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

Percentage Accurate: 85.6% → 95.3%

Time: 9.8s

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: 85.6% 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: 95.3% 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 87.1%

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

   1. sub-neg 87.1%

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

   2. +-commutative 87.1%

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

   3. neg-sub0 87.1%

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

   4. associate-+l- 87.1%

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

   5. sub0-neg 87.1%

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

   6. neg-mul-1 87.1%

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

   7. sub-neg 87.1%

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

   8. +-commutative 87.1%

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

   9. neg-sub0 87.1%

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

   10. associate-+l- 87.1%

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

   11. sub0-neg 87.1%

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

   12. neg-mul-1 87.1%

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

   13. times-frac 87.1%

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

   14. metadata-eval 87.1%

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

   15. *-lft-identity 87.1%

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

   16. *-commutative 87.1%

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

3. Simplified 87.1%

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

   1. div-sub 86.7%

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

   2. associate-/l* 89.8%

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

5. Applied egg-rr 89.8%

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

6. Taylor expanded in z around 0 95.0%

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

   1. neg-mul-1 95.0%

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

   2. unsub-neg 95.0%

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

8. Simplified 95.0%

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

9. Final simplification 95.0%

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

Alternative 2: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ t_3 := \frac{-x}{a \cdot z - t}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-30} \lor \neg \left(z \leq 1.16 \cdot 10^{-8}\right) \land z \leq 24500000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t))
        (t_2 (/ (- y (/ x z)) a))
        (t_3 (/ (- x) (- (* a z) t))))
   (if (<= z -2.15e+16)
     t_2
     (if (<= z -1.3e-171)
       t_1
       (if (<= z 3.1e-281)
         t_3
         (if (<= z 2.8e-120)
           t_1
           (if (<= z 3.2e-92)
             t_2
             (if (or (<= z 1.28e-30)
                     (and (not (<= z 1.16e-8)) (<= z 24500000000.0)))
               t_3
               (/ y (- a (/ t z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double t_3 = -x / ((a * z) - t);
	double tmp;
	if (z <= -2.15e+16) {
		tmp = t_2;
	} else if (z <= -1.3e-171) {
		tmp = t_1;
	} else if (z <= 3.1e-281) {
		tmp = t_3;
	} else if (z <= 2.8e-120) {
		tmp = t_1;
	} else if (z <= 3.2e-92) {
		tmp = t_2;
	} else if ((z <= 1.28e-30) || (!(z <= 1.16e-8) && (z <= 24500000000.0))) {
		tmp = t_3;
	} else {
		tmp = y / (a - (t / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    t_2 = (y - (x / z)) / a
    t_3 = -x / ((a * z) - t)
    if (z <= (-2.15d+16)) then
        tmp = t_2
    else if (z <= (-1.3d-171)) then
        tmp = t_1
    else if (z <= 3.1d-281) then
        tmp = t_3
    else if (z <= 2.8d-120) then
        tmp = t_1
    else if (z <= 3.2d-92) then
        tmp = t_2
    else if ((z <= 1.28d-30) .or. (.not. (z <= 1.16d-8)) .and. (z <= 24500000000.0d0)) then
        tmp = t_3
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double t_2 = (y - (x / z)) / a;
	double t_3 = -x / ((a * z) - t);
	double tmp;
	if (z <= -2.15e+16) {
		tmp = t_2;
	} else if (z <= -1.3e-171) {
		tmp = t_1;
	} else if (z <= 3.1e-281) {
		tmp = t_3;
	} else if (z <= 2.8e-120) {
		tmp = t_1;
	} else if (z <= 3.2e-92) {
		tmp = t_2;
	} else if ((z <= 1.28e-30) || (!(z <= 1.16e-8) && (z <= 24500000000.0))) {
		tmp = t_3;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	t_2 = (y - (x / z)) / a
	t_3 = -x / ((a * z) - t)
	tmp = 0
	if z <= -2.15e+16:
		tmp = t_2
	elif z <= -1.3e-171:
		tmp = t_1
	elif z <= 3.1e-281:
		tmp = t_3
	elif z <= 2.8e-120:
		tmp = t_1
	elif z <= 3.2e-92:
		tmp = t_2
	elif (z <= 1.28e-30) or (not (z <= 1.16e-8) and (z <= 24500000000.0)):
		tmp = t_3
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	t_3 = Float64(Float64(-x) / Float64(Float64(a * z) - t))
	tmp = 0.0
	if (z <= -2.15e+16)
		tmp = t_2;
	elseif (z <= -1.3e-171)
		tmp = t_1;
	elseif (z <= 3.1e-281)
		tmp = t_3;
	elseif (z <= 2.8e-120)
		tmp = t_1;
	elseif (z <= 3.2e-92)
		tmp = t_2;
	elseif ((z <= 1.28e-30) || (!(z <= 1.16e-8) && (z <= 24500000000.0)))
		tmp = t_3;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	t_2 = (y - (x / z)) / a;
	t_3 = -x / ((a * z) - t);
	tmp = 0.0;
	if (z <= -2.15e+16)
		tmp = t_2;
	elseif (z <= -1.3e-171)
		tmp = t_1;
	elseif (z <= 3.1e-281)
		tmp = t_3;
	elseif (z <= 2.8e-120)
		tmp = t_1;
	elseif (z <= 3.2e-92)
		tmp = t_2;
	elseif ((z <= 1.28e-30) || (~((z <= 1.16e-8)) && (z <= 24500000000.0)))
		tmp = t_3;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[((-x) / N[(N[(a * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+16], t$95$2, If[LessEqual[z, -1.3e-171], t$95$1, If[LessEqual[z, 3.1e-281], t$95$3, If[LessEqual[z, 2.8e-120], t$95$1, If[LessEqual[z, 3.2e-92], t$95$2, If[Or[LessEqual[z, 1.28e-30], And[N[Not[LessEqual[z, 1.16e-8]], $MachinePrecision], LessEqual[z, 24500000000.0]]], t$95$3, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15e16 or 2.79999999999999994e-120 < z < 3.1999999999999997e-92

   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 74.4%

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

      2. associate-/l* 84.4%

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

   5. Applied egg-rr 84.4%

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

   6. Taylor expanded in a around inf 84.3%

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

   if -2.15e16 < z < -1.30000000000000002e-171 or 3.1000000000000002e-281 < z < 2.79999999999999994e-120

   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 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

      3. neg-sub0 77.9%

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

      4. sub-neg 77.9%

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

      5. +-commutative 77.9%

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

      6. associate--r+ 77.9%

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

      7. neg-sub0 77.9%

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

      8. remove-double-neg 77.9%

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

      9. *-commutative 77.9%

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

   6. Simplified 77.9%

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

   if -1.30000000000000002e-171 < z < 3.1000000000000002e-281 or 3.1999999999999997e-92 < z < 1.28000000000000007e-30 or 1.15999999999999996e-8 < z < 2.45e10

   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 y around 0 86.6%

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

      1. neg-mul-1 86.6%

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

   6. Simplified 86.6%

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

   if 1.28000000000000007e-30 < z < 1.15999999999999996e-8 or 2.45e10 < z

   1. Initial program 75.1%

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

      1. sub-neg 75.1%

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

      2. +-commutative 75.1%

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

      3. neg-sub0 75.1%

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

      4. associate-+l- 75.1%

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

      5. sub0-neg 75.1%

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

      6. neg-mul-1 75.1%

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

      7. sub-neg 75.1%

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

      8. +-commutative 75.1%

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

      9. neg-sub0 75.1%

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

      10. associate-+l- 75.1%

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

      11. sub0-neg 75.1%

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

      12. neg-mul-1 75.1%

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

      13. times-frac 75.1%

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

      14. metadata-eval 75.1%

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

      15. *-lft-identity 75.1%

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

      16. *-commutative 75.1%

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

   3. Simplified 75.1%

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

      1. div-sub 75.2%

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

      2. associate-/l* 83.0%

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

   5. Applied egg-rr 83.0%

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

   6. Taylor expanded in z around 0 96.6%

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

      1. neg-mul-1 96.6%

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

      2. unsub-neg 96.6%

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

   8. Simplified 96.6%

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

   9. Taylor expanded in y around inf 79.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-171}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-30} \lor \neg \left(z \leq 1.16 \cdot 10^{-8}\right) \land z \leq 24500000000:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 3: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{-x}{a \cdot z - t}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{-1}{t} \cdot \left(y \cdot z - x\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-120}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-34} \lor \neg \left(z \leq 2.65 \cdot 10^{-8}\right) \land z \leq 23000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (/ (- x) (- (* a z) t))))
   (if (<= z -3e+16)
     t_1
     (if (<= z -5.2e-175)
       (* (/ -1.0 t) (- (* y z) x))
       (if (<= z 3.35e-281)
         t_2
         (if (<= z 2.35e-120)
           (/ (- x (* y z)) t)
           (if (<= z 3.2e-92)
             t_1
             (if (or (<= z 8.5e-34)
                     (and (not (<= z 2.65e-8)) (<= z 23000000000.0)))
               t_2
               (/ y (- a (/ t z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = -x / ((a * z) - t);
	double tmp;
	if (z <= -3e+16) {
		tmp = t_1;
	} else if (z <= -5.2e-175) {
		tmp = (-1.0 / t) * ((y * z) - x);
	} else if (z <= 3.35e-281) {
		tmp = t_2;
	} else if (z <= 2.35e-120) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 3.2e-92) {
		tmp = t_1;
	} else if ((z <= 8.5e-34) || (!(z <= 2.65e-8) && (z <= 23000000000.0))) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    t_2 = -x / ((a * z) - t)
    if (z <= (-3d+16)) then
        tmp = t_1
    else if (z <= (-5.2d-175)) then
        tmp = ((-1.0d0) / t) * ((y * z) - x)
    else if (z <= 3.35d-281) then
        tmp = t_2
    else if (z <= 2.35d-120) then
        tmp = (x - (y * z)) / t
    else if (z <= 3.2d-92) then
        tmp = t_1
    else if ((z <= 8.5d-34) .or. (.not. (z <= 2.65d-8)) .and. (z <= 23000000000.0d0)) then
        tmp = t_2
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = -x / ((a * z) - t);
	double tmp;
	if (z <= -3e+16) {
		tmp = t_1;
	} else if (z <= -5.2e-175) {
		tmp = (-1.0 / t) * ((y * z) - x);
	} else if (z <= 3.35e-281) {
		tmp = t_2;
	} else if (z <= 2.35e-120) {
		tmp = (x - (y * z)) / t;
	} else if (z <= 3.2e-92) {
		tmp = t_1;
	} else if ((z <= 8.5e-34) || (!(z <= 2.65e-8) && (z <= 23000000000.0))) {
		tmp = t_2;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = -x / ((a * z) - t)
	tmp = 0
	if z <= -3e+16:
		tmp = t_1
	elif z <= -5.2e-175:
		tmp = (-1.0 / t) * ((y * z) - x)
	elif z <= 3.35e-281:
		tmp = t_2
	elif z <= 2.35e-120:
		tmp = (x - (y * z)) / t
	elif z <= 3.2e-92:
		tmp = t_1
	elif (z <= 8.5e-34) or (not (z <= 2.65e-8) and (z <= 23000000000.0)):
		tmp = t_2
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(-x) / Float64(Float64(a * z) - t))
	tmp = 0.0
	if (z <= -3e+16)
		tmp = t_1;
	elseif (z <= -5.2e-175)
		tmp = Float64(Float64(-1.0 / t) * Float64(Float64(y * z) - x));
	elseif (z <= 3.35e-281)
		tmp = t_2;
	elseif (z <= 2.35e-120)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (z <= 3.2e-92)
		tmp = t_1;
	elseif ((z <= 8.5e-34) || (!(z <= 2.65e-8) && (z <= 23000000000.0)))
		tmp = t_2;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = -x / ((a * z) - t);
	tmp = 0.0;
	if (z <= -3e+16)
		tmp = t_1;
	elseif (z <= -5.2e-175)
		tmp = (-1.0 / t) * ((y * z) - x);
	elseif (z <= 3.35e-281)
		tmp = t_2;
	elseif (z <= 2.35e-120)
		tmp = (x - (y * z)) / t;
	elseif (z <= 3.2e-92)
		tmp = t_1;
	elseif ((z <= 8.5e-34) || (~((z <= 2.65e-8)) && (z <= 23000000000.0)))
		tmp = t_2;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(N[(a * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+16], t$95$1, If[LessEqual[z, -5.2e-175], N[(N[(-1.0 / t), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e-281], t$95$2, If[LessEqual[z, 2.35e-120], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.2e-92], t$95$1, If[Or[LessEqual[z, 8.5e-34], And[N[Not[LessEqual[z, 2.65e-8]], $MachinePrecision], LessEqual[z, 23000000000.0]]], t$95$2, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3e16 or 2.35000000000000008e-120 < z < 3.1999999999999997e-92

   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 74.4%

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

      2. associate-/l* 84.4%

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

   5. Applied egg-rr 84.4%

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

   6. Taylor expanded in a around inf 84.3%

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

   if -3e16 < z < -5.2e-175

   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. Step-by-step derivation

      1. clear-num 97.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 70.9%

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

   if -5.2e-175 < z < 3.3499999999999998e-281 or 3.1999999999999997e-92 < z < 8.5000000000000001e-34 or 2.6499999999999999e-8 < z < 2.3e10

   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 y around 0 86.6%

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

      1. neg-mul-1 86.6%

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

   6. Simplified 86.6%

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

   if 3.3499999999999998e-281 < z < 2.35000000000000008e-120

   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 a around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. neg-mul-1 84.6%

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

      3. neg-sub0 84.6%

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

      4. sub-neg 84.6%

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

      5. +-commutative 84.6%

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

      6. associate--r+ 84.6%

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

      7. neg-sub0 84.6%

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

      8. remove-double-neg 84.6%

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

      9. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   if 8.5000000000000001e-34 < z < 2.6499999999999999e-8 or 2.3e10 < z

   1. Initial program 75.1%

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

      1. sub-neg 75.1%

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

      2. +-commutative 75.1%

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

      3. neg-sub0 75.1%

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

      4. associate-+l- 75.1%

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

      5. sub0-neg 75.1%

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

      6. neg-mul-1 75.1%

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

      7. sub-neg 75.1%

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

      8. +-commutative 75.1%

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

      9. neg-sub0 75.1%

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

      10. associate-+l- 75.1%

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

      11. sub0-neg 75.1%

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

      12. neg-mul-1 75.1%

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

      13. times-frac 75.1%

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

      14. metadata-eval 75.1%

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

      15. *-lft-identity 75.1%

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

      16. *-commutative 75.1%

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

   3. Simplified 75.1%

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

      1. div-sub 75.2%

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

      2. associate-/l* 83.0%

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

   5. Applied egg-rr 83.0%

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

   6. Taylor expanded in z around 0 96.6%

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

      1. neg-mul-1 96.6%

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

      2. unsub-neg 96.6%

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

   8. Simplified 96.6%

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

   9. Taylor expanded in y around inf 79.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{-1}{t} \cdot \left(y \cdot z - x\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-281}:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-120}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-34} \lor \neg \left(z \leq 2.65 \cdot 10^{-8}\right) \land z \leq 23000000000:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 4: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{-x}{a \cdot z - t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155} \lor \neg \left(y \leq 1.65 \cdot 10^{+184}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z)))) (t_2 (/ (- x) (- (* a z) t))))
   (if (<= y -5.5e+159)
     t_1
     (if (<= y -7e+148)
       (/ (- x (* y z)) t)
       (if (<= y -4.5e-33)
         t_1
         (if (<= y 1.56e-207)
           t_2
           (if (<= y 1.5e-80)
             (- (/ y a) (/ (/ x a) z))
             (if (or (<= y 1.3e+155) (not (<= y 1.65e+184))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double t_2 = -x / ((a * z) - t);
	double tmp;
	if (y <= -5.5e+159) {
		tmp = t_1;
	} else if (y <= -7e+148) {
		tmp = (x - (y * z)) / t;
	} else if (y <= -4.5e-33) {
		tmp = t_1;
	} else if (y <= 1.56e-207) {
		tmp = t_2;
	} else if (y <= 1.5e-80) {
		tmp = (y / a) - ((x / a) / z);
	} else if ((y <= 1.3e+155) || !(y <= 1.65e+184)) {
		tmp = 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 = y / (a - (t / z))
    t_2 = -x / ((a * z) - t)
    if (y <= (-5.5d+159)) then
        tmp = t_1
    else if (y <= (-7d+148)) then
        tmp = (x - (y * z)) / t
    else if (y <= (-4.5d-33)) then
        tmp = t_1
    else if (y <= 1.56d-207) then
        tmp = t_2
    else if (y <= 1.5d-80) then
        tmp = (y / a) - ((x / a) / z)
    else if ((y <= 1.3d+155) .or. (.not. (y <= 1.65d+184))) then
        tmp = 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 = y / (a - (t / z));
	double t_2 = -x / ((a * z) - t);
	double tmp;
	if (y <= -5.5e+159) {
		tmp = t_1;
	} else if (y <= -7e+148) {
		tmp = (x - (y * z)) / t;
	} else if (y <= -4.5e-33) {
		tmp = t_1;
	} else if (y <= 1.56e-207) {
		tmp = t_2;
	} else if (y <= 1.5e-80) {
		tmp = (y / a) - ((x / a) / z);
	} else if ((y <= 1.3e+155) || !(y <= 1.65e+184)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - (t / z))
	t_2 = -x / ((a * z) - t)
	tmp = 0
	if y <= -5.5e+159:
		tmp = t_1
	elif y <= -7e+148:
		tmp = (x - (y * z)) / t
	elif y <= -4.5e-33:
		tmp = t_1
	elif y <= 1.56e-207:
		tmp = t_2
	elif y <= 1.5e-80:
		tmp = (y / a) - ((x / a) / z)
	elif (y <= 1.3e+155) or not (y <= 1.65e+184):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - Float64(t / z)))
	t_2 = Float64(Float64(-x) / Float64(Float64(a * z) - t))
	tmp = 0.0
	if (y <= -5.5e+159)
		tmp = t_1;
	elseif (y <= -7e+148)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (y <= -4.5e-33)
		tmp = t_1;
	elseif (y <= 1.56e-207)
		tmp = t_2;
	elseif (y <= 1.5e-80)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif ((y <= 1.3e+155) || !(y <= 1.65e+184))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - (t / z));
	t_2 = -x / ((a * z) - t);
	tmp = 0.0;
	if (y <= -5.5e+159)
		tmp = t_1;
	elseif (y <= -7e+148)
		tmp = (x - (y * z)) / t;
	elseif (y <= -4.5e-33)
		tmp = t_1;
	elseif (y <= 1.56e-207)
		tmp = t_2;
	elseif (y <= 1.5e-80)
		tmp = (y / a) - ((x / a) / z);
	elseif ((y <= 1.3e+155) || ~((y <= 1.65e+184)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(N[(a * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+159], t$95$1, If[LessEqual[y, -7e+148], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -4.5e-33], t$95$1, If[LessEqual[y, 1.56e-207], t$95$2, If[LessEqual[y, 1.5e-80], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.3e+155], N[Not[LessEqual[y, 1.65e+184]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4999999999999998e159 or -6.9999999999999998e148 < y < -4.49999999999999991e-33 or 1.50000000000000004e-80 < y < 1.3000000000000001e155 or 1.6499999999999999e184 < y

   1. Initial program 81.2%

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

      1. sub-neg 81.2%

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

      2. +-commutative 81.2%

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

      3. neg-sub0 81.2%

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

      4. associate-+l- 81.2%

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

      5. sub0-neg 81.2%

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

      6. neg-mul-1 81.2%

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

      7. sub-neg 81.2%

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

      8. +-commutative 81.2%

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

      9. neg-sub0 81.2%

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

      10. associate-+l- 81.2%

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

      11. sub0-neg 81.2%

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

      12. neg-mul-1 81.2%

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

      13. times-frac 81.2%

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

      14. metadata-eval 81.2%

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

      15. *-lft-identity 81.2%

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

      16. *-commutative 81.2%

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

   3. Simplified 81.2%

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

      1. div-sub 80.5%

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

      2. associate-/l* 87.4%

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

   5. Applied egg-rr 87.4%

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

   6. Taylor expanded in z around 0 96.4%

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

      1. neg-mul-1 96.4%

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

      2. unsub-neg 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in y around inf 75.7%

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

   if -5.4999999999999998e159 < y < -6.9999999999999998e148

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. neg-sub0 99.4%

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

      4. associate-+l- 99.4%

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

      5. sub0-neg 99.4%

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

      6. neg-mul-1 99.4%

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

      7. sub-neg 99.4%

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

      8. +-commutative 99.4%

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

      9. neg-sub0 99.4%

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

      10. associate-+l- 99.4%

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

      11. sub0-neg 99.4%

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

      12. neg-mul-1 99.4%

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

      13. times-frac 99.4%

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

      14. metadata-eval 99.4%

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

      15. *-lft-identity 99.4%

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

      16. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. neg-mul-1 99.4%

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

      3. neg-sub0 99.4%

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

      4. sub-neg 99.4%

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

      5. +-commutative 99.4%

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

      6. associate--r+ 99.4%

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

      7. neg-sub0 99.4%

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

      8. remove-double-neg 99.4%

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

      9. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if -4.49999999999999991e-33 < y < 1.56000000000000001e-207 or 1.3000000000000001e155 < y < 1.6499999999999999e184

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. +-commutative 97.4%

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

      3. neg-sub0 97.4%

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

      4. associate-+l- 97.4%

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

      5. sub0-neg 97.4%

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

      6. neg-mul-1 97.4%

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

      7. sub-neg 97.4%

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

      8. +-commutative 97.4%

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

      9. neg-sub0 97.4%

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

      10. associate-+l- 97.4%

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

      11. sub0-neg 97.4%

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

      12. neg-mul-1 97.4%

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

      13. times-frac 97.4%

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

      14. metadata-eval 97.4%

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

      15. *-lft-identity 97.4%

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

      16. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around 0 86.1%

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

      1. neg-mul-1 86.1%

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

   6. Simplified 86.1%

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

   if 1.56000000000000001e-207 < y < 1.50000000000000004e-80

   1. Initial program 84.7%

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

      1. sub-neg 84.7%

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

      2. +-commutative 84.7%

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

      3. neg-sub0 84.7%

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

      4. associate-+l- 84.7%

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

      5. sub0-neg 84.7%

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

      6. neg-mul-1 84.7%

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

      7. sub-neg 84.7%

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

      8. +-commutative 84.7%

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

      9. neg-sub0 84.7%

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

      10. associate-+l- 84.7%

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

      11. sub0-neg 84.7%

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

      12. neg-mul-1 84.7%

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

      13. times-frac 84.7%

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

      14. metadata-eval 84.7%

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

      15. *-lft-identity 84.7%

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

      16. *-commutative 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in z around inf 53.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.5%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{a \cdot z}\right)} + \frac{y}{a}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]

      2. +-commutative 53.5%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + \left(-\frac{x}{a \cdot z}\right)\right)} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]

      3. associate--l+ 53.5%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(\left(-\frac{x}{a \cdot z}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right)} \]

      4. associate-/r* 68.3%

         \[\leadsto \frac{y}{a} + \left(\left(-\color{blue}{\frac{\frac{x}{a}}{z}}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      5. distribute-neg-frac 68.3%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-\frac{x}{a}}{z}} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      6. mul-1-neg 68.3%

         \[\leadsto \frac{y}{a} + \left(\frac{\color{blue}{-1 \cdot \frac{x}{a}}}{z} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      7. associate-/r* 71.5%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      8. associate-*r/ 71.5%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      9. div-sub 71.5%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 71.5%

          \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}\right)}}{z} \]

      11. associate-*r/ 71.5%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 84.5%

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

   7. Taylor expanded in x around inf 84.5%

      \[\leadsto \frac{y}{a} - \frac{\color{blue}{\frac{x}{a}}}{z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+148}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-207}:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+155} \lor \neg \left(y \leq 1.65 \cdot 10^{+184}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{a \cdot z - t}\\ \end{array} \]

Alternative 5: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+16} \lor \neg \left(z \leq 1.22 \cdot 10^{-120} \lor \neg \left(z \leq 1.8 \cdot 10^{-88}\right) \land z \leq 44\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.16e+16)
         (not (or (<= z 1.22e-120) (and (not (<= z 1.8e-88)) (<= z 44.0)))))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.16e+16) || !((z <= 1.22e-120) || (!(z <= 1.8e-88) && (z <= 44.0)))) {
		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 ((z <= (-1.16d+16)) .or. (.not. (z <= 1.22d-120) .or. (.not. (z <= 1.8d-88)) .and. (z <= 44.0d0))) 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 ((z <= -1.16e+16) || !((z <= 1.22e-120) || (!(z <= 1.8e-88) && (z <= 44.0)))) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.16e+16) or not ((z <= 1.22e-120) or (not (z <= 1.8e-88) and (z <= 44.0))):
		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 ((z <= -1.16e+16) || !((z <= 1.22e-120) || (!(z <= 1.8e-88) && (z <= 44.0))))
		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 ((z <= -1.16e+16) || ~(((z <= 1.22e-120) || (~((z <= 1.8e-88)) && (z <= 44.0)))))
		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[z, -1.16e+16], N[Not[Or[LessEqual[z, 1.22e-120], And[N[Not[LessEqual[z, 1.8e-88]], $MachinePrecision], LessEqual[z, 44.0]]]], $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 z < -1.16e16 or 1.21999999999999996e-120 < z < 1.8e-88 or 44 < z

   1. Initial program 74.2%

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

      1. sub-neg 74.2%

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

      2. +-commutative 74.2%

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

      3. neg-sub0 74.2%

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

      4. associate-+l- 74.2%

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

      5. sub0-neg 74.2%

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

      6. neg-mul-1 74.2%

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

      7. sub-neg 74.2%

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

      8. +-commutative 74.2%

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

      9. neg-sub0 74.2%

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

      10. associate-+l- 74.2%

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

      11. sub0-neg 74.2%

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

      12. neg-mul-1 74.2%

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

      13. times-frac 74.2%

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

      14. metadata-eval 74.2%

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

      15. *-lft-identity 74.2%

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

      16. *-commutative 74.2%

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

   3. Simplified 74.2%

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

      1. div-sub 74.2%

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

      2. associate-/l* 83.3%

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

   5. Applied egg-rr 83.3%

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

   6. Taylor expanded in a around inf 81.2%

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

   if -1.16e16 < z < 1.21999999999999996e-120 or 1.8e-88 < z < 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 a around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

      3. neg-sub0 74.8%

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

      4. sub-neg 74.8%

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

      5. +-commutative 74.8%

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

      6. associate--r+ 74.8%

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

      7. neg-sub0 74.8%

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

      8. remove-double-neg 74.8%

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

      9. *-commutative 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+16} \lor \neg \left(z \leq 1.22 \cdot 10^{-120} \lor \neg \left(z \leq 1.8 \cdot 10^{-88}\right) \land z \leq 44\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 6: 90.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+171}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+211}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+171)
   (- (/ y a) (/ (/ x a) z))
   (if (<= z 3.8e+211) (/ (- x (* y z)) (- t (* a z))) (/ y (- a (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+171) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= 3.8e+211) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = y / (a - (t / 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 (z <= (-1.1d+171)) then
        tmp = (y / a) - ((x / a) / z)
    else if (z <= 3.8d+211) then
        tmp = (x - (y * z)) / (t - (a * z))
    else
        tmp = y / (a - (t / 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 (z <= -1.1e+171) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= 3.8e+211) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+171:
		tmp = (y / a) - ((x / a) / z)
	elif z <= 3.8e+211:
		tmp = (x - (y * z)) / (t - (a * z))
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+171)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (z <= 3.8e+211)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+171)
		tmp = (y / a) - ((x / a) / z);
	elseif (z <= 3.8e+211)
		tmp = (x - (y * z)) / (t - (a * z));
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+171], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+211], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e171

   1. Initial program 68.6%

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

      1. sub-neg 68.6%

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

      2. +-commutative 68.6%

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

      3. neg-sub0 68.6%

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

      4. associate-+l- 68.6%

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

      5. sub0-neg 68.6%

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

      6. neg-mul-1 68.6%

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

      7. sub-neg 68.6%

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

      8. +-commutative 68.6%

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

      9. neg-sub0 68.6%

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

      10. associate-+l- 68.6%

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

      11. sub0-neg 68.6%

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

      12. neg-mul-1 68.6%

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

      13. times-frac 68.6%

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

      14. metadata-eval 68.6%

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

      15. *-lft-identity 68.6%

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

      16. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.3%

         \[\leadsto \left(\color{blue}{\left(-\frac{x}{a \cdot z}\right)} + \frac{y}{a}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]

      2. +-commutative 65.3%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + \left(-\frac{x}{a \cdot z}\right)\right)} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]

      3. associate--l+ 65.3%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(\left(-\frac{x}{a \cdot z}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right)} \]

      4. associate-/r* 73.6%

         \[\leadsto \frac{y}{a} + \left(\left(-\color{blue}{\frac{\frac{x}{a}}{z}}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      5. distribute-neg-frac 73.6%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-\frac{x}{a}}{z}} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      6. mul-1-neg 73.6%

         \[\leadsto \frac{y}{a} + \left(\frac{\color{blue}{-1 \cdot \frac{x}{a}}}{z} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]

      7. associate-/r* 73.6%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      8. associate-*r/ 73.6%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}}\right) \]

      9. div-sub 73.6%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]

      10. distribute-lft-out-- 73.6%

          \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}\right)}}{z} \]

      11. associate-*r/ 73.6%

          \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   6. Simplified 82.5%

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

   7. Taylor expanded in x around inf 91.4%

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

   if -1.1e171 < z < 3.80000000000000016e211

   1. Initial program 93.8%

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

   if 3.80000000000000016e211 < z

   1. Initial program 46.1%

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

      1. sub-neg 46.1%

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

      2. +-commutative 46.1%

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

      3. neg-sub0 46.1%

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

      4. associate-+l- 46.1%

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

      5. sub0-neg 46.1%

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

      6. neg-mul-1 46.1%

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

      7. sub-neg 46.1%

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

      8. +-commutative 46.1%

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

      9. neg-sub0 46.1%

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

      10. associate-+l- 46.1%

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

      11. sub0-neg 46.1%

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

      12. neg-mul-1 46.1%

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

      13. times-frac 46.1%

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

      14. metadata-eval 46.1%

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

      15. *-lft-identity 46.1%

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

      16. *-commutative 46.1%

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

   3. Simplified 46.1%

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

      1. div-sub 46.1%

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

      2. associate-/l* 62.6%

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

   5. Applied egg-rr 62.6%

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

   6. Taylor expanded in z around 0 94.5%

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

      1. neg-mul-1 94.5%

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

      2. unsub-neg 94.5%

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

   8. Simplified 94.5%

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

   9. Taylor expanded in y around inf 89.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+171}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+211}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 7: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-131} \lor \neg \left(z \leq 6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.4e-131) (not (<= z 6e-35))) (/ y (- a (/ t z))) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.4e-131) || !(z <= 6e-35)) {
		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 <= (-8.4d-131)) .or. (.not. (z <= 6d-35))) 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 <= -8.4e-131) || !(z <= 6e-35)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.4e-131) or not (z <= 6e-35):
		tmp = y / (a - (t / z))
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.4e-131) || !(z <= 6e-35))
		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 <= -8.4e-131) || ~((z <= 6e-35)))
		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, -8.4e-131], N[Not[LessEqual[z, 6e-35]], $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 < -8.39999999999999988e-131 or 5.99999999999999978e-35 < z

   1. Initial program 79.6%

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

      1. sub-neg 79.6%

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

      2. +-commutative 79.6%

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

      3. neg-sub0 79.6%

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

      4. associate-+l- 79.6%

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

      5. sub0-neg 79.6%

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

      6. neg-mul-1 79.6%

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

      7. sub-neg 79.6%

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

      8. +-commutative 79.6%

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

      9. neg-sub0 79.6%

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

      10. associate-+l- 79.6%

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

      11. sub0-neg 79.6%

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

      12. neg-mul-1 79.6%

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

      13. times-frac 79.6%

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

      14. metadata-eval 79.6%

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

      15. *-lft-identity 79.6%

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

      16. *-commutative 79.6%

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

   3. Simplified 79.6%

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

      1. div-sub 79.6%

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

      2. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in z around 0 95.1%

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

      1. neg-mul-1 95.1%

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

      2. unsub-neg 95.1%

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

   8. Simplified 95.1%

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

   9. Taylor expanded in y around inf 72.8%

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

   if -8.39999999999999988e-131 < z < 5.99999999999999978e-35

   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 64.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-131} \lor \neg \left(z \leq 6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 8: 71.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-100} \lor \neg \left(z \leq 1.35 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e-100) (not (<= z 1.35e-33)))
   (/ 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 <= -2.05e-100) || !(z <= 1.35e-33)) {
		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 <= (-2.05d-100)) .or. (.not. (z <= 1.35d-33))) 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 <= -2.05e-100) || !(z <= 1.35e-33)) {
		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 <= -2.05e-100) or not (z <= 1.35e-33):
		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 <= -2.05e-100) || !(z <= 1.35e-33))
		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 <= -2.05e-100) || ~((z <= 1.35e-33)))
		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, -2.05e-100], N[Not[LessEqual[z, 1.35e-33]], $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 < -2.0499999999999999e-100 or 1.35e-33 < z

   1. Initial program 78.7%

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

      1. sub-neg 78.7%

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

      2. +-commutative 78.7%

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

      3. neg-sub0 78.7%

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

      4. associate-+l- 78.7%

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

      5. sub0-neg 78.7%

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

      6. neg-mul-1 78.7%

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

      7. sub-neg 78.7%

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

      8. +-commutative 78.7%

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

      9. neg-sub0 78.7%

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

      10. associate-+l- 78.7%

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

      11. sub0-neg 78.7%

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

      12. neg-mul-1 78.7%

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

      13. times-frac 78.7%

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

      14. metadata-eval 78.7%

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

      15. *-lft-identity 78.7%

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

      16. *-commutative 78.7%

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

   3. Simplified 78.7%

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

      1. div-sub 78.7%

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

      2. associate-/l* 86.2%

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

   5. Applied egg-rr 86.2%

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

   6. Taylor expanded in z around 0 94.9%

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

      1. neg-mul-1 94.9%

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

      2. unsub-neg 94.9%

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

   8. Simplified 94.9%

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

   9. Taylor expanded in y around inf 73.4%

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

   if -2.0499999999999999e-100 < z < 1.35e-33

   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 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

      3. neg-sub0 76.3%

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

      4. sub-neg 76.3%

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

      5. +-commutative 76.3%

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

      6. associate--r+ 76.3%

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

      7. neg-sub0 76.3%

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

      8. remove-double-neg 76.3%

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

      9. *-commutative 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-100} \lor \neg \left(z \leq 1.35 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 9: 54.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-62) (/ y a) (if (<= z 4.5e-31) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-62) {
		tmp = y / a;
	} else if (z <= 4.5e-31) {
		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 <= (-2.9d-62)) then
        tmp = y / a
    else if (z <= 4.5d-31) 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 <= -2.9e-62) {
		tmp = y / a;
	} else if (z <= 4.5e-31) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-62:
		tmp = y / a
	elif z <= 4.5e-31:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-62)
		tmp = Float64(y / a);
	elseif (z <= 4.5e-31)
		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 <= -2.9e-62)
		tmp = y / a;
	elseif (z <= 4.5e-31)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-62], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.5e-31], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999986e-62 or 4.5000000000000004e-31 < z

   1. Initial program 76.9%

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

      1. sub-neg 76.9%

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

      2. +-commutative 76.9%

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

      3. neg-sub0 76.9%

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

      4. associate-+l- 76.9%

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

      5. sub0-neg 76.9%

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

      6. neg-mul-1 76.9%

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

      7. sub-neg 76.9%

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

      8. +-commutative 76.9%

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

      9. neg-sub0 76.9%

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

      10. associate-+l- 76.9%

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

      11. sub0-neg 76.9%

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

      12. neg-mul-1 76.9%

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

      13. times-frac 76.9%

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

      14. metadata-eval 76.9%

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

      15. *-lft-identity 76.9%

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

      16. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 55.2%

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

   if -2.89999999999999986e-62 < z < 4.5000000000000004e-31

   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 60.1%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 34.9% 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 87.1%

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

   1. sub-neg 87.1%

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

   2. +-commutative 87.1%

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

   3. neg-sub0 87.1%

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

   4. associate-+l- 87.1%

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

   5. sub0-neg 87.1%

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

   6. neg-mul-1 87.1%

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

   7. sub-neg 87.1%

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

   8. +-commutative 87.1%

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

   9. neg-sub0 87.1%

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

   10. associate-+l- 87.1%

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

   11. sub0-neg 87.1%

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

   12. neg-mul-1 87.1%

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

   13. times-frac 87.1%

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

   14. metadata-eval 87.1%

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

   15. *-lft-identity 87.1%

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

   16. *-commutative 87.1%

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

3. Simplified 87.1%

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

4. Taylor expanded in z around 0 32.9%

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

5. Final simplification 32.9%

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

Developer target: 97.0% 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 2023189 
(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))))