)) + (b / z)) / c
    if (z <= (-3.2d+68)) then
        tmp = t_1
    else if (z <= 4000000.0d0) then
        tmp = (1.0d0 / z) * ((b + (y * (x * 9.0d0))) / c)
    else if ((z <= 8.8d+130) .or. (.not. (z <= 8.5d+150))) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((x / z) * (y / c))
    end if
    code = tmp
end function

Java

assert x < y;
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 * (t * a)) + (b / z)) / c;
	double tmp;
	if (z <= -3.2e+68) {
		tmp = t_1;
	} else if (z <= 4000000.0) {
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	} else if ((z <= 8.8e+130) || !(z <= 8.5e+150)) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c
	tmp = 0
	if z <= -3.2e+68:
		tmp = t_1
	elif z <= 4000000.0:
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c)
	elif (z <= 8.8e+130) or not (z <= 8.5e+150):
		tmp = t_1
	else:
		tmp = 9.0 * ((x / z) * (y / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -3.2e+68)
		tmp = t_1;
	elseif (z <= 4000000.0)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(y * Float64(x * 9.0))) / c));
	elseif ((z <= 8.8e+130) || !(z <= 8.5e+150))
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (t * a)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -3.2e+68)
		tmp = t_1;
	elseif (z <= 4000000.0)
		tmp = (1.0 / z) * ((b + (y * (x * 9.0))) / c);
	elseif ((z <= 8.8e+130) || ~((z <= 8.5e+150)))
		tmp = t_1;
	else
		tmp = 9.0 * ((x / z) * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.2e+68], t$95$1, If[LessEqual[z, 4000000.0], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8.8e+130], N[Not[LessEqual[z, 8.5e+150]], $MachinePrecision]], t$95$1, N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999994e68 or 4e6 < z < 8.79999999999999974e130 or 8.4999999999999999e150 < z

   1. Initial program 61.6%

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

      1. associate-+l- 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r* 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-+l- 59.8%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in x around 0 79.1%

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

      1. cancel-sign-sub-inv 79.1%

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

      2. metadata-eval 79.1%

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

      3. +-commutative 79.1%

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

      4. *-commutative 79.1%

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

      5. fma-def 79.1%

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

      6. associate-/l* 79.8%

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

      7. associate-*r/ 79.8%

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

      8. associate-*r* 79.8%

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

      9. *-commutative 79.8%

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

      10. associate-*r* 79.8%

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

      11. *-commutative 79.8%

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

      12. times-frac 89.7%

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

      13. fma-def 89.7%

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

      14. associate-/l* 89.7%

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

      15. associate-/r* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around -inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

      3. associate-*l/ 81.2%

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

      4. *-commutative 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-*l* 81.2%

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

      7. mul-1-neg 81.2%

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

      8. unsub-neg 81.2%

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

      9. *-commutative 81.2%

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

      10. associate-/l* 87.0%

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

   9. Simplified 87.0%

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

   10. Taylor expanded in c around 0 85.8%

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

   11. Taylor expanded in x around 0 74.0%

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

   if -3.19999999999999994e68 < z < 4e6

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 94.9%

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

      4. *-commutative 94.9%

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

      5. associate-+l- 94.9%

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

   3. Simplified 92.0%

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

      1. *-un-lft-identity 92.0%

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

      2. times-frac 93.2%

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

      3. associate-+l- 93.2%

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

      4. associate-*r* 96.8%

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

      5. associate-+l- 96.8%

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

      6. associate-*l* 96.8%

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

      7. associate-*r* 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in x around inf 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-*r* 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*l* 81.4%

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

   8. Simplified 81.4%

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

   if 8.79999999999999974e130 < z < 8.4999999999999999e150

   1. Initial program 31.5%

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

      1. associate-+l- 31.5%

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

      2. *-commutative 31.5%

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

      3. associate-*r* 45.8%

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

      4. *-commutative 45.8%

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

      5. associate-+l- 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in x around inf 45.8%

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

      1. div-inv 45.5%

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

      2. *-commutative 45.5%

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

   6. Applied egg-rr 45.5%

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

      1. associate-*r/ 45.8%

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

      2. *-rgt-identity 45.8%

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

      3. times-frac 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + y \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+130} \lor \neg \left(z \leq 8.5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 8: 70.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+137}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= x -1.28e+137)
   (* 9.0 (* (/ x c) (/ y z)))
   (if (<= x 8e-11)
     (/ (+ (* -4.0 (* t a)) (/ b z)) c)
     (* (/ 9.0 z) (* x (/ y c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.28e+137) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (x <= 8e-11) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.28d+137)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (x <= 8d-11) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c
    else
        tmp = (9.0d0 / z) * (x * (y / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.28e+137) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (x <= 8e-11) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	} else {
		tmp = (9.0 / z) * (x * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.28e+137:
		tmp = 9.0 * ((x / c) * (y / z))
	elif x <= 8e-11:
		tmp = ((-4.0 * (t * a)) + (b / z)) / c
	else:
		tmp = (9.0 / z) * (x * (y / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.28e+137)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (x <= 8e-11)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(9.0 / z) * Float64(x * Float64(y / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.28e+137)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (x <= 8e-11)
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	else
		tmp = (9.0 / z) * (x * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.28e+137], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-11], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(9.0 / z), $MachinePrecision] * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.27999999999999995e137

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-+l- 75.1%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in x around inf 60.9%

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

      1. times-frac 77.8%

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

   6. Applied egg-rr 77.8%

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

   if -1.27999999999999995e137 < x < 7.99999999999999952e-11

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*r* 82.8%

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

      4. *-commutative 82.8%

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

      5. associate-+l- 82.8%

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

   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 x around 0 85.0%

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

      1. cancel-sign-sub-inv 85.0%

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

      2. metadata-eval 85.0%

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

      3. +-commutative 85.0%

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

      4. *-commutative 85.0%

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

      5. fma-def 85.0%

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

      6. associate-/l* 87.7%

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

      7. associate-*r/ 87.7%

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

      8. associate-*r* 87.7%

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

      9. *-commutative 87.7%

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

      10. associate-*r* 87.7%

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

      11. *-commutative 87.7%

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

      12. times-frac 85.6%

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

      13. fma-def 86.3%

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

      14. associate-/l* 86.3%

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

      15. associate-/r* 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in z around -inf 90.7%

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

      1. mul-1-neg 90.7%

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

      2. unsub-neg 90.7%

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

      3. associate-*l/ 93.7%

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

      4. *-commutative 93.7%

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

      5. *-commutative 93.7%

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

      6. associate-*l* 93.7%

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

      7. mul-1-neg 93.7%

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

      8. unsub-neg 93.7%

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

      9. *-commutative 93.7%

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

      10. associate-/l* 93.8%

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

   9. Simplified 93.8%

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

   10. Taylor expanded in c around 0 89.5%

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

   11. Taylor expanded in x around 0 80.1%

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

   if 7.99999999999999952e-11 < x

   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* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-+l- 70.0%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in x around inf 45.3%

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

      1. associate-*r/ 45.3%

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

      2. *-commutative 45.3%

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

   6. Simplified 45.3%

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

      1. times-frac 45.8%

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

   8. Applied egg-rr 45.8%

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

      1. expm1-log1p-u 28.6%

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot y}{c}\right)\right)} \]

      2. expm1-udef 21.8%

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x \cdot y}{c}\right)} - 1\right)} \]

      3. associate-/l* 25.2%

         \[\leadsto \frac{9}{z} \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{c}{y}}}\right)} - 1\right) \]

   10. Applied egg-rr 25.2%

       \[\leadsto \frac{9}{z} \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{\frac{c}{y}}\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 29.4%

          \[\leadsto \frac{9}{z} \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{c}{y}}\right)\right)} \]

       2. expm1-log1p 48.4%

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

       3. associate-/l* 45.8%

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

       4. *-rgt-identity 45.8%

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

       5. associate-*r/ 45.8%

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

       6. associate-*l* 49.9%

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

       7. associate-*r/ 49.9%

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

       8. *-rgt-identity 49.9%

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

   12. Simplified 49.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+137}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \left(x \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 9: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+73}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -1.22e+73)
   (* -4.0 (/ a (/ c t)))
   (if (<= t -2.9e-196)
     (* 9.0 (* (/ x c) (/ y z)))
     (if (<= t 3.4e-187) (* (/ b c) (/ 1.0 z)) (* t (* (/ a c) -4.0))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.22e+73) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -2.9e-196) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (t <= 3.4e-187) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.22d+73)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-2.9d-196)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (t <= 3.4d-187) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = t * ((a / c) * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -1.22e+73) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -2.9e-196) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (t <= 3.4e-187) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.22e+73:
		tmp = -4.0 * (a / (c / t))
	elif t <= -2.9e-196:
		tmp = 9.0 * ((x / c) * (y / z))
	elif t <= 3.4e-187:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t * ((a / c) * -4.0)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.22e+73)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -2.9e-196)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (t <= 3.4e-187)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(t * Float64(Float64(a / c) * -4.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.22e+73)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -2.9e-196)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (t <= 3.4e-187)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = t * ((a / c) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -1.22e+73], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-196], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-187], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.21999999999999998e73

   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* 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-+l- 71.7%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-/l* 59.5%

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

   6. Simplified 59.5%

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

   if -1.21999999999999998e73 < t < -2.89999999999999987e-196

   1. Initial program 89.3%

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

      1. associate-+l- 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-+l- 83.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around inf 44.8%

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

      1. times-frac 47.4%

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

   6. Applied egg-rr 47.4%

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

   if -2.89999999999999987e-196 < t < 3.4000000000000001e-187

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-+l- 77.5%

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

   3. Simplified 85.9%

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

      1. *-un-lft-identity 85.9%

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

      2. times-frac 91.7%

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

      3. associate-+l- 91.7%

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

      4. associate-*r* 91.7%

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

      5. associate-+l- 91.7%

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

      6. associate-*l* 91.7%

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

      7. associate-*r* 91.7%

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

   5. Applied egg-rr 91.7%

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

   6. Taylor expanded in b around inf 51.2%

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

   if 3.4000000000000001e-187 < t

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-+l- 78.2%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. cancel-sign-sub-inv 80.1%

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

      2. metadata-eval 80.1%

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

      3. +-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. fma-def 80.1%

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

      6. associate-/l* 81.7%

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

      7. associate-*r/ 81.7%

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

      8. associate-*r* 81.7%

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

      9. *-commutative 81.7%

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

      10. associate-*r* 81.7%

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

      11. *-commutative 81.7%

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

      12. times-frac 82.3%

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

      13. fma-def 83.2%

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

      14. associate-/l* 82.5%

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

      15. associate-/r* 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in a around inf 44.3%

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

      1. associate-*l/ 48.2%

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

      2. *-commutative 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l* 48.2%

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

   9. Simplified 48.2%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+73}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \]

Alternative 10: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+71}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-201}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -1.6e+71)
   (* -4.0 (/ a (/ c t)))
   (if (<= t -8e-201)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= t 8.5e-188) (* (/ b c) (/ 1.0 z)) (* t (* (/ a c) -4.0))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.6e+71) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -8e-201) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t <= 8.5e-188) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.6d+71)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-8d-201)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (t <= 8.5d-188) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = t * ((a / c) * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -1.6e+71) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -8e-201) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t <= 8.5e-188) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.6e+71:
		tmp = -4.0 * (a / (c / t))
	elif t <= -8e-201:
		tmp = 9.0 * ((x / z) * (y / c))
	elif t <= 8.5e-188:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t * ((a / c) * -4.0)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.6e+71)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -8e-201)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (t <= 8.5e-188)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(t * Float64(Float64(a / c) * -4.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.6e+71)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -8e-201)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (t <= 8.5e-188)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = t * ((a / c) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -1.6e+71], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-201], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-188], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.60000000000000012e71

   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* 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-+l- 71.7%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-/l* 59.5%

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

   6. Simplified 59.5%

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

   if -1.60000000000000012e71 < t < -7.99999999999999957e-201

   1. Initial program 89.5%

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

      1. associate-+l- 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*r* 83.7%

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

      4. *-commutative 83.7%

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

      5. associate-+l- 83.7%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around inf 43.9%

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

      1. div-inv 43.8%

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

      2. *-commutative 43.8%

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

   6. Applied egg-rr 43.8%

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

      1. associate-*r/ 43.9%

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

      2. *-rgt-identity 43.9%

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

      3. times-frac 44.3%

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

   8. Simplified 44.3%

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

   if -7.99999999999999957e-201 < t < 8.5000000000000004e-188

   1. Initial program 85.6%

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

      1. associate-+l- 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-+l- 77.0%

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

   3. Simplified 85.6%

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

      1. *-un-lft-identity 85.6%

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

      2. times-frac 93.6%

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

      3. associate-+l- 93.6%

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

      4. associate-*r* 93.6%

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

      5. associate-+l- 93.6%

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

      6. associate-*l* 93.6%

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

      7. associate-*r* 93.6%

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

   5. Applied egg-rr 93.6%

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

   6. Taylor expanded in b around inf 52.2%

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

   if 8.5000000000000004e-188 < t

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-+l- 78.2%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. cancel-sign-sub-inv 80.1%

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

      2. metadata-eval 80.1%

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

      3. +-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. fma-def 80.1%

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

      6. associate-/l* 81.7%

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

      7. associate-*r/ 81.7%

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

      8. associate-*r* 81.7%

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

      9. *-commutative 81.7%

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

      10. associate-*r* 81.7%

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

      11. *-commutative 81.7%

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

      12. times-frac 82.3%

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

      13. fma-def 83.2%

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

      14. associate-/l* 82.5%

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

      15. associate-/r* 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in a around inf 44.3%

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

      1. associate-*l/ 48.2%

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

      2. *-commutative 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l* 48.2%

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

   9. Simplified 48.2%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+71}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-201}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \]

Alternative 11: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-199}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-187}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -3.7e+71)
   (* -4.0 (/ a (/ c t)))
   (if (<= t -8.6e-199)
     (* 9.0 (/ y (/ z (/ x c))))
     (if (<= t 7.8e-187) (* (/ b c) (/ 1.0 z)) (* t (* (/ a c) -4.0))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.7e+71) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -8.6e-199) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (t <= 7.8e-187) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-3.7d+71)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-8.6d-199)) then
        tmp = 9.0d0 * (y / (z / (x / c)))
    else if (t <= 7.8d-187) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = t * ((a / c) * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -3.7e+71) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -8.6e-199) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (t <= 7.8e-187) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t * ((a / c) * -4.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.7e+71:
		tmp = -4.0 * (a / (c / t))
	elif t <= -8.6e-199:
		tmp = 9.0 * (y / (z / (x / c)))
	elif t <= 7.8e-187:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t * ((a / c) * -4.0)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.7e+71)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -8.6e-199)
		tmp = Float64(9.0 * Float64(y / Float64(z / Float64(x / c))));
	elseif (t <= 7.8e-187)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(t * Float64(Float64(a / c) * -4.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.7e+71)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -8.6e-199)
		tmp = 9.0 * (y / (z / (x / c)));
	elseif (t <= 7.8e-187)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = t * ((a / c) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -3.7e+71], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.6e-199], N[(9.0 * N[(y / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-187], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7e71

   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* 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-+l- 71.7%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-/l* 59.5%

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

   6. Simplified 59.5%

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

   if -3.7e71 < t < -8.6000000000000007e-199

   1. Initial program 89.3%

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

      1. associate-+l- 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-+l- 83.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 83.2%

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

      1. cancel-sign-sub-inv 83.2%

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

      2. metadata-eval 83.2%

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

      3. +-commutative 83.2%

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

      4. *-commutative 83.2%

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

      5. fma-def 83.2%

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

      6. associate-/l* 83.2%

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

      7. associate-*r/ 83.1%

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

      8. associate-*r* 83.3%

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

      9. *-commutative 83.3%

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

      10. associate-*r* 83.2%

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

      11. *-commutative 83.2%

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

      12. times-frac 87.1%

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

      13. fma-def 87.1%

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

      14. associate-/l* 87.1%

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

      15. associate-/r* 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in z around -inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

      3. associate-*l/ 83.4%

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

      4. *-commutative 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-*l* 83.4%

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

      7. mul-1-neg 83.4%

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

      8. unsub-neg 83.4%

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

      9. *-commutative 83.4%

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

      10. associate-/l* 87.4%

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

   9. Simplified 87.4%

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

   10. Taylor expanded in x around inf 44.8%

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

       1. *-commutative 44.8%

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

       2. associate-/r* 39.4%

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

       3. associate-*l/ 43.5%

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

       4. *-commutative 43.5%

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

       5. associate-/l* 45.4%

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

   12. Simplified 45.4%

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

   if -8.6000000000000007e-199 < t < 7.7999999999999998e-187

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-+l- 77.5%

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

   3. Simplified 85.9%

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

      1. *-un-lft-identity 85.9%

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

      2. times-frac 91.7%

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

      3. associate-+l- 91.7%

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

      4. associate-*r* 91.7%

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

      5. associate-+l- 91.7%

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

      6. associate-*l* 91.7%

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

      7. associate-*r* 91.7%

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

   5. Applied egg-rr 91.7%

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

   6. Taylor expanded in b around inf 51.2%

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

   if 7.7999999999999998e-187 < t

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-+l- 78.2%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. cancel-sign-sub-inv 80.1%

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

      2. metadata-eval 80.1%

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

      3. +-commutative 80.1%

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

      4. *-commutative 80.1%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 81.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-*r/ 81.7%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \frac{b}{c \cdot z}\right) \]

      8. associate-*r* 81.7%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      9. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      10. associate-*r* 81.7%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      11. *-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{z \cdot c}} + \frac{b}{c \cdot z}\right) \]

      12. times-frac 82.3%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\frac{x}{z} \cdot \frac{9 \cdot y}{c}} + \frac{b}{c \cdot z}\right) \]

      13. fma-def 83.2%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\mathsf{fma}\left(\frac{x}{z}, \frac{9 \cdot y}{c}, \frac{b}{c \cdot z}\right)}\right) \]

      14. associate-/l* 82.5%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \color{blue}{\frac{9}{\frac{c}{y}}}, \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/r* 82.6%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   6. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   7. Taylor expanded in a around inf 44.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 48.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 48.2%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

      3. *-commutative 48.2%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

      4. associate-*l* 48.2%

         \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]

   9. Simplified 48.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-199}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-187}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \end{array} \]

Alternative 12: 47.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+27} \lor \neg \left(t \leq 1.4 \cdot 10^{-186}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -1.95e+27) (not (<= t 1.4e-186)))
   (* -4.0 (/ (* t a) c))
   (/ (/ b c) z)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.95e+27) || !(t <= 1.4e-186)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.95d+27)) .or. (.not. (t <= 1.4d-186))) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -1.95e+27) || !(t <= 1.4e-186)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.95e+27) or not (t <= 1.4e-186):
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.95e+27) || !(t <= 1.4e-186))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.95e+27) || ~((t <= 1.4e-186)))
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -1.95e+27], N[Not[LessEqual[t, 1.4e-186]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e27 or 1.39999999999999992e-186 < t

   1. Initial program 73.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 45.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -1.9499999999999999e27 < t < 1.39999999999999992e-186

   1. Initial program 87.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 46.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 48.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+27} \lor \neg \left(t \leq 1.4 \cdot 10^{-186}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 13: 49.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+27} \lor \neg \left(t \leq 4.4 \cdot 10^{-187}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -8.2e+27) (not (<= t 4.4e-187)))
   (* t (* (/ a c) -4.0))
   (/ (/ b c) z)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -8.2e+27) || !(t <= 4.4e-187)) {
		tmp = t * ((a / c) * -4.0);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-8.2d+27)) .or. (.not. (t <= 4.4d-187))) then
        tmp = t * ((a / c) * (-4.0d0))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -8.2e+27) || !(t <= 4.4e-187)) {
		tmp = t * ((a / c) * -4.0);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -8.2e+27) or not (t <= 4.4e-187):
		tmp = t * ((a / c) * -4.0)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -8.2e+27) || !(t <= 4.4e-187))
		tmp = Float64(t * Float64(Float64(a / c) * -4.0));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -8.2e+27) || ~((t <= 4.4e-187)))
		tmp = t * ((a / c) * -4.0);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -8.2e+27], N[Not[LessEqual[t, 4.4e-187]], $MachinePrecision]], N[(t * N[(N[(a / c), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2000000000000005e27 or 4.40000000000000016e-187 < t

   1. Initial program 73.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around 0 76.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 76.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 76.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 76.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 76.1%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 76.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 79.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-*r/ 79.4%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \frac{b}{c \cdot z}\right) \]

      8. associate-*r* 79.4%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      9. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      10. associate-*r* 79.4%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      11. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{z \cdot c}} + \frac{b}{c \cdot z}\right) \]

      12. times-frac 82.1%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\frac{x}{z} \cdot \frac{9 \cdot y}{c}} + \frac{b}{c \cdot z}\right) \]

      13. fma-def 83.3%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \color{blue}{\mathsf{fma}\left(\frac{x}{z}, \frac{9 \cdot y}{c}, \frac{b}{c \cdot z}\right)}\right) \]

      14. associate-/l* 82.8%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \color{blue}{\frac{9}{\frac{c}{y}}}, \frac{b}{c \cdot z}\right)\right) \]

      15. associate-/r* 83.3%

          \[\leadsto \mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \color{blue}{\frac{\frac{b}{c}}{z}}\right)\right) \]

   6. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{\frac{c}{t}}, -4, \mathsf{fma}\left(\frac{x}{z}, \frac{9}{\frac{c}{y}}, \frac{\frac{b}{c}}{z}\right)\right)} \]

   7. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 49.8%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 49.8%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot -4} \]

      3. *-commutative 49.8%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

      4. associate-*l* 49.8%

         \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]

   9. Simplified 49.8%

      \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]

   if -8.2000000000000005e27 < t < 4.40000000000000016e-187

   1. Initial program 87.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 46.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 48.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+27} \lor \neg \left(t \leq 4.4 \cdot 10^{-187}\right):\\ \;\;\;\;t \cdot \left(\frac{a}{c} \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 35.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.5%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 77.8%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 78.9%

   \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 33.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 33.3%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 33.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 33.3%

   \[\leadsto \frac{b}{c \cdot z} \]

Alternative 15: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ (/ b c) z))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b / c) / z
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 78.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.5%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 77.8%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 78.9%

   \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 33.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. associate-/r* 34.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

6. Simplified 34.0%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Final simplification 34.0%

   \[\leadsto \frac{\frac{b}{c}}{z} \]

Developer target: 80.7% 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 2023290 
(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)))