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

Percentage Accurate: 84.9% → 89.6%

Time: 10.7s

Alternatives: 10

Speedup: 0.5×

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: 84.9% 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: 89.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x}{t_1}\\ \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+230}:\\ \;\;\;\;\frac{y \cdot z}{t_1} - t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ x t_1)))
   (if (<= (/ (- x (* y z)) (- t (* z a))) 2e+230)
     (- (/ (* y z) t_1) t_2)
     (- (/ y a) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = x / t_1;
	double tmp;
	if (((x - (y * z)) / (t - (z * a))) <= 2e+230) {
		tmp = ((y * z) / t_1) - t_2;
	} else {
		tmp = (y / a) - 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 = (z * a) - t
    t_2 = x / t_1
    if (((x - (y * z)) / (t - (z * a))) <= 2d+230) then
        tmp = ((y * z) / t_1) - t_2
    else
        tmp = (y / a) - 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 = (z * a) - t;
	double t_2 = x / t_1;
	double tmp;
	if (((x - (y * z)) / (t - (z * a))) <= 2e+230) {
		tmp = ((y * z) / t_1) - t_2;
	} else {
		tmp = (y / a) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = x / t_1
	tmp = 0
	if ((x - (y * z)) / (t - (z * a))) <= 2e+230:
		tmp = ((y * z) / t_1) - t_2
	else:
		tmp = (y / a) - t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(x / t_1)
	tmp = 0.0
	if (Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a))) <= 2e+230)
		tmp = Float64(Float64(Float64(y * z) / t_1) - t_2);
	else
		tmp = Float64(Float64(y / a) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = x / t_1;
	tmp = 0.0;
	if (((x - (y * z)) / (t - (z * a))) <= 2e+230)
		tmp = ((y * z) / t_1) - t_2;
	else
		tmp = (y / a) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+230], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(y / a), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000002e230

   1. Initial program 95.1%

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

      1. sub-neg 95.1%

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

      2. +-commutative 95.1%

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

      3. neg-sub0 95.1%

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

      4. associate-+l- 95.1%

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

      5. sub0-neg 95.1%

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

      6. neg-mul-1 95.1%

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

      7. sub-neg 95.1%

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

      8. +-commutative 95.1%

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

      9. neg-sub0 95.1%

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

      10. associate-+l- 95.1%

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

      11. sub0-neg 95.1%

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

      12. neg-mul-1 95.1%

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

      13. times-frac 95.1%

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

      14. metadata-eval 95.1%

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

      15. *-lft-identity 95.1%

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

      16. *-commutative 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 95.1%

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

   if 2.0000000000000002e230 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 34.7%

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

      1. sub-neg 34.7%

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

      2. +-commutative 34.7%

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

      3. neg-sub0 34.7%

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

      4. associate-+l- 34.7%

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

      5. sub0-neg 34.7%

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

      6. neg-mul-1 34.7%

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

      7. sub-neg 34.7%

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

      8. +-commutative 34.7%

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

      9. neg-sub0 34.7%

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

      10. associate-+l- 34.7%

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

      11. sub0-neg 34.7%

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

      12. neg-mul-1 34.7%

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

      13. times-frac 34.7%

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

      14. metadata-eval 34.7%

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

      15. *-lft-identity 34.7%

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

      16. *-commutative 34.7%

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

   3. Simplified 34.7%

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

      1. div-sub 34.7%

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

      2. associate-/l* 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in z around inf 93.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+230}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 2e+230) t_1 (- (/ y a) (/ x (- (* z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= 2e+230) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (x / ((z * a) - 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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= 2d+230) then
        tmp = t_1
    else
        tmp = (y / a) - (x / ((z * a) - t))
    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 - (z * a));
	double tmp;
	if (t_1 <= 2e+230) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (x / ((z * a) - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= 2e+230:
		tmp = t_1
	else:
		tmp = (y / a) - (x / ((z * a) - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= 2e+230)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(Float64(z * a) - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= 2e+230)
		tmp = t_1;
	else
		tmp = (y / a) - (x / ((z * a) - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+230], t$95$1, N[(N[(y / a), $MachinePrecision] - N[(x / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2.0000000000000002e230

   1. Initial program 95.1%

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

   if 2.0000000000000002e230 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 34.7%

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

      1. sub-neg 34.7%

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

      2. +-commutative 34.7%

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

      3. neg-sub0 34.7%

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

      4. associate-+l- 34.7%

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

      5. sub0-neg 34.7%

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

      6. neg-mul-1 34.7%

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

      7. sub-neg 34.7%

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

      8. +-commutative 34.7%

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

      9. neg-sub0 34.7%

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

      10. associate-+l- 34.7%

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

      11. sub0-neg 34.7%

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

      12. neg-mul-1 34.7%

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

      13. times-frac 34.7%

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

      14. metadata-eval 34.7%

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

      15. *-lft-identity 34.7%

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

      16. *-commutative 34.7%

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

   3. Simplified 34.7%

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

      1. div-sub 34.7%

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

      2. associate-/l* 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in z around inf 93.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+230}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \end{array} \]

Alternative 3: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-182}:\\ \;\;\;\;-\frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+67)
   (/ y a)
   (if (<= z -1.8e-165)
     (/ x t)
     (if (<= z -2.4e-182)
       (- (/ x (* z a)))
       (if (<= z 9.5e-33)
         (/ x t)
         (if (<= z 5.8e+61)
           (/ (* y (- z)) t)
           (if (<= z 3.7e+67) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+67) {
		tmp = y / a;
	} else if (z <= -1.8e-165) {
		tmp = x / t;
	} else if (z <= -2.4e-182) {
		tmp = -(x / (z * a));
	} else if (z <= 9.5e-33) {
		tmp = x / t;
	} else if (z <= 5.8e+61) {
		tmp = (y * -z) / t;
	} else if (z <= 3.7e+67) {
		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 <= (-9.5d+67)) then
        tmp = y / a
    else if (z <= (-1.8d-165)) then
        tmp = x / t
    else if (z <= (-2.4d-182)) then
        tmp = -(x / (z * a))
    else if (z <= 9.5d-33) then
        tmp = x / t
    else if (z <= 5.8d+61) then
        tmp = (y * -z) / t
    else if (z <= 3.7d+67) 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 <= -9.5e+67) {
		tmp = y / a;
	} else if (z <= -1.8e-165) {
		tmp = x / t;
	} else if (z <= -2.4e-182) {
		tmp = -(x / (z * a));
	} else if (z <= 9.5e-33) {
		tmp = x / t;
	} else if (z <= 5.8e+61) {
		tmp = (y * -z) / t;
	} else if (z <= 3.7e+67) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+67:
		tmp = y / a
	elif z <= -1.8e-165:
		tmp = x / t
	elif z <= -2.4e-182:
		tmp = -(x / (z * a))
	elif z <= 9.5e-33:
		tmp = x / t
	elif z <= 5.8e+61:
		tmp = (y * -z) / t
	elif z <= 3.7e+67:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+67)
		tmp = Float64(y / a);
	elseif (z <= -1.8e-165)
		tmp = Float64(x / t);
	elseif (z <= -2.4e-182)
		tmp = Float64(-Float64(x / Float64(z * a)));
	elseif (z <= 9.5e-33)
		tmp = Float64(x / t);
	elseif (z <= 5.8e+61)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 3.7e+67)
		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 <= -9.5e+67)
		tmp = y / a;
	elseif (z <= -1.8e-165)
		tmp = x / t;
	elseif (z <= -2.4e-182)
		tmp = -(x / (z * a));
	elseif (z <= 9.5e-33)
		tmp = x / t;
	elseif (z <= 5.8e+61)
		tmp = (y * -z) / t;
	elseif (z <= 3.7e+67)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+67], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.8e-165], N[(x / t), $MachinePrecision], If[LessEqual[z, -2.4e-182], (-N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 9.5e-33], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.8e+61], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.7e+67], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000002e67 or 3.6999999999999997e67 < z

   1. Initial program 68.2%

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

      1. sub-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. neg-sub0 68.2%

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

      4. associate-+l- 68.2%

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

      5. sub0-neg 68.2%

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

      6. neg-mul-1 68.2%

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

      7. sub-neg 68.2%

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

      8. +-commutative 68.2%

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

      9. neg-sub0 68.2%

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

      10. associate-+l- 68.2%

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

      11. sub0-neg 68.2%

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

      12. neg-mul-1 68.2%

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

      13. times-frac 68.2%

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

      14. metadata-eval 68.2%

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

      15. *-lft-identity 68.2%

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

      16. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 72.7%

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

   if -9.5000000000000002e67 < z < -1.79999999999999992e-165 or -2.3999999999999998e-182 < z < 9.50000000000000019e-33 or 5.8000000000000001e61 < z < 3.6999999999999997e67

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate-+l- 99.2%

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

      5. sub0-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. sub-neg 99.2%

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

      8. +-commutative 99.2%

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

      9. neg-sub0 99.2%

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

      10. associate-+l- 99.2%

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

      11. sub0-neg 99.2%

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

      12. neg-mul-1 99.2%

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

      13. times-frac 99.2%

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

      14. metadata-eval 99.2%

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

      15. *-lft-identity 99.2%

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

      16. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 60.1%

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

   if -1.79999999999999992e-165 < z < -2.3999999999999998e-182

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

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

      4. associate-+l- 99.6%

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

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. sub-neg 99.6%

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

      8. +-commutative 99.6%

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

      9. neg-sub0 99.6%

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

      10. associate-+l- 99.6%

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

      11. sub0-neg 99.6%

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

      12. neg-mul-1 99.6%

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

      13. times-frac 99.6%

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

      14. metadata-eval 99.6%

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

      15. *-lft-identity 99.6%

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

      16. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 51.9%

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

      1. neg-mul-1 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in z around inf 63.0%

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

   if 9.50000000000000019e-33 < z < 5.8000000000000001e61

   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 50.9%

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

      1. associate-*r/ 50.9%

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

      2. neg-mul-1 50.9%

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

      3. neg-sub0 50.9%

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

      4. sub-neg 50.9%

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

      5. +-commutative 50.9%

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

      6. associate--r+ 50.9%

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

      7. neg-sub0 50.9%

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

      8. remove-double-neg 50.9%

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

      9. *-commutative 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in x around 0 40.2%

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

      1. associate-*r* 40.2%

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

      2. neg-mul-1 40.2%

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

      3. *-commutative 40.2%

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

   9. Simplified 40.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-182}:\\ \;\;\;\;-\frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+24)
   (/ (- x (* y z)) t)
   (if (<= t 1.2e+45)
     (- (/ y a) (/ x (- (* z a) t)))
     (- (/ x t) (/ (* y z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+24) {
		tmp = (x - (y * z)) / t;
	} else if (t <= 1.2e+45) {
		tmp = (y / a) - (x / ((z * a) - t));
	} else {
		tmp = (x / t) - ((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 (t <= (-1.7d+24)) then
        tmp = (x - (y * z)) / t
    else if (t <= 1.2d+45) then
        tmp = (y / a) - (x / ((z * a) - t))
    else
        tmp = (x / t) - ((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 (t <= -1.7e+24) {
		tmp = (x - (y * z)) / t;
	} else if (t <= 1.2e+45) {
		tmp = (y / a) - (x / ((z * a) - t));
	} else {
		tmp = (x / t) - ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+24:
		tmp = (x - (y * z)) / t
	elif t <= 1.2e+45:
		tmp = (y / a) - (x / ((z * a) - t))
	else:
		tmp = (x / t) - ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+24)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (t <= 1.2e+45)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(Float64(z * a) - t)));
	else
		tmp = Float64(Float64(x / t) - Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+24)
		tmp = (x - (y * z)) / t;
	elseif (t <= 1.2e+45)
		tmp = (y / a) - (x / ((z * a) - t));
	else
		tmp = (x / t) - ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+24], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.2e+45], N[(N[(y / a), $MachinePrecision] - N[(x / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e24

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. +-commutative 87.5%

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

      3. neg-sub0 87.5%

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

      4. associate-+l- 87.5%

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

      5. sub0-neg 87.5%

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

      6. neg-mul-1 87.5%

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

      7. sub-neg 87.5%

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

      8. +-commutative 87.5%

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

      9. neg-sub0 87.5%

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

      10. associate-+l- 87.5%

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

      11. sub0-neg 87.5%

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

      12. neg-mul-1 87.5%

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

      13. times-frac 87.5%

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

      14. metadata-eval 87.5%

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

      15. *-lft-identity 87.5%

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

      16. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in a around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

      3. neg-sub0 72.3%

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

      4. sub-neg 72.3%

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

      5. +-commutative 72.3%

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

      6. associate--r+ 72.3%

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

      7. neg-sub0 72.3%

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

      8. remove-double-neg 72.3%

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

      9. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -1.7e24 < t < 1.19999999999999995e45

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. +-commutative 87.5%

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

      3. neg-sub0 87.5%

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

      4. associate-+l- 87.5%

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

      5. sub0-neg 87.5%

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

      6. neg-mul-1 87.5%

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

      7. sub-neg 87.5%

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

      8. +-commutative 87.5%

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

      9. neg-sub0 87.5%

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

      10. associate-+l- 87.5%

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

      11. sub0-neg 87.5%

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

      12. neg-mul-1 87.5%

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

      13. times-frac 87.5%

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

      14. metadata-eval 87.5%

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

      15. *-lft-identity 87.5%

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

      16. *-commutative 87.5%

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

   3. Simplified 87.5%

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

      1. div-sub 87.5%

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

      2. associate-/l* 91.0%

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

   5. Applied egg-rr 91.0%

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

   6. Taylor expanded in z around inf 84.0%

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

   if 1.19999999999999995e45 < t

   1. Initial program 89.6%

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

      1. sub-neg 89.6%

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

      2. +-commutative 89.6%

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

      3. neg-sub0 89.6%

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

      4. associate-+l- 89.6%

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

      5. sub0-neg 89.6%

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

      6. neg-mul-1 89.6%

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

      7. sub-neg 89.6%

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

      8. +-commutative 89.6%

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

      9. neg-sub0 89.6%

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

      10. associate-+l- 89.6%

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

      11. sub0-neg 89.6%

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

      12. neg-mul-1 89.6%

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

      13. times-frac 89.6%

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

      14. metadata-eval 89.6%

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

      15. *-lft-identity 89.6%

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

      16. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. neg-mul-1 76.5%

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

      3. neg-sub0 76.5%

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

      4. sub-neg 76.5%

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

      5. +-commutative 76.5%

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

      6. associate--r+ 76.5%

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

      7. neg-sub0 76.5%

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

      8. remove-double-neg 76.5%

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

      9. *-commutative 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in x around 0 76.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t} + \frac{x}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 5: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+74} \lor \neg \left(z \leq 3.6 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+74) (not (<= z 3.6e+67)))
   (- (/ y a) (/ (/ x z) a))
   (/ (- x) (- (* z a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+74) || !(z <= 3.6e+67)) {
		tmp = (y / a) - ((x / z) / a);
	} else {
		tmp = -x / ((z * a) - 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 <= (-6.8d+74)) .or. (.not. (z <= 3.6d+67))) then
        tmp = (y / a) - ((x / z) / a)
    else
        tmp = -x / ((z * a) - 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 <= -6.8e+74) || !(z <= 3.6e+67)) {
		tmp = (y / a) - ((x / z) / a);
	} else {
		tmp = -x / ((z * a) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+74) or not (z <= 3.6e+67):
		tmp = (y / a) - ((x / z) / a)
	else:
		tmp = -x / ((z * a) - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+74) || !(z <= 3.6e+67))
		tmp = Float64(Float64(y / a) - Float64(Float64(x / z) / a));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(z * a) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e+74) || ~((z <= 3.6e+67)))
		tmp = (y / a) - ((x / z) / a);
	else
		tmp = -x / ((z * a) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+74], N[Not[LessEqual[z, 3.6e+67]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999998e74 or 3.5999999999999999e67 < z

   1. Initial program 67.9%

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

      1. sub-neg 67.9%

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

      2. +-commutative 67.9%

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

      3. neg-sub0 67.9%

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

      4. associate-+l- 67.9%

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

      5. sub0-neg 67.9%

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

      6. neg-mul-1 67.9%

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

      7. sub-neg 67.9%

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

      8. +-commutative 67.9%

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

      9. neg-sub0 67.9%

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

      10. associate-+l- 67.9%

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

      11. sub0-neg 67.9%

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

      12. neg-mul-1 67.9%

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

      13. times-frac 67.9%

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

      14. metadata-eval 67.9%

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

      15. *-lft-identity 67.9%

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

      16. *-commutative 67.9%

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

   3. Simplified 67.9%

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

      1. clear-num 67.8%

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

      2. associate-/r/ 67.7%

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

   5. Applied egg-rr 67.7%

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

   6. Taylor expanded in a around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   9. Taylor expanded in z around 0 79.4%

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

       1. +-commutative 79.4%

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

       2. mul-1-neg 79.4%

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

       3. unsub-neg 79.4%

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

       4. *-commutative 79.4%

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

       5. associate-/r* 82.6%

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

   11. Simplified 82.6%

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

   if -6.7999999999999998e74 < z < 3.5999999999999999e67

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

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

      4. associate-+l- 99.3%

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

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. sub-neg 99.3%

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

      8. +-commutative 99.3%

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

      9. neg-sub0 99.3%

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

      10. associate-+l- 99.3%

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

      11. sub0-neg 99.3%

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

      12. neg-mul-1 99.3%

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

      13. times-frac 99.3%

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

      14. metadata-eval 99.3%

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

      15. *-lft-identity 99.3%

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

      16. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+74} \lor \neg \left(z \leq 3.6 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \end{array} \]

Alternative 6: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-183}:\\ \;\;\;\;-\frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+67)
   (/ y a)
   (if (<= z -1.55e-165)
     (/ x t)
     (if (<= z -6.5e-183)
       (- (/ x (* z a)))
       (if (<= z 3.6e+67) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+67) {
		tmp = y / a;
	} else if (z <= -1.55e-165) {
		tmp = x / t;
	} else if (z <= -6.5e-183) {
		tmp = -(x / (z * a));
	} else if (z <= 3.6e+67) {
		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 <= (-9.2d+67)) then
        tmp = y / a
    else if (z <= (-1.55d-165)) then
        tmp = x / t
    else if (z <= (-6.5d-183)) then
        tmp = -(x / (z * a))
    else if (z <= 3.6d+67) 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 <= -9.2e+67) {
		tmp = y / a;
	} else if (z <= -1.55e-165) {
		tmp = x / t;
	} else if (z <= -6.5e-183) {
		tmp = -(x / (z * a));
	} else if (z <= 3.6e+67) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+67:
		tmp = y / a
	elif z <= -1.55e-165:
		tmp = x / t
	elif z <= -6.5e-183:
		tmp = -(x / (z * a))
	elif z <= 3.6e+67:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+67)
		tmp = Float64(y / a);
	elseif (z <= -1.55e-165)
		tmp = Float64(x / t);
	elseif (z <= -6.5e-183)
		tmp = Float64(-Float64(x / Float64(z * a)));
	elseif (z <= 3.6e+67)
		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 <= -9.2e+67)
		tmp = y / a;
	elseif (z <= -1.55e-165)
		tmp = x / t;
	elseif (z <= -6.5e-183)
		tmp = -(x / (z * a));
	elseif (z <= 3.6e+67)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+67], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.55e-165], N[(x / t), $MachinePrecision], If[LessEqual[z, -6.5e-183], (-N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 3.6e+67], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999994e67 or 3.5999999999999999e67 < z

   1. Initial program 68.2%

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

      1. sub-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. neg-sub0 68.2%

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

      4. associate-+l- 68.2%

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

      5. sub0-neg 68.2%

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

      6. neg-mul-1 68.2%

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

      7. sub-neg 68.2%

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

      8. +-commutative 68.2%

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

      9. neg-sub0 68.2%

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

      10. associate-+l- 68.2%

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

      11. sub0-neg 68.2%

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

      12. neg-mul-1 68.2%

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

      13. times-frac 68.2%

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

      14. metadata-eval 68.2%

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

      15. *-lft-identity 68.2%

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

      16. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 72.7%

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

   if -9.1999999999999994e67 < z < -1.54999999999999998e-165 or -6.50000000000000014e-183 < z < 3.5999999999999999e67

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

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

      4. associate-+l- 99.3%

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

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. sub-neg 99.3%

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

      8. +-commutative 99.3%

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

      9. neg-sub0 99.3%

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

      10. associate-+l- 99.3%

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

      11. sub0-neg 99.3%

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

      12. neg-mul-1 99.3%

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

      13. times-frac 99.3%

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

      14. metadata-eval 99.3%

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

      15. *-lft-identity 99.3%

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

      16. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 54.7%

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

   if -1.54999999999999998e-165 < z < -6.50000000000000014e-183

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

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

      4. associate-+l- 99.6%

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

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. sub-neg 99.6%

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

      8. +-commutative 99.6%

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

      9. neg-sub0 99.6%

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

      10. associate-+l- 99.6%

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

      11. sub0-neg 99.6%

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

      12. neg-mul-1 99.6%

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

      13. times-frac 99.6%

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

      14. metadata-eval 99.6%

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

      15. *-lft-identity 99.6%

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

      16. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 51.9%

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

      1. neg-mul-1 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in z around inf 63.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-183}:\\ \;\;\;\;-\frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+85)
   (/ y a)
   (if (<= z 9.8e+67) (/ (- x) (- (* z a) t)) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+85) {
		tmp = y / a;
	} else if (z <= 9.8e+67) {
		tmp = -x / ((z * a) - 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 <= (-7.2d+85)) then
        tmp = y / a
    else if (z <= 9.8d+67) then
        tmp = -x / ((z * a) - 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 <= -7.2e+85) {
		tmp = y / a;
	} else if (z <= 9.8e+67) {
		tmp = -x / ((z * a) - t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+85:
		tmp = y / a
	elif z <= 9.8e+67:
		tmp = -x / ((z * a) - t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+85)
		tmp = Float64(y / a);
	elseif (z <= 9.8e+67)
		tmp = Float64(Float64(-x) / Float64(Float64(z * a) - 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 <= -7.2e+85)
		tmp = y / a;
	elseif (z <= 9.8e+67)
		tmp = -x / ((z * a) - t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.8e+67], N[((-x) / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999996e85 or 9.7999999999999998e67 < z

   1. Initial program 66.4%

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

      1. sub-neg 66.4%

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

      2. +-commutative 66.4%

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

      3. neg-sub0 66.4%

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

      4. associate-+l- 66.4%

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

      5. sub0-neg 66.4%

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

      6. neg-mul-1 66.4%

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

      7. sub-neg 66.4%

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

      8. +-commutative 66.4%

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

      9. neg-sub0 66.4%

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

      10. associate-+l- 66.4%

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

      11. sub0-neg 66.4%

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

      12. neg-mul-1 66.4%

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

      13. times-frac 66.4%

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

      14. metadata-eval 66.4%

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

      15. *-lft-identity 66.4%

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

      16. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in z around inf 73.4%

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

   if -7.1999999999999996e85 < z < 9.7999999999999998e67

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

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

      4. associate-+l- 99.3%

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

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. sub-neg 99.3%

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

      8. +-commutative 99.3%

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

      9. neg-sub0 99.3%

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

      10. associate-+l- 99.3%

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

      11. sub0-neg 99.3%

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

      12. neg-mul-1 99.3%

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

      13. times-frac 99.3%

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

      14. metadata-eval 99.3%

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

      15. *-lft-identity 99.3%

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

      16. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 74.2%

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

      1. neg-mul-1 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+85) (/ y a) (if (<= z 1.5e+69) (/ (- x (* y z)) t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+85) {
		tmp = y / a;
	} else if (z <= 1.5e+69) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+85)) then
        tmp = y / a
    else if (z <= 1.5d+69) then
        tmp = (x - (y * z)) / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+85) {
		tmp = y / a;
	} else if (z <= 1.5e+69) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+85:
		tmp = y / a
	elif z <= 1.5e+69:
		tmp = (x - (y * z)) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+85)
		tmp = Float64(y / a);
	elseif (z <= 1.5e+69)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+85)
		tmp = y / a;
	elseif (z <= 1.5e+69)
		tmp = (x - (y * z)) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+85], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.5e+69], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000018e85 or 1.49999999999999992e69 < z

   1. Initial program 66.4%

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

      1. sub-neg 66.4%

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

      2. +-commutative 66.4%

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

      3. neg-sub0 66.4%

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

      4. associate-+l- 66.4%

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

      5. sub0-neg 66.4%

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

      6. neg-mul-1 66.4%

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

      7. sub-neg 66.4%

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

      8. +-commutative 66.4%

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

      9. neg-sub0 66.4%

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

      10. associate-+l- 66.4%

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

      11. sub0-neg 66.4%

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

      12. neg-mul-1 66.4%

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

      13. times-frac 66.4%

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

      14. metadata-eval 66.4%

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

      15. *-lft-identity 66.4%

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

      16. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in z around inf 73.4%

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

   if -3.20000000000000018e85 < z < 1.49999999999999992e69

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

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

      4. associate-+l- 99.3%

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

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. sub-neg 99.3%

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

      8. +-commutative 99.3%

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

      9. neg-sub0 99.3%

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

      10. associate-+l- 99.3%

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

      11. sub0-neg 99.3%

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

      12. neg-mul-1 99.3%

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

      13. times-frac 99.3%

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

      14. metadata-eval 99.3%

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

      15. *-lft-identity 99.3%

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

      16. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. neg-mul-1 67.6%

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

      3. neg-sub0 67.6%

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

      4. sub-neg 67.6%

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

      5. +-commutative 67.6%

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

      6. associate--r+ 67.6%

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

      7. neg-sub0 67.6%

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

      8. remove-double-neg 67.6%

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

      9. *-commutative 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 54.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+67) (/ y a) (if (<= z 4.95e+67) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+67) {
		tmp = y / a;
	} else if (z <= 4.95e+67) {
		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 <= (-9.2d+67)) then
        tmp = y / a
    else if (z <= 4.95d+67) 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 <= -9.2e+67) {
		tmp = y / a;
	} else if (z <= 4.95e+67) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+67:
		tmp = y / a
	elif z <= 4.95e+67:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+67)
		tmp = Float64(y / a);
	elseif (z <= 4.95e+67)
		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 <= -9.2e+67)
		tmp = y / a;
	elseif (z <= 4.95e+67)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+67], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.95e+67], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999994e67 or 4.9499999999999998e67 < z

   1. Initial program 68.2%

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

      1. sub-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. neg-sub0 68.2%

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

      4. associate-+l- 68.2%

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

      5. sub0-neg 68.2%

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

      6. neg-mul-1 68.2%

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

      7. sub-neg 68.2%

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

      8. +-commutative 68.2%

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

      9. neg-sub0 68.2%

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

      10. associate-+l- 68.2%

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

      11. sub0-neg 68.2%

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

      12. neg-mul-1 68.2%

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

      13. times-frac 68.2%

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

      14. metadata-eval 68.2%

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

      15. *-lft-identity 68.2%

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

      16. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 72.7%

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

   if -9.1999999999999994e67 < z < 4.9499999999999998e67

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. neg-sub0 99.3%

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

      4. associate-+l- 99.3%

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

      5. sub0-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. sub-neg 99.3%

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

      8. +-commutative 99.3%

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

      9. neg-sub0 99.3%

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

      10. associate-+l- 99.3%

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

      11. sub0-neg 99.3%

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

      12. neg-mul-1 99.3%

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

      13. times-frac 99.3%

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

      14. metadata-eval 99.3%

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

      15. *-lft-identity 99.3%

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

      16. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 52.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

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 88.0%

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

   1. sub-neg 88.0%

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

   2. +-commutative 88.0%

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

   3. neg-sub0 88.0%

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

   4. associate-+l- 88.0%

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

   5. sub0-neg 88.0%

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

   6. neg-mul-1 88.0%

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

   7. sub-neg 88.0%

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

   8. +-commutative 88.0%

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

   9. neg-sub0 88.0%

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

   10. associate-+l- 88.0%

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

   11. sub0-neg 88.0%

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

   12. neg-mul-1 88.0%

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

   13. times-frac 88.0%

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

   14. metadata-eval 88.0%

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

   15. *-lft-identity 88.0%

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

   16. *-commutative 88.0%

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

3. Simplified 88.0%

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

4. Taylor expanded in z around 0 37.4%

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

5. Final simplification 37.4%

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

Developer target: 97.3% 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 2023195 
(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))))