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

Percentage Accurate: 80.1% → 93.9%

Time: 17.9s

Alternatives: 18

Speedup: 0.8×

• 36.7% 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: 80.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-27} \lor \neg \left(c \leq 8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -4e-27) (not (<= c 8e-15)))
   (+ (* (/ a (/ c t)) -4.0) (/ (- (/ b c) (* -9.0 (* x (/ y c)))) z))
   (* (fma t (* a -4.0) (/ (fma x (* y 9.0) b) z)) (/ 1.0 c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -4e-27) || !(c <= 8e-15)) {
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = fma(t, (a * -4.0), (fma(x, (y * 9.0), b) / z)) * (1.0 / c);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -4e-27) || !(c <= 8e-15))
		tmp = Float64(Float64(Float64(a / Float64(c / t)) * -4.0) + Float64(Float64(Float64(b / c) - Float64(-9.0 * Float64(x * Float64(y / c)))) / z));
	else
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(y * 9.0), b) / z)) * Float64(1.0 / c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -4e-27], N[Not[LessEqual[c, 8e-15]], $MachinePrecision]], N[(N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.0000000000000002e-27 or 8.0000000000000006e-15 < c

   1. Initial program 67.0%

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

      1. associate-*l* 67.0%

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

      2. associate-*l* 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in x around 0 77.4%

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

      1. associate--l+ 77.4%

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

      2. associate-/r* 81.2%

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

      3. times-frac 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in z around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. *-commutative 83.1%

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

      5. associate-/l* 89.4%

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

      6. neg-mul-1 89.4%

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

      7. unsub-neg 89.4%

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

      8. *-commutative 89.4%

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

      9. associate-*r/ 94.0%

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

   9. Simplified 94.0%

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

   if -4.0000000000000002e-27 < c < 8.0000000000000006e-15

   1. Initial program 90.4%

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

      1. associate-/r* 92.8%

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

   3. Simplified 95.3%

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

      1. div-inv 95.2%

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

      2. +-commutative 95.2%

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

      3. fma-def 98.1%

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

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right) \cdot \frac{1}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-27} \lor \neg \left(c \leq 8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{-29} \lor \neg \left(c \leq 10^{+15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -5e-29) (not (<= c 1e+15)))
   (+ (* (/ a (/ c t)) -4.0) (/ (- (/ b c) (* -9.0 (* x (/ y c)))) z))
   (/ (+ (/ (fma x (* y 9.0) b) z) (* t (* a -4.0))) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -5e-29) || !(c <= 1e+15)) {
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = ((fma(x, (y * 9.0), b) / z) + (t * (a * -4.0))) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -5e-29) || !(c <= 1e+15))
		tmp = Float64(Float64(Float64(a / Float64(c / t)) * -4.0) + Float64(Float64(Float64(b / c) - Float64(-9.0 * Float64(x * Float64(y / c)))) / z));
	else
		tmp = Float64(Float64(Float64(fma(x, Float64(y * 9.0), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -5e-29], N[Not[LessEqual[c, 1e+15]], $MachinePrecision]], N[(N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.99999999999999986e-29 or 1e15 < c

   1. Initial program 66.3%

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

      1. associate-*l* 66.3%

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

      2. associate-*l* 66.1%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in x around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. associate-/r* 80.4%

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

      3. times-frac 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in z around -inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

      5. associate-/l* 89.0%

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

      6. neg-mul-1 89.0%

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

      7. unsub-neg 89.0%

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

      8. *-commutative 89.0%

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

      9. associate-*r/ 93.8%

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

   9. Simplified 93.8%

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

   if -4.99999999999999986e-29 < c < 1e15

   1. Initial program 90.0%

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

      1. associate-/r* 92.4%

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

   3. Simplified 95.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{-29} \lor \neg \left(c \leq 10^{+15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 3: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot 9\right)\\ t_2 := \frac{b - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - t_1\right)}{c \cdot z}\\ t_3 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{t_3 + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{t_1}{c}}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* y 9.0)))
        (t_2 (/ (- b (- (* (* z 4.0) (* a t)) t_1)) (* c z)))
        (t_3 (* t (* a -4.0))))
   (if (<= z -6.5e+57)
     (/ (+ t_3 (/ (* x 9.0) (/ z y))) c)
     (if (<= z 4e-241)
       t_2
       (if (<= z 6.8e-94)
         (/ (+ (/ b c) (/ t_1 c)) z)
         (if (<= z 2.1e+135) t_2 (/ (+ t_3 (/ b z)) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (y * 9.0);
	double t_2 = (b - (((z * 4.0) * (a * t)) - t_1)) / (c * z);
	double t_3 = t * (a * -4.0);
	double tmp;
	if (z <= -6.5e+57) {
		tmp = (t_3 + ((x * 9.0) / (z / y))) / c;
	} else if (z <= 4e-241) {
		tmp = t_2;
	} else if (z <= 6.8e-94) {
		tmp = ((b / c) + (t_1 / c)) / z;
	} else if (z <= 2.1e+135) {
		tmp = t_2;
	} else {
		tmp = (t_3 + (b / z)) / c;
	}
	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) :: tmp
    t_1 = x * (y * 9.0d0)
    t_2 = (b - (((z * 4.0d0) * (a * t)) - t_1)) / (c * z)
    t_3 = t * (a * (-4.0d0))
    if (z <= (-6.5d+57)) then
        tmp = (t_3 + ((x * 9.0d0) / (z / y))) / c
    else if (z <= 4d-241) then
        tmp = t_2
    else if (z <= 6.8d-94) then
        tmp = ((b / c) + (t_1 / c)) / z
    else if (z <= 2.1d+135) then
        tmp = t_2
    else
        tmp = (t_3 + (b / z)) / c
    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 = x * (y * 9.0);
	double t_2 = (b - (((z * 4.0) * (a * t)) - t_1)) / (c * z);
	double t_3 = t * (a * -4.0);
	double tmp;
	if (z <= -6.5e+57) {
		tmp = (t_3 + ((x * 9.0) / (z / y))) / c;
	} else if (z <= 4e-241) {
		tmp = t_2;
	} else if (z <= 6.8e-94) {
		tmp = ((b / c) + (t_1 / c)) / z;
	} else if (z <= 2.1e+135) {
		tmp = t_2;
	} else {
		tmp = (t_3 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x * (y * 9.0)
	t_2 = (b - (((z * 4.0) * (a * t)) - t_1)) / (c * z)
	t_3 = t * (a * -4.0)
	tmp = 0
	if z <= -6.5e+57:
		tmp = (t_3 + ((x * 9.0) / (z / y))) / c
	elif z <= 4e-241:
		tmp = t_2
	elif z <= 6.8e-94:
		tmp = ((b / c) + (t_1 / c)) / z
	elif z <= 2.1e+135:
		tmp = t_2
	else:
		tmp = (t_3 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(y * 9.0))
	t_2 = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(a * t)) - t_1)) / Float64(c * z))
	t_3 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -6.5e+57)
		tmp = Float64(Float64(t_3 + Float64(Float64(x * 9.0) / Float64(z / y))) / c);
	elseif (z <= 4e-241)
		tmp = t_2;
	elseif (z <= 6.8e-94)
		tmp = Float64(Float64(Float64(b / c) + Float64(t_1 / c)) / z);
	elseif (z <= 2.1e+135)
		tmp = t_2;
	else
		tmp = Float64(Float64(t_3 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x * (y * 9.0);
	t_2 = (b - (((z * 4.0) * (a * t)) - t_1)) / (c * z);
	t_3 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -6.5e+57)
		tmp = (t_3 + ((x * 9.0) / (z / y))) / c;
	elseif (z <= 4e-241)
		tmp = t_2;
	elseif (z <= 6.8e-94)
		tmp = ((b / c) + (t_1 / c)) / z;
	elseif (z <= 2.1e+135)
		tmp = t_2;
	else
		tmp = (t_3 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+57], N[(N[(t$95$3 + N[(N[(x * 9.0), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4e-241], t$95$2, If[LessEqual[z, 6.8e-94], N[(N[(N[(b / c), $MachinePrecision] + N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.1e+135], t$95$2, N[(N[(t$95$3 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4999999999999997e57

   1. Initial program 51.4%

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

      1. associate-/r* 62.6%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in x around inf 66.4%

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

      1. associate-*r/ 66.4%

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

      2. associate-*r* 66.4%

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

      3. *-commutative 66.4%

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

      4. associate-*r* 66.4%

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

      5. associate-/l* 73.4%

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

      6. *-commutative 73.4%

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

   6. Simplified 73.4%

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

   if -6.4999999999999997e57 < z < 3.9999999999999999e-241 or 6.7999999999999996e-94 < z < 2.1000000000000001e135

   1. Initial program 92.0%

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

      1. associate-*l* 92.0%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   if 3.9999999999999999e-241 < z < 6.7999999999999996e-94

   1. Initial program 89.6%

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

      1. associate-*l* 89.6%

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

      2. associate-*l* 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 66.2%

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

      1. associate--l+ 66.2%

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

      2. associate-/r* 77.1%

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

      3. times-frac 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

   9. Simplified 99.7%

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

   if 2.1000000000000001e135 < z

   1. Initial program 53.1%

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

      1. associate-/r* 58.4%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 86.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-241}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - x \cdot \left(y \cdot 9\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(a \cdot t\right) - x \cdot \left(y \cdot 9\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 4: 91.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-23} \lor \neg \left(c \leq 9.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.15e-23) (not (<= c 9.5e-15)))
   (+ (* (/ a (/ c t)) -4.0) (/ (- (/ b c) (* -9.0 (* x (/ y c)))) z))
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.15e-23) || !(c <= 9.5e-15)) {
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	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) :: tmp
    if ((c <= (-1.15d-23)) .or. (.not. (c <= 9.5d-15))) then
        tmp = ((a / (c / t)) * (-4.0d0)) + (((b / c) - ((-9.0d0) * (x * (y / c)))) / z)
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * z)
    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 tmp;
	if ((c <= -1.15e-23) || !(c <= 9.5e-15)) {
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -1.15e-23) or not (c <= 9.5e-15):
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z)
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.15e-23) || !(c <= 9.5e-15))
		tmp = Float64(Float64(Float64(a / Float64(c / t)) * -4.0) + Float64(Float64(Float64(b / c) - Float64(-9.0 * Float64(x * Float64(y / c)))) / z));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -1.15e-23) || ~((c <= 9.5e-15)))
		tmp = ((a / (c / t)) * -4.0) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.15e-23], N[Not[LessEqual[c, 9.5e-15]], $MachinePrecision]], N[(N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $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[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.15000000000000005e-23 or 9.5000000000000005e-15 < c

   1. Initial program 66.6%

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

      1. associate-*l* 66.6%

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

      2. associate-*l* 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in x around 0 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-/r* 81.0%

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

      3. times-frac 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in z around -inf 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. unsub-neg 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-/l* 89.3%

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

      6. neg-mul-1 89.3%

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

      7. unsub-neg 89.3%

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

      8. *-commutative 89.3%

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

      9. associate-*r/ 93.9%

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

   9. Simplified 93.9%

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

   if -1.15000000000000005e-23 < c < 9.5000000000000005e-15

   1. Initial program 90.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-23} \lor \neg \left(c \leq 9.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4 + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 5: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-98}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y z) (/ x c)))))
   (if (<= b -1.02e+133)
     (/ (/ b c) z)
     (if (<= b -5.1e-98)
       (* (* a t) (/ -4.0 c))
       (if (<= b -6.2e-242)
         t_1
         (if (<= b -8.5e-274)
           (* (/ a (/ c t)) -4.0)
           (if (<= b 2e-118)
             t_1
             (if (<= b 3.8e-49)
               (/ -4.0 (/ c (* a t)))
               (if (<= b 5.8e+121)
                 (* 9.0 (* (/ y c) (/ x z)))
                 (/ b (* c z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double tmp;
	if (b <= -1.02e+133) {
		tmp = (b / c) / z;
	} else if (b <= -5.1e-98) {
		tmp = (a * t) * (-4.0 / c);
	} else if (b <= -6.2e-242) {
		tmp = t_1;
	} else if (b <= -8.5e-274) {
		tmp = (a / (c / t)) * -4.0;
	} else if (b <= 2e-118) {
		tmp = t_1;
	} else if (b <= 3.8e-49) {
		tmp = -4.0 / (c / (a * t));
	} else if (b <= 5.8e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = b / (c * z);
	}
	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) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    if (b <= (-1.02d+133)) then
        tmp = (b / c) / z
    else if (b <= (-5.1d-98)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (b <= (-6.2d-242)) then
        tmp = t_1
    else if (b <= (-8.5d-274)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (b <= 2d-118) then
        tmp = t_1
    else if (b <= 3.8d-49) then
        tmp = (-4.0d0) / (c / (a * t))
    else if (b <= 5.8d+121) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = b / (c * z)
    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 = 9.0 * ((y / z) * (x / c));
	double tmp;
	if (b <= -1.02e+133) {
		tmp = (b / c) / z;
	} else if (b <= -5.1e-98) {
		tmp = (a * t) * (-4.0 / c);
	} else if (b <= -6.2e-242) {
		tmp = t_1;
	} else if (b <= -8.5e-274) {
		tmp = (a / (c / t)) * -4.0;
	} else if (b <= 2e-118) {
		tmp = t_1;
	} else if (b <= 3.8e-49) {
		tmp = -4.0 / (c / (a * t));
	} else if (b <= 5.8e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / z) * (x / c))
	tmp = 0
	if b <= -1.02e+133:
		tmp = (b / c) / z
	elif b <= -5.1e-98:
		tmp = (a * t) * (-4.0 / c)
	elif b <= -6.2e-242:
		tmp = t_1
	elif b <= -8.5e-274:
		tmp = (a / (c / t)) * -4.0
	elif b <= 2e-118:
		tmp = t_1
	elif b <= 3.8e-49:
		tmp = -4.0 / (c / (a * t))
	elif b <= 5.8e+121:
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = b / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	tmp = 0.0
	if (b <= -1.02e+133)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -5.1e-98)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (b <= -6.2e-242)
		tmp = t_1;
	elseif (b <= -8.5e-274)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (b <= 2e-118)
		tmp = t_1;
	elseif (b <= 3.8e-49)
		tmp = Float64(-4.0 / Float64(c / Float64(a * t)));
	elseif (b <= 5.8e+121)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / z) * (x / c));
	tmp = 0.0;
	if (b <= -1.02e+133)
		tmp = (b / c) / z;
	elseif (b <= -5.1e-98)
		tmp = (a * t) * (-4.0 / c);
	elseif (b <= -6.2e-242)
		tmp = t_1;
	elseif (b <= -8.5e-274)
		tmp = (a / (c / t)) * -4.0;
	elseif (b <= 2e-118)
		tmp = t_1;
	elseif (b <= 3.8e-49)
		tmp = -4.0 / (c / (a * t));
	elseif (b <= 5.8e+121)
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+133], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -5.1e-98], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-242], t$95$1, If[LessEqual[b, -8.5e-274], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 2e-118], t$95$1, If[LessEqual[b, 3.8e-49], N[(-4.0 / N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+121], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.02e133

   1. Initial program 76.6%

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

      1. associate-*l* 76.6%

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

      2. associate-*l* 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in b around inf 70.2%

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

      1. associate-/r* 82.8%

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

   6. Simplified 82.8%

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

   if -1.02e133 < b < -5.10000000000000022e-98

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

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

      2. associate-*l* 81.4%

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

   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. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*r/ 50.6%

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

      3. associate-/l* 50.6%

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

      4. *-commutative 50.6%

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

   6. Simplified 50.6%

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

      1. associate-/r/ 50.7%

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

   8. Applied egg-rr 50.7%

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

   if -5.10000000000000022e-98 < b < -6.20000000000000031e-242 or -8.49999999999999978e-274 < b < 1.99999999999999997e-118

   1. Initial program 78.3%

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

      1. associate-/r* 78.3%

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

   3. Simplified 84.7%

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

      1. div-inv 84.6%

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

      2. +-commutative 84.6%

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

      3. fma-def 85.9%

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

   5. Applied egg-rr 85.9%

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

   6. Taylor expanded in x around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. *-commutative 57.4%

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

      3. associate-*r/ 57.4%

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

      4. times-frac 59.0%

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

   8. Simplified 59.0%

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

   if -6.20000000000000031e-242 < b < -8.49999999999999978e-274

   1. Initial program 56.4%

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

      1. associate-/r* 57.9%

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

   3. Simplified 68.5%

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

      1. div-inv 68.5%

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

      2. +-commutative 68.5%

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

      3. fma-def 68.5%

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

   5. Applied egg-rr 68.5%

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

   6. Taylor expanded in t around inf 47.1%

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

      1. associate-/l* 67.8%

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

   8. Simplified 67.8%

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

   if 1.99999999999999997e-118 < b < 3.7999999999999997e-49

   1. Initial program 54.9%

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

      1. associate-*l* 54.9%

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

      2. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*r/ 77.4%

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

      3. associate-/l* 77.4%

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

      4. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   if 3.7999999999999997e-49 < b < 5.7999999999999998e121

   1. Initial program 79.9%

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

      1. associate-*l* 79.9%

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

      2. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around inf 57.6%

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

      1. times-frac 59.6%

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

   6. Simplified 59.6%

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

   if 5.7999999999999998e121 < b

   1. Initial program 80.4%

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

      1. associate-*l* 80.4%

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

      2. associate-*l* 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in b around inf 64.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-98}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-274}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-118}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 6: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-274}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-122}:\\ \;\;\;\;9 \cdot \left(\frac{1}{c} \cdot \left(x \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.1e+133)
   (/ (/ b c) z)
   (if (<= b -7.5e-94)
     (* (* a t) (/ -4.0 c))
     (if (<= b -1.85e-239)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= b -8.2e-274)
         (* (/ a (/ c t)) -4.0)
         (if (<= b 8.6e-122)
           (* 9.0 (* (/ 1.0 c) (* x (/ y z))))
           (if (<= b 2.8e-49)
             (/ -4.0 (/ c (* a t)))
             (if (<= b 5.6e+121)
               (* 9.0 (* (/ y c) (/ x z)))
               (/ b (* c z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.1e+133) {
		tmp = (b / c) / z;
	} else if (b <= -7.5e-94) {
		tmp = (a * t) * (-4.0 / c);
	} else if (b <= -1.85e-239) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= -8.2e-274) {
		tmp = (a / (c / t)) * -4.0;
	} else if (b <= 8.6e-122) {
		tmp = 9.0 * ((1.0 / c) * (x * (y / z)));
	} else if (b <= 2.8e-49) {
		tmp = -4.0 / (c / (a * t));
	} else if (b <= 5.6e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = b / (c * z);
	}
	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) :: tmp
    if (b <= (-3.1d+133)) then
        tmp = (b / c) / z
    else if (b <= (-7.5d-94)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (b <= (-1.85d-239)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (b <= (-8.2d-274)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (b <= 8.6d-122) then
        tmp = 9.0d0 * ((1.0d0 / c) * (x * (y / z)))
    else if (b <= 2.8d-49) then
        tmp = (-4.0d0) / (c / (a * t))
    else if (b <= 5.6d+121) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = b / (c * z)
    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 tmp;
	if (b <= -3.1e+133) {
		tmp = (b / c) / z;
	} else if (b <= -7.5e-94) {
		tmp = (a * t) * (-4.0 / c);
	} else if (b <= -1.85e-239) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= -8.2e-274) {
		tmp = (a / (c / t)) * -4.0;
	} else if (b <= 8.6e-122) {
		tmp = 9.0 * ((1.0 / c) * (x * (y / z)));
	} else if (b <= 2.8e-49) {
		tmp = -4.0 / (c / (a * t));
	} else if (b <= 5.6e+121) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.1e+133:
		tmp = (b / c) / z
	elif b <= -7.5e-94:
		tmp = (a * t) * (-4.0 / c)
	elif b <= -1.85e-239:
		tmp = 9.0 * ((y / z) * (x / c))
	elif b <= -8.2e-274:
		tmp = (a / (c / t)) * -4.0
	elif b <= 8.6e-122:
		tmp = 9.0 * ((1.0 / c) * (x * (y / z)))
	elif b <= 2.8e-49:
		tmp = -4.0 / (c / (a * t))
	elif b <= 5.6e+121:
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = b / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.1e+133)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -7.5e-94)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (b <= -1.85e-239)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (b <= -8.2e-274)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (b <= 8.6e-122)
		tmp = Float64(9.0 * Float64(Float64(1.0 / c) * Float64(x * Float64(y / z))));
	elseif (b <= 2.8e-49)
		tmp = Float64(-4.0 / Float64(c / Float64(a * t)));
	elseif (b <= 5.6e+121)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.1e+133)
		tmp = (b / c) / z;
	elseif (b <= -7.5e-94)
		tmp = (a * t) * (-4.0 / c);
	elseif (b <= -1.85e-239)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (b <= -8.2e-274)
		tmp = (a / (c / t)) * -4.0;
	elseif (b <= 8.6e-122)
		tmp = 9.0 * ((1.0 / c) * (x * (y / z)));
	elseif (b <= 2.8e-49)
		tmp = -4.0 / (c / (a * t));
	elseif (b <= 5.6e+121)
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.1e+133], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -7.5e-94], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.85e-239], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-274], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[b, 8.6e-122], N[(9.0 * N[(N[(1.0 / c), $MachinePrecision] * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-49], N[(-4.0 / N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+121], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -3.1e133

   1. Initial program 76.6%

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

      1. associate-*l* 76.6%

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

      2. associate-*l* 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in b around inf 70.2%

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

      1. associate-/r* 82.8%

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

   6. Simplified 82.8%

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

   if -3.1e133 < b < -7.5000000000000003e-94

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

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

      2. associate-*l* 81.4%

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

   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. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*r/ 50.6%

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

      3. associate-/l* 50.6%

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

      4. *-commutative 50.6%

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

   6. Simplified 50.6%

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

      1. associate-/r/ 50.7%

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

   8. Applied egg-rr 50.7%

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

   if -7.5000000000000003e-94 < b < -1.85000000000000008e-239

   1. Initial program 84.0%

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

      1. associate-/r* 86.6%

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

   3. Simplified 83.2%

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

      1. div-inv 83.2%

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

      2. +-commutative 83.2%

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

      3. fma-def 86.7%

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

   5. Applied egg-rr 86.7%

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

   6. Taylor expanded in x around inf 61.6%

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

      1. associate-*r/ 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*r/ 61.6%

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

      4. times-frac 63.0%

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

   8. Simplified 63.0%

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

   if -1.85000000000000008e-239 < b < -8.19999999999999975e-274

   1. Initial program 56.4%

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

      1. associate-/r* 57.9%

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

   3. Simplified 68.5%

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

      1. div-inv 68.5%

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

      2. +-commutative 68.5%

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

      3. fma-def 68.5%

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

   5. Applied egg-rr 68.5%

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

   6. Taylor expanded in t around inf 47.1%

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

      1. associate-/l* 67.8%

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

   8. Simplified 67.8%

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

   if -8.19999999999999975e-274 < b < 8.60000000000000037e-122

   1. Initial program 74.7%

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

      1. associate-/r* 73.2%

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

   3. Simplified 85.6%

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

      1. div-inv 85.4%

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

      2. +-commutative 85.4%

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

      3. fma-def 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in x around inf 57.0%

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

      1. associate-*r/ 60.8%

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

   8. Simplified 60.8%

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

      1. un-div-inv 60.9%

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

   10. Applied egg-rr 60.9%

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

       1. div-inv 60.8%

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

       2. inv-pow 60.8%

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

   12. Applied egg-rr 60.8%

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

       1. associate-*l* 60.9%

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

       2. *-commutative 60.9%

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

       3. unpow-1 60.9%

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

       4. associate-*r/ 57.0%

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

       5. associate-/l* 60.9%

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

       6. associate-/r/ 58.9%

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

   14. Simplified 58.9%

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

   if 8.60000000000000037e-122 < b < 2.79999999999999997e-49

   1. Initial program 54.9%

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

      1. associate-*l* 54.9%

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

      2. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*r/ 77.4%

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

      3. associate-/l* 77.4%

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

      4. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   if 2.79999999999999997e-49 < b < 5.60000000000000012e121

   1. Initial program 79.9%

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

      1. associate-*l* 79.9%

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

      2. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around inf 57.6%

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

      1. times-frac 59.6%

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

   6. Simplified 59.6%

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

   if 5.60000000000000012e121 < b

   1. Initial program 80.4%

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

      1. associate-*l* 80.4%

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

      2. associate-*l* 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in b around inf 64.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-274}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-122}:\\ \;\;\;\;9 \cdot \left(\frac{1}{c} \cdot \left(x \cdot \frac{y}{z}\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 7: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+52}:\\ \;\;\;\;\frac{t_1 + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -3e+52)
     (/ (+ t_1 (/ (* x 9.0) (/ z y))) c)
     (if (<= z 2.7e+112)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
       (/ (+ t_1 (/ b z)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -3e+52) {
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	} else if (z <= 2.7e+112) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-3d+52)) then
        tmp = (t_1 + ((x * 9.0d0) / (z / y))) / c
    else if (z <= 2.7d+112) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else
        tmp = (t_1 + (b / z)) / c
    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 = t * (a * -4.0);
	double tmp;
	if (z <= -3e+52) {
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	} else if (z <= 2.7e+112) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -3e+52:
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c
	elif z <= 2.7e+112:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -3e+52)
		tmp = Float64(Float64(t_1 + Float64(Float64(x * 9.0) / Float64(z / y))) / c);
	elseif (z <= 2.7e+112)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -3e+52)
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	elseif (z <= 2.7e+112)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+52], N[(N[(t$95$1 + N[(N[(x * 9.0), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.7e+112], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e52

   1. Initial program 50.5%

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

      1. associate-/r* 61.5%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in x around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. associate-*r* 67.0%

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

      3. *-commutative 67.0%

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

      4. associate-*r* 67.0%

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

      5. associate-/l* 73.9%

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

      6. *-commutative 73.9%

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

   6. Simplified 73.9%

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

   if -3e52 < z < 2.7000000000000001e112

   1. Initial program 93.2%

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

   if 2.7000000000000001e112 < z

   1. Initial program 53.0%

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

      1. associate-/r* 57.8%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 85.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+52}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 8: 71.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.65e+114)
     t_1
     (if (<= z -6e+44)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (or (<= z -5.4e-58) (not (<= z 1.02e-33)))
         t_1
         (/ (+ (/ b c) (/ (* x (* y 9.0)) c)) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+114) {
		tmp = t_1;
	} else if (z <= -6e+44) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -5.4e-58) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.65d+114)) then
        tmp = t_1
    else if (z <= (-6d+44)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if ((z <= (-5.4d-58)) .or. (.not. (z <= 1.02d-33))) then
        tmp = t_1
    else
        tmp = ((b / c) + ((x * (y * 9.0d0)) / c)) / z
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+114) {
		tmp = t_1;
	} else if (z <= -6e+44) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -5.4e-58) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.65e+114:
		tmp = t_1
	elif z <= -6e+44:
		tmp = 9.0 * ((y / c) * (x / z))
	elif (z <= -5.4e-58) or not (z <= 1.02e-33):
		tmp = t_1
	else:
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.65e+114)
		tmp = t_1;
	elseif (z <= -6e+44)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif ((z <= -5.4e-58) || !(z <= 1.02e-33))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b / c) + Float64(Float64(x * Float64(y * 9.0)) / c)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.65e+114)
		tmp = t_1;
	elseif (z <= -6e+44)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif ((z <= -5.4e-58) || ~((z <= 1.02e-33)))
		tmp = t_1;
	else
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.65e+114], t$95$1, If[LessEqual[z, -6e+44], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.4e-58], N[Not[LessEqual[z, 1.02e-33]], $MachinePrecision]], t$95$1, N[(N[(N[(b / c), $MachinePrecision] + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e114 or -5.99999999999999974e44 < z < -5.3999999999999998e-58 or 1.02e-33 < z

   1. Initial program 63.6%

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

      1. associate-/r* 69.6%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around 0 76.7%

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

   if -1.65e114 < z < -5.99999999999999974e44

   1. Initial program 63.0%

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

      1. associate-*l* 63.0%

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

      2. associate-*l* 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in x around inf 48.6%

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

      1. times-frac 70.2%

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

   6. Simplified 70.2%

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

   if -5.3999999999999998e-58 < z < 1.02e-33

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 87.3%

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

   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. Taylor expanded in x around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-/r* 72.9%

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

      3. times-frac 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 84.2%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.2%

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

   9. Simplified 84.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \]

Alternative 9: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -122:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-57} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -2.05e+116)
     t_1
     (if (<= z -122.0)
       (/ (+ (/ b z) (* 9.0 (/ y (/ z x)))) c)
       (if (or (<= z -1.55e-57) (not (<= z 1.02e-33)))
         t_1
         (/ (+ (/ b c) (/ (* x (* y 9.0)) c)) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.05e+116) {
		tmp = t_1;
	} else if (z <= -122.0) {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	} else if ((z <= -1.55e-57) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-2.05d+116)) then
        tmp = t_1
    else if (z <= (-122.0d0)) then
        tmp = ((b / z) + (9.0d0 * (y / (z / x)))) / c
    else if ((z <= (-1.55d-57)) .or. (.not. (z <= 1.02d-33))) then
        tmp = t_1
    else
        tmp = ((b / c) + ((x * (y * 9.0d0)) / c)) / z
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.05e+116) {
		tmp = t_1;
	} else if (z <= -122.0) {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	} else if ((z <= -1.55e-57) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -2.05e+116:
		tmp = t_1
	elif z <= -122.0:
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c
	elif (z <= -1.55e-57) or not (z <= 1.02e-33):
		tmp = t_1
	else:
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.05e+116)
		tmp = t_1;
	elseif (z <= -122.0)
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	elseif ((z <= -1.55e-57) || !(z <= 1.02e-33))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b / c) + Float64(Float64(x * Float64(y * 9.0)) / c)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -2.05e+116)
		tmp = t_1;
	elseif (z <= -122.0)
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	elseif ((z <= -1.55e-57) || ~((z <= 1.02e-33)))
		tmp = t_1;
	else
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.05e+116], t$95$1, If[LessEqual[z, -122.0], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -1.55e-57], N[Not[LessEqual[z, 1.02e-33]], $MachinePrecision]], t$95$1, N[(N[(N[(b / c), $MachinePrecision] + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0499999999999999e116 or -122 < z < -1.54999999999999988e-57 or 1.02e-33 < z

   1. Initial program 62.5%

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

      1. associate-/r* 68.7%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around 0 77.2%

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

   if -2.0499999999999999e116 < z < -122

   1. Initial program 70.8%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   if -1.54999999999999988e-57 < z < 1.02e-33

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 87.3%

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

   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. Taylor expanded in x around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-/r* 72.9%

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

      3. times-frac 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 84.2%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.2%

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

   9. Simplified 84.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+116}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -122:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-57} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \]

Alternative 10: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.202:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-57} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.8e+114)
     t_1
     (if (<= z -0.202)
       (/ (+ (/ b z) (* 9.0 (/ (* x y) z))) c)
       (if (or (<= z -1.4e-57) (not (<= z 1.02e-33)))
         t_1
         (/ (+ (/ b c) (/ (* x (* y 9.0)) c)) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e+114) {
		tmp = t_1;
	} else if (z <= -0.202) {
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	} else if ((z <= -1.4e-57) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.8d+114)) then
        tmp = t_1
    else if (z <= (-0.202d0)) then
        tmp = ((b / z) + (9.0d0 * ((x * y) / z))) / c
    else if ((z <= (-1.4d-57)) .or. (.not. (z <= 1.02d-33))) then
        tmp = t_1
    else
        tmp = ((b / c) + ((x * (y * 9.0d0)) / c)) / z
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e+114) {
		tmp = t_1;
	} else if (z <= -0.202) {
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	} else if ((z <= -1.4e-57) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.8e+114:
		tmp = t_1
	elif z <= -0.202:
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c
	elif (z <= -1.4e-57) or not (z <= 1.02e-33):
		tmp = t_1
	else:
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.8e+114)
		tmp = t_1;
	elseif (z <= -0.202)
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif ((z <= -1.4e-57) || !(z <= 1.02e-33))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b / c) + Float64(Float64(x * Float64(y * 9.0)) / c)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.8e+114)
		tmp = t_1;
	elseif (z <= -0.202)
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	elseif ((z <= -1.4e-57) || ~((z <= 1.02e-33)))
		tmp = t_1;
	else
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.8e+114], t$95$1, If[LessEqual[z, -0.202], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -1.4e-57], N[Not[LessEqual[z, 1.02e-33]], $MachinePrecision]], t$95$1, N[(N[(N[(b / c), $MachinePrecision] + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e114 or -0.20200000000000001 < z < -1.4e-57 or 1.02e-33 < z

   1. Initial program 62.5%

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

      1. associate-/r* 68.7%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around 0 77.2%

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

   if -1.8e114 < z < -0.20200000000000001

   1. Initial program 70.8%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around 0 71.3%

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

   if -1.4e-57 < z < 1.02e-33

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 87.3%

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

   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. Taylor expanded in x around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-/r* 72.9%

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

      3. times-frac 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 84.2%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.2%

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

   9. Simplified 84.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -0.202:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-57} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \end{array} \]

Alternative 11: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.21:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.8e+114)
     t_1
     (if (<= z -0.21)
       (/ (+ (/ b z) (* 9.0 (/ (* x y) z))) c)
       (if (<= z -1.9e-58)
         (/ (- b (* 4.0 (* a (* t z)))) (* c z))
         (if (<= z 5.8e-34) (/ (+ (/ b c) (/ (* x (* y 9.0)) c)) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e+114) {
		tmp = t_1;
	} else if (z <= -0.21) {
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= -1.9e-58) {
		tmp = (b - (4.0 * (a * (t * z)))) / (c * z);
	} else if (z <= 5.8e-34) {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.8d+114)) then
        tmp = t_1
    else if (z <= (-0.21d0)) then
        tmp = ((b / z) + (9.0d0 * ((x * y) / z))) / c
    else if (z <= (-1.9d-58)) then
        tmp = (b - (4.0d0 * (a * (t * z)))) / (c * z)
    else if (z <= 5.8d-34) then
        tmp = ((b / c) + ((x * (y * 9.0d0)) / c)) / z
    else
        tmp = t_1
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e+114) {
		tmp = t_1;
	} else if (z <= -0.21) {
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= -1.9e-58) {
		tmp = (b - (4.0 * (a * (t * z)))) / (c * z);
	} else if (z <= 5.8e-34) {
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.8e+114:
		tmp = t_1
	elif z <= -0.21:
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c
	elif z <= -1.9e-58:
		tmp = (b - (4.0 * (a * (t * z)))) / (c * z)
	elif z <= 5.8e-34:
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.8e+114)
		tmp = t_1;
	elseif (z <= -0.21)
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (z <= -1.9e-58)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(c * z));
	elseif (z <= 5.8e-34)
		tmp = Float64(Float64(Float64(b / c) + Float64(Float64(x * Float64(y * 9.0)) / c)) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.8e+114)
		tmp = t_1;
	elseif (z <= -0.21)
		tmp = ((b / z) + (9.0 * ((x * y) / z))) / c;
	elseif (z <= -1.9e-58)
		tmp = (b - (4.0 * (a * (t * z)))) / (c * z);
	elseif (z <= 5.8e-34)
		tmp = ((b / c) + ((x * (y * 9.0)) / c)) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.8e+114], t$95$1, If[LessEqual[z, -0.21], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -1.9e-58], N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-34], N[(N[(N[(b / c), $MachinePrecision] + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e114 or 5.8000000000000004e-34 < z

   1. Initial program 58.3%

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

      1. associate-/r* 65.3%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in x around 0 75.5%

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

   if -1.8e114 < z < -0.209999999999999992

   1. Initial program 70.8%

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

      1. associate-/r* 80.7%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around 0 71.3%

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

   if -0.209999999999999992 < z < -1.8999999999999999e-58

   1. Initial program 99.6%

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

      1. associate-*l* 99.6%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 93.0%

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

   if -1.8999999999999999e-58 < z < 5.8000000000000004e-34

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 87.3%

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

   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. Taylor expanded in x around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-/r* 72.9%

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

      3. times-frac 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 84.2%

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

      1. associate-*r/ 84.1%

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

      2. associate-*r* 84.2%

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

   9. Simplified 84.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -0.21:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 12: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.65e+114)
     t_1
     (if (<= z -6e+44)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (or (<= z -1.9e-58) (not (<= z 1.02e-33)))
         t_1
         (/ (+ b (* 9.0 (* x y))) (* c z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+114) {
		tmp = t_1;
	} else if (z <= -6e+44) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -1.9e-58) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.65d+114)) then
        tmp = t_1
    else if (z <= (-6d+44)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if ((z <= (-1.9d-58)) .or. (.not. (z <= 1.02d-33))) then
        tmp = t_1
    else
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+114) {
		tmp = t_1;
	} else if (z <= -6e+44) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -1.9e-58) || !(z <= 1.02e-33)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.65e+114:
		tmp = t_1
	elif z <= -6e+44:
		tmp = 9.0 * ((y / c) * (x / z))
	elif (z <= -1.9e-58) or not (z <= 1.02e-33):
		tmp = t_1
	else:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.65e+114)
		tmp = t_1;
	elseif (z <= -6e+44)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif ((z <= -1.9e-58) || !(z <= 1.02e-33))
		tmp = t_1;
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.65e+114)
		tmp = t_1;
	elseif (z <= -6e+44)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif ((z <= -1.9e-58) || ~((z <= 1.02e-33)))
		tmp = t_1;
	else
		tmp = (b + (9.0 * (x * y))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.65e+114], t$95$1, If[LessEqual[z, -6e+44], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.9e-58], N[Not[LessEqual[z, 1.02e-33]], $MachinePrecision]], t$95$1, N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e114 or -5.99999999999999974e44 < z < -1.8999999999999999e-58 or 1.02e-33 < z

   1. Initial program 63.6%

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

      1. associate-/r* 69.6%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around 0 76.7%

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

   if -1.65e114 < z < -5.99999999999999974e44

   1. Initial program 63.0%

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

      1. associate-*l* 63.0%

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

      2. associate-*l* 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in x around inf 48.6%

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

      1. times-frac 70.2%

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

   6. Simplified 70.2%

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

   if -1.8999999999999999e-58 < z < 1.02e-33

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 87.3%

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

   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. Taylor expanded in x around inf 83.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+114}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-58} \lor \neg \left(z \leq 1.02 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]

Alternative 13: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{t_1 + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -2.15e+136)
     (/ (/ b c) z)
     (if (<= b 7.5e+19)
       (/ (+ t_1 (/ (* x 9.0) (/ z y))) c)
       (if (<= b 6.7e+177)
         (/ (+ b (* 9.0 (* x y))) (* c z))
         (/ (+ t_1 (/ b z)) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -2.15e+136) {
		tmp = (b / c) / z;
	} else if (b <= 7.5e+19) {
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	} else if (b <= 6.7e+177) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-2.15d+136)) then
        tmp = (b / c) / z
    else if (b <= 7.5d+19) then
        tmp = (t_1 + ((x * 9.0d0) / (z / y))) / c
    else if (b <= 6.7d+177) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = (t_1 + (b / z)) / c
    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 = t * (a * -4.0);
	double tmp;
	if (b <= -2.15e+136) {
		tmp = (b / c) / z;
	} else if (b <= 7.5e+19) {
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	} else if (b <= 6.7e+177) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -2.15e+136:
		tmp = (b / c) / z
	elif b <= 7.5e+19:
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c
	elif b <= 6.7e+177:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -2.15e+136)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 7.5e+19)
		tmp = Float64(Float64(t_1 + Float64(Float64(x * 9.0) / Float64(z / y))) / c);
	elseif (b <= 6.7e+177)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -2.15e+136)
		tmp = (b / c) / z;
	elseif (b <= 7.5e+19)
		tmp = (t_1 + ((x * 9.0) / (z / y))) / c;
	elseif (b <= 6.7e+177)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+136], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 7.5e+19], N[(N[(t$95$1 + N[(N[(x * 9.0), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 6.7e+177], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.1499999999999999e136

   1. Initial program 76.6%

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

      1. associate-*l* 76.6%

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

      2. associate-*l* 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in b around inf 70.2%

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

      1. associate-/r* 82.8%

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

   6. Simplified 82.8%

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

   if -2.1499999999999999e136 < b < 7.5e19

   1. Initial program 74.8%

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

      1. associate-/r* 74.4%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around inf 75.5%

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

      1. associate-*r/ 75.5%

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

      2. associate-*r* 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*r* 75.5%

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

      5. associate-/l* 76.1%

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

      6. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   if 7.5e19 < b < 6.7000000000000004e177

   1. Initial program 86.2%

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

      1. associate-*l* 86.2%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around inf 79.9%

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

   if 6.7000000000000004e177 < b

   1. Initial program 76.2%

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

      1. associate-/r* 79.5%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around 0 94.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{x \cdot 9}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 14: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-242}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= y -200000.0)
     t_1
     (if (<= y 7e-242)
       (/ -4.0 (/ c (* a t)))
       (if (<= y 3e-82)
         (/ 1.0 (* c (/ z b)))
         (if (<= y 1.3e+51) (* -4.0 (* t (/ a c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -200000.0) {
		tmp = t_1;
	} else if (y <= 7e-242) {
		tmp = -4.0 / (c / (a * t));
	} else if (y <= 3e-82) {
		tmp = 1.0 / (c * (z / b));
	} else if (y <= 1.3e+51) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = 9.0d0 * ((y / c) * (x / z))
    if (y <= (-200000.0d0)) then
        tmp = t_1
    else if (y <= 7d-242) then
        tmp = (-4.0d0) / (c / (a * t))
    else if (y <= 3d-82) then
        tmp = 1.0d0 / (c * (z / b))
    else if (y <= 1.3d+51) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = t_1
    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 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -200000.0) {
		tmp = t_1;
	} else if (y <= 7e-242) {
		tmp = -4.0 / (c / (a * t));
	} else if (y <= 3e-82) {
		tmp = 1.0 / (c * (z / b));
	} else if (y <= 1.3e+51) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if y <= -200000.0:
		tmp = t_1
	elif y <= 7e-242:
		tmp = -4.0 / (c / (a * t))
	elif y <= 3e-82:
		tmp = 1.0 / (c * (z / b))
	elif y <= 1.3e+51:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (y <= -200000.0)
		tmp = t_1;
	elseif (y <= 7e-242)
		tmp = Float64(-4.0 / Float64(c / Float64(a * t)));
	elseif (y <= 3e-82)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	elseif (y <= 1.3e+51)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (y <= -200000.0)
		tmp = t_1;
	elseif (y <= 7e-242)
		tmp = -4.0 / (c / (a * t));
	elseif (y <= 3e-82)
		tmp = 1.0 / (c * (z / b));
	elseif (y <= 1.3e+51)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -200000.0], t$95$1, If[LessEqual[y, 7e-242], N[(-4.0 / N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-82], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+51], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2e5 or 1.3000000000000001e51 < y

   1. Initial program 73.9%

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

      1. associate-*l* 73.9%

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

      2. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around inf 54.8%

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

      1. times-frac 66.0%

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

   6. Simplified 66.0%

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

   if -2e5 < y < 6.9999999999999998e-242

   1. Initial program 80.6%

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

      1. associate-*l* 80.6%

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

      2. associate-*l* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-*r/ 47.3%

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

      3. associate-/l* 47.2%

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

      4. *-commutative 47.2%

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

   6. Simplified 47.2%

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

   if 6.9999999999999998e-242 < y < 2.9999999999999999e-82

   1. Initial program 90.3%

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

      1. associate-/r* 87.2%

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

   3. Simplified 87.3%

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

      1. div-inv 87.3%

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

      2. +-commutative 87.3%

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

      3. fma-def 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{\frac{b}{z}} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. clear-num 51.3%

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

      2. frac-times 54.4%

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

      3. metadata-eval 54.4%

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

   8. Applied egg-rr 54.4%

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

   if 2.9999999999999999e-82 < y < 1.3000000000000001e51

   1. Initial program 65.9%

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

      1. associate-/r* 66.3%

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

   3. Simplified 84.5%

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

      1. div-inv 84.5%

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

      2. +-commutative 84.5%

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

      3. fma-def 84.5%

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

   5. Applied egg-rr 84.5%

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

   6. Taylor expanded in t around inf 47.1%

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

      1. associate-/l* 50.0%

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

      2. associate-/r/ 53.1%

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

   8. Simplified 53.1%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -200000:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-242}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 15: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+134}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.4e+124)
   (* (/ a (/ c t)) -4.0)
   (if (<= z 2.6e+134)
     (/ (+ b (* 9.0 (* x y))) (* c z))
     (/ (* -4.0 (* a t)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.4e+124) {
		tmp = (a / (c / t)) * -4.0;
	} else if (z <= 2.6e+134) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (-4.0 * (a * t)) / c;
	}
	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) :: tmp
    if (z <= (-7.4d+124)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (z <= 2.6d+134) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = ((-4.0d0) * (a * t)) / c
    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 tmp;
	if (z <= -7.4e+124) {
		tmp = (a / (c / t)) * -4.0;
	} else if (z <= 2.6e+134) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (-4.0 * (a * t)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.4e+124:
		tmp = (a / (c / t)) * -4.0
	elif z <= 2.6e+134:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = (-4.0 * (a * t)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.4e+124)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (z <= 2.6e+134)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.4e+124)
		tmp = (a / (c / t)) * -4.0;
	elseif (z <= 2.6e+134)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = (-4.0 * (a * t)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.4e+124], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 2.6e+134], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.40000000000000016e124

   1. Initial program 46.6%

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

      1. associate-/r* 56.4%

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

   3. Simplified 77.2%

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

      1. div-inv 77.2%

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

      2. +-commutative 77.2%

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

      3. fma-def 77.2%

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

   5. Applied egg-rr 77.2%

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

   6. Taylor expanded in t around inf 59.5%

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

      1. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   if -7.40000000000000016e124 < z < 2.6000000000000002e134

   1. Initial program 89.9%

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

      1. associate-*l* 89.9%

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

      2. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around inf 74.5%

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

   if 2.6000000000000002e134 < z

   1. Initial program 53.1%

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

      1. associate-/r* 58.4%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 72.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+134}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 16: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -8e+30)
   (/ (/ b c) z)
   (if (<= b 3.5e+97) (* -4.0 (* t (/ a c))) (/ b (* c z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -8e+30) {
		tmp = (b / c) / z;
	} else if (b <= 3.5e+97) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (c * z);
	}
	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) :: tmp
    if (b <= (-8d+30)) then
        tmp = (b / c) / z
    else if (b <= 3.5d+97) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (c * z)
    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 tmp;
	if (b <= -8e+30) {
		tmp = (b / c) / z;
	} else if (b <= 3.5e+97) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -8e+30:
		tmp = (b / c) / z
	elif b <= 3.5e+97:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -8e+30)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 3.5e+97)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -8e+30)
		tmp = (b / c) / z;
	elseif (b <= 3.5e+97)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -8e+30], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 3.5e+97], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.0000000000000002e30

   1. Initial program 67.7%

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

      1. associate-*l* 67.7%

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

      2. associate-*l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in b around inf 61.1%

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

      1. associate-/r* 70.3%

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

   6. Simplified 70.3%

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

   if -8.0000000000000002e30 < b < 3.5000000000000001e97

   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-/r* 77.5%

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

   3. Simplified 84.8%

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

      1. div-inv 84.7%

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

      2. +-commutative 84.7%

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

      3. fma-def 86.0%

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

   5. Applied egg-rr 86.0%

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

   6. Taylor expanded in t around inf 42.7%

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

      1. associate-/l* 43.8%

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

      2. associate-/r/ 44.5%

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

   8. Simplified 44.5%

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

   if 3.5000000000000001e97 < b

   1. Initial program 81.2%

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

      1. associate-*l* 81.3%

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

      2. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in b around inf 61.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 17: 35.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4e-129) (/ (/ b c) z) (/ b (* c z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e-129) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (c * z);
	}
	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) :: tmp
    if (b <= (-4d-129)) then
        tmp = (b / c) / z
    else
        tmp = b / (c * z)
    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 tmp;
	if (b <= -4e-129) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4e-129:
		tmp = (b / c) / z
	else:
		tmp = b / (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4e-129)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4e-129)
		tmp = (b / c) / z;
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4e-129], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.9999999999999997e-129

   1. Initial program 77.4%

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

      1. associate-*l* 77.4%

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

      2. associate-*l* 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in b around inf 39.3%

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

      1. associate-/r* 45.4%

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

   6. Simplified 45.4%

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

   if -3.9999999999999997e-129 < b

   1. Initial program 76.5%

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

      1. associate-*l* 76.5%

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

      2. associate-*l* 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in b around inf 35.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 18: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

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

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 = b / (c * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

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

   1. associate-*l* 76.8%

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

   2. associate-*l* 77.3%

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

3. Simplified 77.3%

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

4. Taylor expanded in b around inf 36.9%

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

5. Final simplification 36.9%

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

Developer target: 80.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

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

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