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

Percentage Accurate: 80.6% → 88.4%

Time: 14.2s

Alternatives: 16

Speedup: 0.7×

• 38.3% 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: 80.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{z}\\ \mathbf{elif}\;z \leq 2250000000000:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{z \cdot y}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7e-23)
   (* (/ 1.0 c) (/ (+ b (fma x (* 9.0 y) (* z (* a (* t -4.0))))) z))
   (if (<= z 2250000000000.0)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (*
      (/ 1.0 c)
      (* y (+ (* -4.0 (/ (* a t) y)) (+ (* 9.0 (/ x z)) (/ b (* z y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e-23) {
		tmp = (1.0 / c) * ((b + fma(x, (9.0 * y), (z * (a * (t * -4.0))))) / z);
	} else if (z <= 2250000000000.0) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (1.0 / c) * (y * ((-4.0 * ((a * t) / y)) + ((9.0 * (x / z)) + (b / (z * y)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7e-23)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(z * Float64(a * Float64(t * -4.0))))) / z));
	elseif (z <= 2250000000000.0)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(y * Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + Float64(Float64(9.0 * Float64(x / z)) + Float64(b / Float64(z * y))))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7e-23], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2250000000000.0], 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[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(y * N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999987e-23

   1. Initial program 67.1%

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

   3. Simplified 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. *-commutative 74.3%

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

      3. times-frac 88.9%

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

      4. +-commutative 88.9%

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

   6. Applied egg-rr 88.9%

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

   if -6.99999999999999987e-23 < z < 2.25e12

   1. Initial program 93.7%

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

   if 2.25e12 < z

   1. Initial program 56.4%

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

   3. Simplified 71.6%

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

      1. *-un-lft-identity 71.6%

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

      2. *-commutative 71.6%

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

      3. times-frac 76.6%

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

      4. +-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

   7. Taylor expanded in y around inf 88.5%

      \[\leadsto \frac{1}{c} \cdot \color{blue}{\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{z}\\ \mathbf{elif}\;z \leq 2250000000000:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{z \cdot y}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+91}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1000000:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{z \cdot y}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.52e+91)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= z 1000000.0)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (*
      (/ 1.0 c)
      (* y (+ (* -4.0 (/ (* a t) y)) (+ (* 9.0 (/ x z)) (/ b (* z y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.52e+91) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 1000000.0) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (1.0 / c) * (y * ((-4.0 * ((a * t) / y)) + ((9.0 * (x / z)) + (b / (z * y)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.52d+91)) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else if (z <= 1000000.0d0) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (1.0d0 / c) * (y * (((-4.0d0) * ((a * t) / y)) + ((9.0d0 * (x / z)) + (b / (z * y)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.52e+91) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 1000000.0) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (1.0 / c) * (y * ((-4.0 * ((a * t) / y)) + ((9.0 * (x / z)) + (b / (z * y)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.52e+91:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif z <= 1000000.0:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (1.0 / c) * (y * ((-4.0 * ((a * t) / y)) + ((9.0 * (x / z)) + (b / (z * y)))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.52e+91)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (z <= 1000000.0)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(y * Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + Float64(Float64(9.0 * Float64(x / z)) + Float64(b / Float64(z * y))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.52e+91)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (z <= 1000000.0)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (1.0 / c) * (y * ((-4.0 * ((a * t) / y)) + ((9.0 * (x / z)) + (b / (z * y)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.52e+91], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1000000.0], 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[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(y * N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52e91

   1. Initial program 54.5%

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

   3. Simplified 65.4%

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

      1. *-un-lft-identity 65.4%

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

      2. *-commutative 65.4%

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

      3. times-frac 87.4%

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

      4. +-commutative 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in y around inf 79.1%

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

   8. Taylor expanded in y around 0 87.3%

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

   if -1.52e91 < z < 1e6

   1. Initial program 93.4%

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

   if 1e6 < z

   1. Initial program 56.4%

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

   3. Simplified 71.6%

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

      1. *-un-lft-identity 71.6%

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

      2. *-commutative 71.6%

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

      3. times-frac 76.6%

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

      4. +-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

   7. Taylor expanded in y around inf 88.5%

      \[\leadsto \frac{1}{c} \cdot \color{blue}{\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{y \cdot z}\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+91}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1000000:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + \left(9 \cdot \frac{x}{z} + \frac{b}{z \cdot y}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b \cdot \frac{1}{z \cdot c}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (/ 1.0 (* z c)))))
   (if (<= z -2.9e+14)
     (* (* a t) (/ -4.0 c))
     (if (<= z 5.2e-272)
       t_1
       (if (<= z 2.6e-242)
         (/ (* 9.0 (/ (* x y) c)) z)
         (if (<= z 1.6e-87)
           t_1
           (if (<= z 0.00024)
             (* 9.0 (* y (/ x (* z c))))
             (* a (/ (* t -4.0) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double tmp;
	if (z <= -2.9e+14) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 5.2e-272) {
		tmp = t_1;
	} else if (z <= 2.6e-242) {
		tmp = (9.0 * ((x * y) / c)) / z;
	} else if (z <= 1.6e-87) {
		tmp = t_1;
	} else if (z <= 0.00024) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = b * (1.0d0 / (z * c))
    if (z <= (-2.9d+14)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= 5.2d-272) then
        tmp = t_1
    else if (z <= 2.6d-242) then
        tmp = (9.0d0 * ((x * y) / c)) / z
    else if (z <= 1.6d-87) then
        tmp = t_1
    else if (z <= 0.00024d0) then
        tmp = 9.0d0 * (y * (x / (z * c)))
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double tmp;
	if (z <= -2.9e+14) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 5.2e-272) {
		tmp = t_1;
	} else if (z <= 2.6e-242) {
		tmp = (9.0 * ((x * y) / c)) / z;
	} else if (z <= 1.6e-87) {
		tmp = t_1;
	} else if (z <= 0.00024) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b * (1.0 / (z * c))
	tmp = 0
	if z <= -2.9e+14:
		tmp = (a * t) * (-4.0 / c)
	elif z <= 5.2e-272:
		tmp = t_1
	elif z <= 2.6e-242:
		tmp = (9.0 * ((x * y) / c)) / z
	elif z <= 1.6e-87:
		tmp = t_1
	elif z <= 0.00024:
		tmp = 9.0 * (y * (x / (z * c)))
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(1.0 / Float64(z * c)))
	tmp = 0.0
	if (z <= -2.9e+14)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= 5.2e-272)
		tmp = t_1;
	elseif (z <= 2.6e-242)
		tmp = Float64(Float64(9.0 * Float64(Float64(x * y) / c)) / z);
	elseif (z <= 1.6e-87)
		tmp = t_1;
	elseif (z <= 0.00024)
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (1.0 / (z * c));
	tmp = 0.0;
	if (z <= -2.9e+14)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= 5.2e-272)
		tmp = t_1;
	elseif (z <= 2.6e-242)
		tmp = (9.0 * ((x * y) / c)) / z;
	elseif (z <= 1.6e-87)
		tmp = t_1;
	elseif (z <= 0.00024)
		tmp = 9.0 * (y * (x / (z * c)));
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+14], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-272], t$95$1, If[LessEqual[z, 2.6e-242], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.6e-87], t$95$1, If[LessEqual[z, 0.00024], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.9e14

   1. Initial program 64.7%

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

      1. associate-+l- 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-+l- 60.6%

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

      6. associate-*l* 60.6%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/l* 56.1%

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

      2. associate-*r/ 56.0%

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

      3. associate-*r* 61.7%

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

   9. Applied egg-rr 61.7%

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

   if -2.9e14 < z < 5.19999999999999983e-272 or 2.60000000000000017e-242 < z < 1.59999999999999989e-87

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r* 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-+l- 95.2%

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

      6. associate-*l* 95.2%

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

      7. associate-*l* 92.6%

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

      8. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

   7. Simplified 56.6%

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

      1. div-inv 57.6%

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

   9. Applied egg-rr 57.6%

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

   if 5.19999999999999983e-272 < z < 2.60000000000000017e-242

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-+l- 99.8%

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

      6. associate-*l* 99.8%

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

      7. associate-*l* 87.3%

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

      8. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in a around 0 99.8%

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

   7. Taylor expanded in x around inf 87.6%

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

   if 1.59999999999999989e-87 < z < 2.40000000000000006e-4

   1. Initial program 99.9%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 81.4%

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

      1. associate-*r/ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r* 81.5%

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

      4. associate-*l/ 75.0%

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

      5. *-commutative 75.0%

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

      6. associate-*r/ 75.1%

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

      7. associate-*l* 75.0%

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

      8. *-commutative 75.0%

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

   9. Simplified 75.0%

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

   if 2.40000000000000006e-4 < z

   1. Initial program 56.3%

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

      1. associate-+l- 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*r* 66.0%

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

      4. *-commutative 66.0%

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

      5. associate-+l- 66.0%

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

      6. associate-*l* 66.1%

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

      7. associate-*l* 67.6%

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

      8. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in z around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/l* 58.1%

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

      3. associate-*r* 58.1%

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

      4. *-commutative 58.1%

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

      5. associate-*r/ 58.1%

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

      6. *-commutative 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b \cdot \frac{1}{z \cdot c}\\ t_2 := 9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.105:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (/ 1.0 (* z c)))) (t_2 (* 9.0 (* y (/ x (* z c))))))
   (if (<= z -2.6e+14)
     (* (* a t) (/ -4.0 c))
     (if (<= z 3.5e-273)
       t_1
       (if (<= z 1e-242)
         t_2
         (if (<= z 1.95e-87)
           t_1
           (if (<= z 0.105) t_2 (* a (/ (* t -4.0) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (z <= -2.6e+14) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 3.5e-273) {
		tmp = t_1;
	} else if (z <= 1e-242) {
		tmp = t_2;
	} else if (z <= 1.95e-87) {
		tmp = t_1;
	} else if (z <= 0.105) {
		tmp = t_2;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = b * (1.0d0 / (z * c))
    t_2 = 9.0d0 * (y * (x / (z * c)))
    if (z <= (-2.6d+14)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= 3.5d-273) then
        tmp = t_1
    else if (z <= 1d-242) then
        tmp = t_2
    else if (z <= 1.95d-87) then
        tmp = t_1
    else if (z <= 0.105d0) then
        tmp = t_2
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (z <= -2.6e+14) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 3.5e-273) {
		tmp = t_1;
	} else if (z <= 1e-242) {
		tmp = t_2;
	} else if (z <= 1.95e-87) {
		tmp = t_1;
	} else if (z <= 0.105) {
		tmp = t_2;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b * (1.0 / (z * c))
	t_2 = 9.0 * (y * (x / (z * c)))
	tmp = 0
	if z <= -2.6e+14:
		tmp = (a * t) * (-4.0 / c)
	elif z <= 3.5e-273:
		tmp = t_1
	elif z <= 1e-242:
		tmp = t_2
	elif z <= 1.95e-87:
		tmp = t_1
	elif z <= 0.105:
		tmp = t_2
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(1.0 / Float64(z * c)))
	t_2 = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))))
	tmp = 0.0
	if (z <= -2.6e+14)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= 3.5e-273)
		tmp = t_1;
	elseif (z <= 1e-242)
		tmp = t_2;
	elseif (z <= 1.95e-87)
		tmp = t_1;
	elseif (z <= 0.105)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (1.0 / (z * c));
	t_2 = 9.0 * (y * (x / (z * c)));
	tmp = 0.0;
	if (z <= -2.6e+14)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= 3.5e-273)
		tmp = t_1;
	elseif (z <= 1e-242)
		tmp = t_2;
	elseif (z <= 1.95e-87)
		tmp = t_1;
	elseif (z <= 0.105)
		tmp = t_2;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+14], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-273], t$95$1, If[LessEqual[z, 1e-242], t$95$2, If[LessEqual[z, 1.95e-87], t$95$1, If[LessEqual[z, 0.105], t$95$2, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e14

   1. Initial program 64.7%

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

      1. associate-+l- 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-+l- 60.6%

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

      6. associate-*l* 60.6%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/l* 56.1%

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

      2. associate-*r/ 56.0%

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

      3. associate-*r* 61.7%

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

   9. Applied egg-rr 61.7%

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

   if -2.6e14 < z < 3.49999999999999992e-273 or 1e-242 < z < 1.9499999999999999e-87

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r* 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-+l- 95.2%

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

      6. associate-*l* 95.2%

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

      7. associate-*l* 92.6%

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

      8. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

   7. Simplified 56.6%

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

      1. div-inv 57.6%

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

   9. Applied egg-rr 57.6%

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

   if 3.49999999999999992e-273 < z < 1e-242 or 1.9499999999999999e-87 < z < 0.104999999999999996

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 83.6%

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

      1. associate-*r/ 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*r* 83.7%

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

      4. associate-*l/ 79.6%

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

      5. *-commutative 79.6%

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

      6. associate-*r/ 79.7%

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

      7. associate-*l* 79.5%

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

      8. *-commutative 79.5%

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

   9. Simplified 79.5%

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

   if 0.104999999999999996 < z

   1. Initial program 56.3%

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

      1. associate-+l- 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*r* 66.0%

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

      4. *-commutative 66.0%

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

      5. associate-+l- 66.0%

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

      6. associate-*l* 66.1%

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

      7. associate-*l* 67.6%

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

      8. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in z around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/l* 58.1%

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

      3. associate-*r* 58.1%

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

      4. *-commutative 58.1%

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

      5. associate-*r/ 58.1%

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

      6. *-commutative 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 10^{-242}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.105:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+90}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right) + y \cdot \frac{\frac{b}{y} - x \cdot -9}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7e+90)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= z 2.15e+45)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (+ (* -4.0 (* a (/ t c))) (* y (/ (- (/ b y) (* x -9.0)) (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e+90) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 2.15e+45) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (-4.0 * (a * (t / c))) + (y * (((b / y) - (x * -9.0)) / (z * c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-7d+90)) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else if (z <= 2.15d+45) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((-4.0d0) * (a * (t / c))) + (y * (((b / y) - (x * (-9.0d0))) / (z * c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7e+90) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 2.15e+45) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (-4.0 * (a * (t / c))) + (y * (((b / y) - (x * -9.0)) / (z * c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7e+90:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif z <= 2.15e+45:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (-4.0 * (a * (t / c))) + (y * (((b / y) - (x * -9.0)) / (z * c)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7e+90)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (z <= 2.15e+45)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * Float64(a * Float64(t / c))) + Float64(y * Float64(Float64(Float64(b / y) - Float64(x * -9.0)) / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7e+90)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (z <= 2.15e+45)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (-4.0 * (a * (t / c))) + (y * (((b / y) - (x * -9.0)) / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7e+90], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.15e+45], 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[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(N[(b / y), $MachinePrecision] - N[(x * -9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999997e90

   1. Initial program 54.5%

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

   3. Simplified 65.4%

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

      1. *-un-lft-identity 65.4%

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

      2. *-commutative 65.4%

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

      3. times-frac 87.4%

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

      4. +-commutative 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in y around inf 79.1%

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

   8. Taylor expanded in y around 0 87.3%

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

   if -6.9999999999999997e90 < z < 2.1500000000000002e45

   1. Initial program 92.5%

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

   if 2.1500000000000002e45 < z

   1. Initial program 53.5%

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

   3. Simplified 67.0%

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

      1. *-un-lft-identity 67.0%

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

      2. *-commutative 67.0%

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

      3. times-frac 72.9%

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

      4. +-commutative 72.9%

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

   6. Applied egg-rr 72.9%

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

   7. Taylor expanded in y around inf 86.7%

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

   8. Taylor expanded in z around -inf 79.3%

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

      1. fma-define 79.3%

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

      2. mul-1-neg 79.3%

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

      3. fma-neg 79.3%

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

      4. associate-/l* 71.9%

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

      5. associate-/l* 77.3%

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

      6. mul-1-neg 77.3%

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

      7. unsub-neg 77.3%

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

      8. *-commutative 77.3%

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

      9. *-commutative 77.3%

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

   10. Simplified 77.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+90}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right) + y \cdot \frac{\frac{b}{y} - x \cdot -9}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+90} \lor \neg \left(z \leq 3.9 \cdot 10^{+179}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.2e+90) (not (<= z 3.9e+179)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.2e+90) || !(z <= 3.9e+179)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-4.2d+90)) .or. (.not. (z <= 3.9d+179))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.2e+90) || !(z <= 3.9e+179)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4.2e+90) or not (z <= 3.9e+179):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.2e+90) || !(z <= 3.9e+179))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4.2e+90) || ~((z <= 3.9e+179)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.2e+90], N[Not[LessEqual[z, 3.9e+179]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], 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[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999961e90 or 3.89999999999999974e179 < z

   1. Initial program 47.4%

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

   3. Simplified 61.3%

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

      1. *-un-lft-identity 61.3%

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

      2. *-commutative 61.3%

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

      3. times-frac 79.7%

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

      4. +-commutative 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in y around inf 82.4%

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

   8. Taylor expanded in y around 0 87.8%

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

   if -4.19999999999999961e90 < z < 3.89999999999999974e179

   1. Initial program 89.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+90} \lor \neg \left(z \leq 3.9 \cdot 10^{+179}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+79} \lor \neg \left(z \leq 3.7 \cdot 10^{+179}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.4e+79) (not (<= z 3.7e+179)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (+ (* x (* 9.0 y)) (* t (* a (* z -4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+79) || !(z <= 3.7e+179)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) + (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.4d+79)) .or. (.not. (z <= 3.7d+179))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) + (t * (a * (z * (-4.0d0)))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+79) || !(z <= 3.7e+179)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) + (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.4e+79) or not (z <= 3.7e+179):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + ((x * (9.0 * y)) + (t * (a * (z * -4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.4e+79) || !(z <= 3.7e+179))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) + Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.4e+79) || ~((z <= 3.7e+179)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + ((x * (9.0 * y)) + (t * (a * (z * -4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.4e+79], N[Not[LessEqual[z, 3.7e+179]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e79 or 3.6999999999999999e179 < z

   1. Initial program 49.5%

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

   3. Simplified 62.8%

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

      1. *-un-lft-identity 62.8%

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

      2. *-commutative 62.8%

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

      3. times-frac 80.5%

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

      4. +-commutative 80.5%

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

   6. Applied egg-rr 80.5%

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

   7. Taylor expanded in y around inf 81.9%

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

   8. Taylor expanded in y around 0 87.0%

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

   if -1.4000000000000001e79 < z < 3.6999999999999999e179

   1. Initial program 89.7%

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

   3. Simplified 92.8%

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

      1. fma-undefine 91.7%

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

   6. Applied egg-rr 91.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+79} \lor \neg \left(z \leq 3.7 \cdot 10^{+179}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b \cdot \frac{1}{z \cdot c}\\ \mathbf{if}\;z \leq -48000000000:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-247}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (/ 1.0 (* z c)))))
   (if (<= z -48000000000.0)
     (* (* a t) (/ -4.0 c))
     (if (<= z 2.8e-272)
       t_1
       (if (<= z 2.45e-247)
         (* 9.0 (* x (/ (/ y c) z)))
         (if (<= z 1.6e-14) t_1 (* a (/ (* t -4.0) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double tmp;
	if (z <= -48000000000.0) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 2.8e-272) {
		tmp = t_1;
	} else if (z <= 2.45e-247) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else if (z <= 1.6e-14) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = b * (1.0d0 / (z * c))
    if (z <= (-48000000000.0d0)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= 2.8d-272) then
        tmp = t_1
    else if (z <= 2.45d-247) then
        tmp = 9.0d0 * (x * ((y / c) / z))
    else if (z <= 1.6d-14) then
        tmp = t_1
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (1.0 / (z * c));
	double tmp;
	if (z <= -48000000000.0) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 2.8e-272) {
		tmp = t_1;
	} else if (z <= 2.45e-247) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else if (z <= 1.6e-14) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b * (1.0 / (z * c))
	tmp = 0
	if z <= -48000000000.0:
		tmp = (a * t) * (-4.0 / c)
	elif z <= 2.8e-272:
		tmp = t_1
	elif z <= 2.45e-247:
		tmp = 9.0 * (x * ((y / c) / z))
	elif z <= 1.6e-14:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(1.0 / Float64(z * c)))
	tmp = 0.0
	if (z <= -48000000000.0)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= 2.8e-272)
		tmp = t_1;
	elseif (z <= 2.45e-247)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c) / z)));
	elseif (z <= 1.6e-14)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (1.0 / (z * c));
	tmp = 0.0;
	if (z <= -48000000000.0)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= 2.8e-272)
		tmp = t_1;
	elseif (z <= 2.45e-247)
		tmp = 9.0 * (x * ((y / c) / z));
	elseif (z <= 1.6e-14)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -48000000000.0], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-272], t$95$1, If[LessEqual[z, 2.45e-247], N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-14], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e10

   1. Initial program 64.7%

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

      1. associate-+l- 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-+l- 60.6%

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

      6. associate-*l* 60.6%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/l* 56.1%

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

      2. associate-*r/ 56.0%

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

      3. associate-*r* 61.7%

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

   9. Applied egg-rr 61.7%

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

   if -4.8e10 < z < 2.79999999999999994e-272 or 2.45e-247 < z < 1.6000000000000001e-14

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*r* 95.6%

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

      4. *-commutative 95.6%

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

      5. associate-+l- 95.6%

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

      6. associate-*l* 95.6%

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

      7. associate-*l* 93.2%

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

      8. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in b around inf 57.0%

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

      1. *-commutative 57.0%

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

   7. Simplified 57.0%

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

      1. div-inv 57.9%

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

   9. Applied egg-rr 57.9%

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

   if 2.79999999999999994e-272 < z < 2.45e-247

   1. Initial program 99.8%

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

   3. Simplified 87.3%

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

      1. *-un-lft-identity 87.3%

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

      2. *-commutative 87.3%

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

      3. times-frac 63.8%

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

      4. +-commutative 63.8%

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

   6. Applied egg-rr 63.8%

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

   7. Taylor expanded in x around inf 87.4%

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

      1. associate-/l* 75.9%

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

      2. associate-/r* 75.9%

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

   9. Simplified 75.9%

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

   if 1.6000000000000001e-14 < z

   1. Initial program 59.0%

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

      1. associate-+l- 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-*r* 68.1%

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

      4. *-commutative 68.1%

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

      5. associate-+l- 68.1%

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

      6. associate-*l* 68.2%

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

      7. associate-*l* 69.6%

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

      8. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 57.7%

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

      3. associate-*r* 57.6%

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

      4. *-commutative 57.6%

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

      5. associate-*r/ 57.6%

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

      6. *-commutative 57.6%

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

   7. Simplified 57.6%

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

Alternative 9: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-28} \lor \neg \left(z \leq 15.2\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.75e-28) (not (<= z 15.2)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* y (* x 9.0))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.75e-28) || !(z <= 15.2)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.75d-28)) .or. (.not. (z <= 15.2d0))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (y * (x * 9.0d0))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.75e-28) || !(z <= 15.2)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (x * 9.0))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.75e-28) or not (z <= 15.2):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (y * (x * 9.0))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.75e-28) || !(z <= 15.2))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.75e-28) || ~((z <= 15.2)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (y * (x * 9.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.75e-28], N[Not[LessEqual[z, 15.2]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-28 or 15.199999999999999 < z

   1. Initial program 63.2%

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

   3. Simplified 73.7%

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

      1. *-un-lft-identity 73.7%

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

      2. *-commutative 73.7%

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

      3. times-frac 83.7%

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

      4. +-commutative 83.7%

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

   6. Applied egg-rr 83.7%

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

   7. Taylor expanded in y around inf 84.6%

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

   8. Taylor expanded in y around 0 79.7%

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

   if -1.75e-28 < z < 15.199999999999999

   1. Initial program 93.6%

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

   3. Simplified 92.0%

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

      1. *-un-lft-identity 92.0%

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

      2. *-commutative 92.0%

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

      3. times-frac 83.8%

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

      4. +-commutative 83.8%

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

   6. Applied egg-rr 83.8%

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

   7. Taylor expanded in z around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-*r* 84.3%

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

      3. *-commutative 84.3%

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

   9. Simplified 84.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-28} \lor \neg \left(z \leq 15.2\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-28} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -8e-28) (not (<= z 2.2)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -8e-28) || !(z <= 2.2)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-8d-28)) .or. (.not. (z <= 2.2d0))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -8e-28) || !(z <= 2.2)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -8e-28) or not (z <= 2.2):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -8e-28) || !(z <= 2.2))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -8e-28) || ~((z <= 2.2)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -8e-28], N[Not[LessEqual[z, 2.2]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999977e-28 or 2.2000000000000002 < z

   1. Initial program 63.2%

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

   3. Simplified 73.7%

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

      1. *-un-lft-identity 73.7%

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

      2. *-commutative 73.7%

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

      3. times-frac 83.7%

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

      4. +-commutative 83.7%

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

   6. Applied egg-rr 83.7%

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

   7. Taylor expanded in y around inf 84.6%

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

   8. Taylor expanded in y around 0 79.7%

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

   if -7.99999999999999977e-28 < z < 2.2000000000000002

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 95.1%

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

      4. *-commutative 95.1%

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

      5. associate-+l- 95.1%

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

      6. associate-*l* 95.1%

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

      7. associate-*l* 92.0%

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

      8. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around inf 84.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-28} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+184}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -4.6e+58)
   (* 9.0 (* x (/ (/ y c) z)))
   (if (<= y 4e+184)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (* 9.0 (* y (/ x (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -4.6e+58) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else if (y <= 4e+184) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = 9.0 * (y * (x / (z * c)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (y <= (-4.6d+58)) then
        tmp = 9.0d0 * (x * ((y / c) / z))
    else if (y <= 4d+184) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = 9.0d0 * (y * (x / (z * c)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -4.6e+58) {
		tmp = 9.0 * (x * ((y / c) / z));
	} else if (y <= 4e+184) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = 9.0 * (y * (x / (z * c)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -4.6e+58:
		tmp = 9.0 * (x * ((y / c) / z))
	elif y <= 4e+184:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = 9.0 * (y * (x / (z * c)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -4.6e+58)
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c) / z)));
	elseif (y <= 4e+184)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -4.6e+58)
		tmp = 9.0 * (x * ((y / c) / z));
	elseif (y <= 4e+184)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = 9.0 * (y * (x / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -4.6e+58], N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+184], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000005e58

   1. Initial program 76.4%

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

   3. Simplified 81.1%

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

      1. *-un-lft-identity 81.1%

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

      2. *-commutative 81.1%

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

      3. times-frac 85.9%

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

      4. +-commutative 85.9%

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

   6. Applied egg-rr 85.9%

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

   7. Taylor expanded in x around inf 46.3%

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

      1. associate-/l* 55.4%

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

      2. associate-/r* 60.1%

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

   9. Simplified 60.1%

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

   if -4.60000000000000005e58 < y < 4.00000000000000007e184

   1. Initial program 78.8%

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

   3. Simplified 84.2%

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

      1. *-un-lft-identity 84.2%

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

      2. *-commutative 84.2%

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

      3. times-frac 84.8%

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

      4. +-commutative 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in y around inf 72.6%

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

   8. Taylor expanded in y around 0 77.7%

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

   if 4.00000000000000007e184 < y

   1. Initial program 74.6%

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

   3. Simplified 74.7%

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

      1. fma-undefine 74.7%

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

   6. Applied egg-rr 74.7%

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

   7. Taylor expanded in x around inf 68.1%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r* 68.2%

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

      4. associate-*l/ 80.8%

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

      5. *-commutative 80.8%

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

      6. associate-*r/ 80.8%

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

      7. associate-*l* 80.8%

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

      8. *-commutative 80.8%

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

   9. Simplified 80.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+58}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+184}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -360000 \lor \neg \left(b \leq 1.12 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -360000.0) (not (<= b 1.12e-13)))
   (/ (/ b c) z)
   (* a (/ (* t -4.0) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -360000.0) || !(b <= 1.12e-13)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-360000.0d0)) .or. (.not. (b <= 1.12d-13))) then
        tmp = (b / c) / z
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -360000.0) || !(b <= 1.12e-13)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -360000.0) or not (b <= 1.12e-13):
		tmp = (b / c) / z
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -360000.0) || !(b <= 1.12e-13))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -360000.0) || ~((b <= 1.12e-13)))
		tmp = (b / c) / z;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -360000.0], N[Not[LessEqual[b, 1.12e-13]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e5 or 1.12e-13 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 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%

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

      6. associate-*l* 83.3%

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

      7. associate-*l* 85.3%

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

      8. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in b around inf 54.5%

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

      1. associate-/r* 58.9%

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

   7. Simplified 58.9%

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

   if -3.6e5 < b < 1.12e-13

   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* 75.9%

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

      4. *-commutative 75.9%

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

      5. associate-+l- 75.9%

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

      6. associate-*l* 75.8%

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

      7. associate-*l* 76.9%

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

      8. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

      5. associate-*r/ 54.9%

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

      6. *-commutative 54.9%

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

   7. Simplified 54.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -360000 \lor \neg \left(b \leq 1.12 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -13500 \lor \neg \left(b \leq 1.55 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -13500.0) (not (<= b 1.55e-9)))
   (/ (/ b c) z)
   (* a (* t (/ -4.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -13500.0) || !(b <= 1.55e-9)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-13500.0d0)) .or. (.not. (b <= 1.55d-9))) then
        tmp = (b / c) / z
    else
        tmp = a * (t * ((-4.0d0) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -13500.0) || !(b <= 1.55e-9)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -13500.0) or not (b <= 1.55e-9):
		tmp = (b / c) / z
	else:
		tmp = a * (t * (-4.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -13500.0) || !(b <= 1.55e-9))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -13500.0) || ~((b <= 1.55e-9)))
		tmp = (b / c) / z;
	else
		tmp = a * (t * (-4.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -13500.0], N[Not[LessEqual[b, 1.55e-9]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -13500 or 1.55000000000000002e-9 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 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%

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

      6. associate-*l* 83.3%

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

      7. associate-*l* 85.3%

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

      8. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in b around inf 54.5%

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

      1. associate-/r* 58.9%

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

   7. Simplified 58.9%

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

   if -13500 < b < 1.55000000000000002e-9

   1. Initial program 71.1%

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

   3. Simplified 79.4%

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

      1. *-un-lft-identity 79.4%

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

      2. *-commutative 79.4%

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

      3. times-frac 85.2%

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

      4. +-commutative 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

      5. associate-*r/ 54.9%

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

      6. *-commutative 54.9%

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

      7. associate-/l* 54.8%

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

   9. Simplified 54.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -13500 \lor \neg \left(b \leq 1.55 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -780000000000:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -780000000000.0)
   (* (* a t) (/ -4.0 c))
   (if (<= z 1.05e-11) (* b (/ 1.0 (* z c))) (* a (/ (* t -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -780000000000.0) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 1.05e-11) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-780000000000.0d0)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= 1.05d-11) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -780000000000.0) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= 1.05e-11) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -780000000000.0:
		tmp = (a * t) * (-4.0 / c)
	elif z <= 1.05e-11:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -780000000000.0)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= 1.05e-11)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -780000000000.0)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= 1.05e-11)
		tmp = b * (1.0 / (z * c));
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -780000000000.0], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-11], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e11

   1. Initial program 64.7%

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

      1. associate-+l- 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-+l- 60.6%

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

      6. associate-*l* 60.6%

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

      7. associate-*l* 71.0%

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

      8. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r/ 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/l* 56.1%

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

      2. associate-*r/ 56.0%

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

      3. associate-*r* 61.7%

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

   9. Applied egg-rr 61.7%

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

   if -7.8e11 < z < 1.0499999999999999e-11

   1. Initial program 94.4%

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

      1. associate-+l- 94.4%

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

      2. *-commutative 94.4%

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

      3. associate-*r* 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-+l- 95.9%

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

      6. associate-*l* 95.9%

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

      7. associate-*l* 92.9%

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

      8. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in b around inf 55.0%

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

      1. *-commutative 55.0%

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

   7. Simplified 55.0%

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

      1. div-inv 55.8%

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

   9. Applied egg-rr 55.8%

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

   if 1.0499999999999999e-11 < z

   1. Initial program 59.0%

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

      1. associate-+l- 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-*r* 68.1%

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

      4. *-commutative 68.1%

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

      5. associate-+l- 68.1%

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

      6. associate-*l* 68.2%

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

      7. associate-*l* 69.6%

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

      8. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 57.7%

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

      3. associate-*r* 57.6%

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

      4. *-commutative 57.6%

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

      5. associate-*r/ 57.6%

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

      6. *-commutative 57.6%

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

   7. Simplified 57.6%

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

Alternative 15: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c 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 && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 && y < z && z < t && t < a && a < b && b < c;
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, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: x, y, z, t, a, b, and c 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 77.9%

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

   1. associate-+l- 77.9%

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

   2. *-commutative 77.9%

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

   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%

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

   6. associate-*l* 79.8%

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

   7. associate-*l* 81.4%

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

   8. *-commutative 81.4%

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

3. Simplified 81.4%

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

5. Taylor expanded in b around inf 37.6%

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

   1. associate-/r* 39.1%

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

7. Simplified 39.1%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
8. Add Preprocessing

Alternative 16: 35.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

   1. associate-+l- 77.9%

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

   2. *-commutative 77.9%

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

   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%

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

   6. associate-*l* 79.8%

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

   7. associate-*l* 81.4%

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

   8. *-commutative 81.4%

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

3. Simplified 81.4%

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

5. Taylor expanded in b around inf 37.6%

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

   1. *-commutative 37.6%

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

7. Simplified 37.6%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer target: 81.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

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