Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 85.5% → 95.5%

Time: 10.2s

Alternatives: 10

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{y}{a - \frac{t}{z}} - \frac{x}{a \cdot z - t} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (y / (a - (t / z))) - (x / ((a * z) - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(a * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. sub-neg 83.7%

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

   2. +-commutative 83.7%

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

   3. neg-sub0 83.7%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

   4. associate-+l- 83.7%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

   5. sub0-neg 83.7%

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

   6. neg-mul-1 83.7%

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

   7. sub-neg 83.7%

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

   8. +-commutative 83.7%

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

   9. neg-sub0 83.7%

      \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

   10. associate-+l- 83.7%

       \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   11. sub0-neg 83.7%

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

   12. neg-mul-1 83.7%

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

   13. times-frac 83.7%

       \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

   14. metadata-eval 83.7%

       \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

   15. *-lft-identity 83.7%

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

   16. *-commutative 83.7%

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

3. Simplified 83.7%

   \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
4. Step-by-step derivation

   1. div-sub 83.4%

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

   2. associate-/l* 85.4%

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

5. Applied egg-rr 85.4%

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

6. Taylor expanded in z around 0 94.2%

   \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} - \frac{x}{z \cdot a - t} \]
7. Step-by-step derivation

   1. neg-mul-1 94.2%

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

   2. unsub-neg 94.2%

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

8. Simplified 94.2%

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

9. Final simplification 94.2%

   \[\leadsto \frac{y}{a - \frac{t}{z}} - \frac{x}{a \cdot z - t} \]

Alternative 2: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-60} \lor \neg \left(z \leq 1.42 \cdot 10^{-154}\right) \land \left(z \leq 6.5 \cdot 10^{-125} \lor \neg \left(z \leq 1.85 \cdot 10^{-44}\right)\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-60)
         (and (not (<= z 1.42e-154))
              (or (<= z 6.5e-125) (not (<= z 1.85e-44)))))
   (/ y (- a (/ t z)))
   (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-60) || (!(z <= 1.42e-154) && ((z <= 6.5e-125) || !(z <= 1.85e-44)))) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-7.2d-60)) .or. (.not. (z <= 1.42d-154)) .and. (z <= 6.5d-125) .or. (.not. (z <= 1.85d-44))) then
        tmp = y / (a - (t / z))
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-60) || (!(z <= 1.42e-154) && ((z <= 6.5e-125) || !(z <= 1.85e-44)))) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-60) or (not (z <= 1.42e-154) and ((z <= 6.5e-125) or not (z <= 1.85e-44))):
		tmp = y / (a - (t / z))
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-60) || (!(z <= 1.42e-154) && ((z <= 6.5e-125) || !(z <= 1.85e-44))))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-60) || (~((z <= 1.42e-154)) && ((z <= 6.5e-125) || ~((z <= 1.85e-44)))))
		tmp = y / (a - (t / z));
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-60], And[N[Not[LessEqual[z, 1.42e-154]], $MachinePrecision], Or[LessEqual[z, 6.5e-125], N[Not[LessEqual[z, 1.85e-44]], $MachinePrecision]]]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e-60 or 1.42e-154 < z < 6.4999999999999999e-125 or 1.85e-44 < z

   1. Initial program 74.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 74.4%

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

      2. +-commutative 74.4%

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

      3. neg-sub0 74.4%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 74.4%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 74.4%

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

      6. neg-mul-1 74.4%

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

      7. sub-neg 74.4%

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

      8. +-commutative 74.4%

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

      9. neg-sub0 74.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 74.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 74.4%

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

      12. neg-mul-1 74.4%

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

      13. times-frac 74.4%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 74.4%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 74.4%

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

      16. *-commutative 74.4%

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

   3. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 73.8%

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

      2. associate-/l* 80.0%

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

   5. Applied egg-rr 80.0%

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

   6. Taylor expanded in z around 0 93.9%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} - \frac{x}{z \cdot a - t} \]
   7. Step-by-step derivation

      1. neg-mul-1 93.9%

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

      2. unsub-neg 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in y around inf 73.7%

      \[\leadsto \color{blue}{\frac{y}{a - \frac{t}{z}}} \]

   if -7.2e-60 < z < 1.42e-154 or 6.4999999999999999e-125 < z < 1.85e-44

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.4%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-60} \lor \neg \left(z \leq 1.42 \cdot 10^{-154}\right) \land \left(z \leq 6.5 \cdot 10^{-125} \lor \neg \left(z \leq 1.85 \cdot 10^{-44}\right)\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 3: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+47} \lor \neg \left(a \leq 2 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{y}{a} + \frac{-1}{z \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e+47) (not (<= a 2e-21)))
   (+ (/ y a) (/ -1.0 (* z (/ a x))))
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e+47) || !(a <= 2e-21)) {
		tmp = (y / a) + (-1.0 / (z * (a / x)));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-1.75d+47)) .or. (.not. (a <= 2d-21))) then
        tmp = (y / a) + ((-1.0d0) / (z * (a / x)))
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e+47) || !(a <= 2e-21)) {
		tmp = (y / a) + (-1.0 / (z * (a / x)));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e+47) or not (a <= 2e-21):
		tmp = (y / a) + (-1.0 / (z * (a / x)))
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e+47) || !(a <= 2e-21))
		tmp = Float64(Float64(y / a) + Float64(-1.0 / Float64(z * Float64(a / x))));
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e+47) || ~((a <= 2e-21)))
		tmp = (y / a) + (-1.0 / (z * (a / x)));
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e+47], N[Not[LessEqual[a, 2e-21]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] + N[(-1.0 / N[(z * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75000000000000008e47 or 1.99999999999999982e-21 < a

   1. Initial program 73.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 73.7%

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

      2. +-commutative 73.7%

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

      3. neg-sub0 73.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 73.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 73.7%

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

      6. neg-mul-1 73.7%

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

      7. sub-neg 73.7%

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

      8. +-commutative 73.7%

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

      9. neg-sub0 73.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 73.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 73.7%

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

      12. neg-mul-1 73.7%

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

      13. times-frac 73.7%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 73.7%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 73.7%

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

      16. *-commutative 73.7%

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

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 73.7%

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

      2. associate-/l* 74.8%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in t around 0 74.9%

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

      1. *-commutative 74.9%

         \[\leadsto \frac{y}{a} - \frac{x}{\color{blue}{z \cdot a}} \]

   8. Simplified 74.9%

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

      1. clear-num 74.8%

         \[\leadsto \frac{y}{a} - \color{blue}{\frac{1}{\frac{z \cdot a}{x}}} \]

      2. inv-pow 74.8%

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

      3. *-commutative 74.8%

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

   10. Applied egg-rr 74.8%

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

       1. unpow-1 74.8%

          \[\leadsto \frac{y}{a} - \color{blue}{\frac{1}{\frac{a \cdot z}{x}}} \]

       2. *-commutative 74.8%

          \[\leadsto \frac{y}{a} - \frac{1}{\frac{\color{blue}{z \cdot a}}{x}} \]

   12. Simplified 74.8%

       \[\leadsto \frac{y}{a} - \color{blue}{\frac{1}{\frac{z \cdot a}{x}}} \]

   13. Taylor expanded in z around 0 74.8%

       \[\leadsto \frac{y}{a} - \frac{1}{\color{blue}{\frac{a \cdot z}{x}}} \]
   14. Step-by-step derivation

       1. *-commutative 74.8%

          \[\leadsto \frac{y}{a} - \frac{1}{\frac{\color{blue}{z \cdot a}}{x}} \]

       2. associate-*r/ 78.8%

          \[\leadsto \frac{y}{a} - \frac{1}{\color{blue}{z \cdot \frac{a}{x}}} \]

   15. Simplified 78.8%

       \[\leadsto \frac{y}{a} - \frac{1}{\color{blue}{z \cdot \frac{a}{x}}} \]

   if -1.75000000000000008e47 < a < 1.99999999999999982e-21

   1. Initial program 93.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. neg-sub0 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 93.9%

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

      6. neg-mul-1 93.9%

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

      7. sub-neg 93.9%

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

      8. +-commutative 93.9%

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

      9. neg-sub0 93.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 93.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 93.9%

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

      12. neg-mul-1 93.9%

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

      13. times-frac 93.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 93.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 93.9%

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

      16. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 80.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z - x}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 80.2%

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

      2. neg-mul-1 80.2%

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

      3. neg-sub0 80.2%

         \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{t} \]

      4. sub-neg 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t} \]

      5. +-commutative 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{t} \]

      6. associate--r+ 80.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{t} \]

      7. neg-sub0 80.2%

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

      8. remove-double-neg 80.2%

         \[\leadsto \frac{\color{blue}{x} - y \cdot z}{t} \]

      9. *-commutative 80.2%

         \[\leadsto \frac{x - \color{blue}{z \cdot y}}{t} \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+47} \lor \neg \left(a \leq 2 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{y}{a} + \frac{-1}{z \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 4: 91.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+159)
   (/ y (- a (/ t z)))
   (if (<= z 3.8e+121) (/ (- x (* y z)) (- t (* a z))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+159) {
		tmp = y / (a - (t / z));
	} else if (z <= 3.8e+121) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-7.2d+159)) then
        tmp = y / (a - (t / z))
    else if (z <= 3.8d+121) then
        tmp = (x - (y * z)) / (t - (a * z))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+159) {
		tmp = y / (a - (t / z));
	} else if (z <= 3.8e+121) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+159:
		tmp = y / (a - (t / z))
	elif z <= 3.8e+121:
		tmp = (x - (y * z)) / (t - (a * z))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+159)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 3.8e+121)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+159)
		tmp = y / (a - (t / z));
	elseif (z <= 3.8e+121)
		tmp = (x - (y * z)) / (t - (a * z));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+159], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+121], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000073e159

   1. Initial program 43.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 43.7%

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

      2. +-commutative 43.7%

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

      3. neg-sub0 43.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 43.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 43.7%

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

      6. neg-mul-1 43.7%

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

      7. sub-neg 43.7%

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

      8. +-commutative 43.7%

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

      9. neg-sub0 43.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 43.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 43.7%

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

      12. neg-mul-1 43.7%

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

      13. times-frac 43.7%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 43.7%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 43.7%

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

      16. *-commutative 43.7%

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

   3. Simplified 43.7%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 43.8%

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

      2. associate-/l* 59.5%

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

   5. Applied egg-rr 59.5%

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

   6. Taylor expanded in z around 0 97.0%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} - \frac{x}{z \cdot a - t} \]
   7. Step-by-step derivation

      1. neg-mul-1 97.0%

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

      2. unsub-neg 97.0%

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

   8. Simplified 97.0%

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

   9. Taylor expanded in y around inf 90.1%

      \[\leadsto \color{blue}{\frac{y}{a - \frac{t}{z}}} \]

   if -7.20000000000000073e159 < z < 3.8e121

   1. Initial program 95.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]

   if 3.8e121 < z

   1. Initial program 52.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 52.7%

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

      2. +-commutative 52.7%

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

      3. neg-sub0 52.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 52.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 52.7%

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

      6. neg-mul-1 52.7%

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

      7. sub-neg 52.7%

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

      8. +-commutative 52.7%

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

      9. neg-sub0 52.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 52.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 52.7%

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

      12. neg-mul-1 52.7%

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

      13. times-frac 52.7%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 52.7%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 52.7%

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

      16. *-commutative 52.7%

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

   3. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 52.7%

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

      2. associate-/l* 70.3%

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

   5. Applied egg-rr 70.3%

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

   6. Taylor expanded in a around inf 85.3%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+49)
   (/ (- y (/ x z)) a)
   (if (<= a 6.3e-21) (/ (- x (* y z)) t) (- (/ y a) (/ x (* a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+49) {
		tmp = (y - (x / z)) / a;
	} else if (a <= 6.3e-21) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y / a) - (x / (a * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-1.1d+49)) then
        tmp = (y - (x / z)) / a
    else if (a <= 6.3d-21) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y / a) - (x / (a * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+49) {
		tmp = (y - (x / z)) / a;
	} else if (a <= 6.3e-21) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y / a) - (x / (a * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+49:
		tmp = (y - (x / z)) / a
	elif a <= 6.3e-21:
		tmp = (x - (y * z)) / t
	else:
		tmp = (y / a) - (x / (a * z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+49)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif (a <= 6.3e-21)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(a * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+49)
		tmp = (y - (x / z)) / a;
	elseif (a <= 6.3e-21)
		tmp = (x - (y * z)) / t;
	else
		tmp = (y / a) - (x / (a * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+49], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 6.3e-21], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - N[(x / N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e49

   1. Initial program 73.4%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 73.4%

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

      2. +-commutative 73.4%

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

      3. neg-sub0 73.4%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 73.4%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 73.4%

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

      6. neg-mul-1 73.4%

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

      7. sub-neg 73.4%

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

      8. +-commutative 73.4%

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

      9. neg-sub0 73.4%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 73.4%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 73.4%

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

      12. neg-mul-1 73.4%

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

      13. times-frac 73.4%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 73.4%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 73.4%

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

      16. *-commutative 73.4%

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

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 73.4%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

   6. Taylor expanded in a around inf 82.8%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]

   if -1.1e49 < a < 6.3e-21

   1. Initial program 93.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. neg-sub0 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 93.9%

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

      6. neg-mul-1 93.9%

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

      7. sub-neg 93.9%

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

      8. +-commutative 93.9%

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

      9. neg-sub0 93.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 93.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 93.9%

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

      12. neg-mul-1 93.9%

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

      13. times-frac 93.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 93.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 93.9%

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

      16. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 80.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z - x}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 80.2%

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

      2. neg-mul-1 80.2%

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

      3. neg-sub0 80.2%

         \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{t} \]

      4. sub-neg 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t} \]

      5. +-commutative 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{t} \]

      6. associate--r+ 80.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{t} \]

      7. neg-sub0 80.2%

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

      8. remove-double-neg 80.2%

         \[\leadsto \frac{\color{blue}{x} - y \cdot z}{t} \]

      9. *-commutative 80.2%

         \[\leadsto \frac{x - \color{blue}{z \cdot y}}{t} \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]

   if 6.3e-21 < a

   1. Initial program 73.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 73.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. sub-neg 73.9%

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

      8. +-commutative 73.9%

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

      9. neg-sub0 73.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 73.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 73.9%

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

      12. neg-mul-1 73.9%

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

      13. times-frac 73.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 73.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 73.9%

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

      16. *-commutative 73.9%

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

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 73.9%

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

      2. associate-/l* 74.3%

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

   5. Applied egg-rr 74.3%

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

   6. Taylor expanded in t around 0 72.4%

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

      1. *-commutative 72.4%

         \[\leadsto \frac{y}{a} - \frac{x}{\color{blue}{z \cdot a}} \]

   8. Simplified 72.4%

      \[\leadsto \color{blue}{\frac{y}{a} - \frac{x}{z \cdot a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{a \cdot z}\\ \end{array} \]

Alternative 6: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.175 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.175e+33)
   (/ y a)
   (if (<= z -2.15e-17)
     (* y (- (/ z t)))
     (if (<= z -3.4e-50) (/ y a) (if (<= z 1.22e-17) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.175e+33) {
		tmp = y / a;
	} else if (z <= -2.15e-17) {
		tmp = y * -(z / t);
	} else if (z <= -3.4e-50) {
		tmp = y / a;
	} else if (z <= 1.22e-17) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-1.175d+33)) then
        tmp = y / a
    else if (z <= (-2.15d-17)) then
        tmp = y * -(z / t)
    else if (z <= (-3.4d-50)) then
        tmp = y / a
    else if (z <= 1.22d-17) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.175e+33) {
		tmp = y / a;
	} else if (z <= -2.15e-17) {
		tmp = y * -(z / t);
	} else if (z <= -3.4e-50) {
		tmp = y / a;
	} else if (z <= 1.22e-17) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.175e+33:
		tmp = y / a
	elif z <= -2.15e-17:
		tmp = y * -(z / t)
	elif z <= -3.4e-50:
		tmp = y / a
	elif z <= 1.22e-17:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.175e+33)
		tmp = Float64(y / a);
	elseif (z <= -2.15e-17)
		tmp = Float64(y * Float64(-Float64(z / t)));
	elseif (z <= -3.4e-50)
		tmp = Float64(y / a);
	elseif (z <= 1.22e-17)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.175e+33)
		tmp = y / a;
	elseif (z <= -2.15e-17)
		tmp = y * -(z / t);
	elseif (z <= -3.4e-50)
		tmp = y / a;
	elseif (z <= 1.22e-17)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.175e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.15e-17], N[(y * (-N[(z / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -3.4e-50], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.22e-17], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.17499999999999995e33 or -2.15000000000000012e-17 < z < -3.40000000000000014e-50 or 1.22e-17 < z

   1. Initial program 67.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 67.9%

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

      2. +-commutative 67.9%

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

      3. neg-sub0 67.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 67.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 67.9%

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

      6. neg-mul-1 67.9%

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

      7. sub-neg 67.9%

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

      8. +-commutative 67.9%

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

      9. neg-sub0 67.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 67.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 67.9%

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

      12. neg-mul-1 67.9%

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

      13. times-frac 67.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 67.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 67.9%

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

      16. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -1.17499999999999995e33 < z < -2.15000000000000012e-17

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

         \[\leadsto \frac{y \cdot z}{\color{blue}{z \cdot a} - t} \]

      2. associate-*r/ 68.4%

         \[\leadsto \color{blue}{y \cdot \frac{z}{z \cdot a - t}} \]

      3. *-commutative 68.4%

         \[\leadsto y \cdot \frac{z}{\color{blue}{a \cdot z} - t} \]

   6. Simplified 68.4%

      \[\leadsto \color{blue}{y \cdot \frac{z}{a \cdot z - t}} \]

   7. Taylor expanded in z around 0 52.4%

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

      1. associate-*r/ 52.4%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot z}{t}} \]

      2. neg-mul-1 52.4%

         \[\leadsto y \cdot \frac{\color{blue}{-z}}{t} \]

   9. Simplified 52.4%

      \[\leadsto y \cdot \color{blue}{\frac{-z}{t}} \]

   if -3.40000000000000014e-50 < z < 1.22e-17

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 63.1%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.175 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-51} \lor \neg \left(z \leq 1.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e-51) (not (<= z 1.1e-39)))
   (/ y (- a (/ t z)))
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-51) || !(z <= 1.1e-39)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-9d-51)) .or. (.not. (z <= 1.1d-39))) then
        tmp = y / (a - (t / z))
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-51) || !(z <= 1.1e-39)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e-51) or not (z <= 1.1e-39):
		tmp = y / (a - (t / z))
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e-51) || !(z <= 1.1e-39))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e-51) || ~((z <= 1.1e-39)))
		tmp = y / (a - (t / z));
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e-51], N[Not[LessEqual[z, 1.1e-39]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999948e-51 or 1.1e-39 < z

   1. Initial program 72.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 72.6%

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

      2. +-commutative 72.6%

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

      3. neg-sub0 72.6%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 72.6%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 72.6%

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

      6. neg-mul-1 72.6%

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

      7. sub-neg 72.6%

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

      8. +-commutative 72.6%

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

      9. neg-sub0 72.6%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 72.6%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 72.6%

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

      12. neg-mul-1 72.6%

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

      13. times-frac 72.6%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 72.6%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 72.6%

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

      16. *-commutative 72.6%

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

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 71.9%

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

      2. associate-/l* 79.8%

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

   5. Applied egg-rr 79.8%

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

   6. Taylor expanded in z around 0 94.7%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} - \frac{x}{z \cdot a - t} \]
   7. Step-by-step derivation

      1. neg-mul-1 94.7%

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

      2. unsub-neg 94.7%

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

   8. Simplified 94.7%

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

   9. Taylor expanded in y around inf 74.3%

      \[\leadsto \color{blue}{\frac{y}{a - \frac{t}{z}}} \]

   if -8.99999999999999948e-51 < z < 1.1e-39

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z - x}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

      3. neg-sub0 78.7%

         \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{t} \]

      4. sub-neg 78.7%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t} \]

      5. +-commutative 78.7%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{t} \]

      6. associate--r+ 78.7%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{t} \]

      7. neg-sub0 78.7%

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

      8. remove-double-neg 78.7%

         \[\leadsto \frac{\color{blue}{x} - y \cdot z}{t} \]

      9. *-commutative 78.7%

         \[\leadsto \frac{x - \color{blue}{z \cdot y}}{t} \]

   6. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-51} \lor \neg \left(z \leq 1.1 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 8: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+47} \lor \neg \left(a \leq 5.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.7e+47) (not (<= a 5.5e-23)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e+47) || !(a <= 5.5e-23)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-3.7d+47)) .or. (.not. (a <= 5.5d-23))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (y * z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e+47) || !(a <= 5.5e-23)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.7e+47) or not (a <= 5.5e-23):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.7e+47) || !(a <= 5.5e-23))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.7e+47) || ~((a <= 5.5e-23)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.7e+47], N[Not[LessEqual[a, 5.5e-23]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.70000000000000041e47 or 5.5000000000000001e-23 < a

   1. Initial program 73.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 73.7%

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

      2. +-commutative 73.7%

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

      3. neg-sub0 73.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 73.7%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 73.7%

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

      6. neg-mul-1 73.7%

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

      7. sub-neg 73.7%

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

      8. +-commutative 73.7%

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

      9. neg-sub0 73.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 73.7%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 73.7%

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

      12. neg-mul-1 73.7%

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

      13. times-frac 73.7%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 73.7%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 73.7%

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

      16. *-commutative 73.7%

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

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
   4. Step-by-step derivation

      1. div-sub 73.7%

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

      2. associate-/l* 74.8%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in a around inf 75.8%

      \[\leadsto \color{blue}{\frac{y - \frac{x}{z}}{a}} \]

   if -3.70000000000000041e47 < a < 5.5000000000000001e-23

   1. Initial program 93.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. neg-sub0 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 93.9%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 93.9%

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

      6. neg-mul-1 93.9%

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

      7. sub-neg 93.9%

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

      8. +-commutative 93.9%

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

      9. neg-sub0 93.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 93.9%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 93.9%

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

      12. neg-mul-1 93.9%

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

      13. times-frac 93.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 93.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 93.9%

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

      16. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around 0 80.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z - x}{t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 80.2%

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

      2. neg-mul-1 80.2%

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

      3. neg-sub0 80.2%

         \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{t} \]

      4. sub-neg 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t} \]

      5. +-commutative 80.2%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{t} \]

      6. associate--r+ 80.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{t} \]

      7. neg-sub0 80.2%

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

      8. remove-double-neg 80.2%

         \[\leadsto \frac{\color{blue}{x} - y \cdot z}{t} \]

      9. *-commutative 80.2%

         \[\leadsto \frac{x - \color{blue}{z \cdot y}}{t} \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+47} \lor \neg \left(a \leq 5.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 9: 55.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e-52) (/ y a) (if (<= z 2.25e-18) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-52) {
		tmp = y / a;
	} else if (z <= 2.25e-18) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-3.2d-52)) then
        tmp = y / a
    else if (z <= 2.25d-18) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-52) {
		tmp = y / a;
	} else if (z <= 2.25e-18) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e-52:
		tmp = y / a
	elif z <= 2.25e-18:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e-52)
		tmp = Float64(y / a);
	elseif (z <= 2.25e-18)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e-52)
		tmp = y / a;
	elseif (z <= 2.25e-18)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e-52], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.25e-18], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e-52 or 2.24999999999999997e-18 < z

   1. Initial program 71.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 71.2%

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

      2. +-commutative 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 71.2%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 71.2%

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

      6. neg-mul-1 71.2%

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

      7. sub-neg 71.2%

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

      8. +-commutative 71.2%

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

      9. neg-sub0 71.2%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 71.2%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 71.2%

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

      12. neg-mul-1 71.2%

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

      13. times-frac 71.2%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 71.2%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 71.2%

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

      16. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -3.2000000000000001e-52 < z < 2.24999999999999997e-18

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

      4. associate-+l- 99.8%

         \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

      10. associate-+l- 99.8%

          \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

      14. metadata-eval 99.8%

          \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

      15. *-lft-identity 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 63.1%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 35.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = x / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 83.7%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. sub-neg 83.7%

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

   2. +-commutative 83.7%

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

   3. neg-sub0 83.7%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]

   4. associate-+l- 83.7%

      \[\leadsto \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]

   5. sub0-neg 83.7%

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

   6. neg-mul-1 83.7%

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

   7. sub-neg 83.7%

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

   8. +-commutative 83.7%

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

   9. neg-sub0 83.7%

      \[\leadsto \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]

   10. associate-+l- 83.7%

       \[\leadsto \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]

   11. sub0-neg 83.7%

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

   12. neg-mul-1 83.7%

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

   13. times-frac 83.7%

       \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]

   14. metadata-eval 83.7%

       \[\leadsto \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]

   15. *-lft-identity 83.7%

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

   16. *-commutative 83.7%

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

3. Simplified 83.7%

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

4. Taylor expanded in z around 0 37.7%

   \[\leadsto \color{blue}{\frac{x}{t}} \]

5. Final simplification 37.7%

   \[\leadsto \frac{x}{t} \]

Developer target: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))