Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.1% → 98.1%

Time: 9.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - 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 + (y * ((z - t) / (a - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - 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 + (y * ((z - t) / (a - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - 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 + (y * ((z - t) / (a - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

2. Final simplification 98.1%

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

Alternative 2: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-104}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-19} \lor \neg \left(z \leq 2.85 \cdot 10^{+17}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))))
   (if (<= z -2.5e+42)
     t_1
     (if (<= z 7e-104)
       (- x (* t (/ y (- a t))))
       (if (or (<= z 7e-19) (not (<= z 2.85e+17))) t_1 (/ y (/ (- t a) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 7e-104) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 7e-19) || !(z <= 2.85e+17)) {
		tmp = t_1;
	} else {
		tmp = y / ((t - 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 / (a - t)))
    if (z <= (-2.5d+42)) then
        tmp = t_1
    else if (z <= 7d-104) then
        tmp = x - (t * (y / (a - t)))
    else if ((z <= 7d-19) .or. (.not. (z <= 2.85d+17))) then
        tmp = t_1
    else
        tmp = y / ((t - 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 / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 7e-104) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 7e-19) || !(z <= 2.85e+17)) {
		tmp = t_1;
	} else {
		tmp = y / ((t - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (a - t)))
	tmp = 0
	if z <= -2.5e+42:
		tmp = t_1
	elif z <= 7e-104:
		tmp = x - (t * (y / (a - t)))
	elif (z <= 7e-19) or not (z <= 2.85e+17):
		tmp = t_1
	else:
		tmp = y / ((t - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 7e-104)
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	elseif ((z <= 7e-19) || !(z <= 2.85e+17))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(t - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 7e-104)
		tmp = x - (t * (y / (a - t)));
	elseif ((z <= 7e-19) || ~((z <= 2.85e+17)))
		tmp = t_1;
	else
		tmp = y / ((t - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+42], t$95$1, If[LessEqual[z, 7e-104], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7e-19], N[Not[LessEqual[z, 2.85e+17]], $MachinePrecision]], t$95$1, N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000003e42 or 7.00000000000000057e-104 < z < 7.00000000000000031e-19 or 2.85e17 < z

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 88.7%

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

   if -2.50000000000000003e42 < z < 7.00000000000000057e-104

   1. Initial program 99.9%

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

      1. associate-*r/ 86.8%

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

   3. Simplified 86.8%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*r/ 92.0%

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

   8. Simplified 92.0%

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

   if 7.00000000000000031e-19 < z < 2.85e17

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 53.4%

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

      4. sub-neg 53.4%

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

      5. +-commutative 53.4%

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

      6. neg-sub0 53.4%

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

      7. associate-+l- 53.4%

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

      8. sub0-neg 53.4%

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

      9. neg-mul-1 53.4%

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

      10. times-frac 99.2%

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

      11. fma-def 99.2%

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

      12. sub-neg 99.2%

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

      13. +-commutative 99.2%

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

      14. neg-sub0 99.2%

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

      15. associate-+l- 99.2%

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

      16. sub0-neg 99.2%

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

      17. neg-mul-1 99.2%

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

      18. *-commutative 99.2%

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

      19. associate-/l* 99.2%

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

      20. metadata-eval 99.2%

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

      21. /-rgt-identity 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around -inf 53.4%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 98.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-104}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-19} \lor \neg \left(z \leq 2.85 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 3: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-21} \lor \neg \left(z \leq 1.9 \cdot 10^{+23}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))))
   (if (<= z -2.5e+42)
     t_1
     (if (<= z 4e-103)
       (- x (* t (/ y (- a t))))
       (if (or (<= z 1.15e-21) (not (<= z 1.9e+23)))
         t_1
         (- x (/ y (+ (/ a t) -1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 4e-103) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 1.15e-21) || !(z <= 1.9e+23)) {
		tmp = t_1;
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	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 / (a - t)))
    if (z <= (-2.5d+42)) then
        tmp = t_1
    else if (z <= 4d-103) then
        tmp = x - (t * (y / (a - t)))
    else if ((z <= 1.15d-21) .or. (.not. (z <= 1.9d+23))) then
        tmp = t_1
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    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 / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 4e-103) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 1.15e-21) || !(z <= 1.9e+23)) {
		tmp = t_1;
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (a - t)))
	tmp = 0
	if z <= -2.5e+42:
		tmp = t_1
	elif z <= 4e-103:
		tmp = x - (t * (y / (a - t)))
	elif (z <= 1.15e-21) or not (z <= 1.9e+23):
		tmp = t_1
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 4e-103)
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	elseif ((z <= 1.15e-21) || !(z <= 1.9e+23))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 4e-103)
		tmp = x - (t * (y / (a - t)));
	elseif ((z <= 1.15e-21) || ~((z <= 1.9e+23)))
		tmp = t_1;
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+42], t$95$1, If[LessEqual[z, 4e-103], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.15e-21], N[Not[LessEqual[z, 1.9e+23]], $MachinePrecision]], t$95$1, N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000003e42 or 3.99999999999999983e-103 < z < 1.15e-21 or 1.89999999999999987e23 < z

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 89.2%

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

   if -2.50000000000000003e42 < z < 3.99999999999999983e-103

   1. Initial program 99.9%

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

      1. associate-*r/ 86.8%

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

   3. Simplified 86.8%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*r/ 92.0%

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

   8. Simplified 92.0%

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

   if 1.15e-21 < z < 1.89999999999999987e23

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 47.1%

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

      1. +-commutative 47.1%

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

      2. mul-1-neg 47.1%

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

      3. unsub-neg 47.1%

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

      4. associate-/l* 88.3%

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

      5. div-sub 88.3%

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

      6. *-inverses 88.3%

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

   4. Simplified 88.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-21} \lor \neg \left(z \leq 1.9 \cdot 10^{+23}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 4: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-27} \lor \neg \left(z \leq 1.45 \cdot 10^{+23}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))))
   (if (<= z -2.5e+42)
     t_1
     (if (<= z 1.85e-103)
       (- x (* t (/ y (- a t))))
       (if (or (<= z 2e-27) (not (<= z 1.45e+23)))
         t_1
         (/ y (/ (- t a) (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 1.85e-103) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 2e-27) || !(z <= 1.45e+23)) {
		tmp = t_1;
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / (a - t)))
    if (z <= (-2.5d+42)) then
        tmp = t_1
    else if (z <= 1.85d-103) then
        tmp = x - (t * (y / (a - t)))
    else if ((z <= 2d-27) .or. (.not. (z <= 1.45d+23))) then
        tmp = t_1
    else
        tmp = y / ((t - a) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 1.85e-103) {
		tmp = x - (t * (y / (a - t)));
	} else if ((z <= 2e-27) || !(z <= 1.45e+23)) {
		tmp = t_1;
	} else {
		tmp = y / ((t - a) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (a - t)))
	tmp = 0
	if z <= -2.5e+42:
		tmp = t_1
	elif z <= 1.85e-103:
		tmp = x - (t * (y / (a - t)))
	elif (z <= 2e-27) or not (z <= 1.45e+23):
		tmp = t_1
	else:
		tmp = y / ((t - a) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 1.85e-103)
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	elseif ((z <= 2e-27) || !(z <= 1.45e+23))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(t - a) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 1.85e-103)
		tmp = x - (t * (y / (a - t)));
	elseif ((z <= 2e-27) || ~((z <= 1.45e+23)))
		tmp = t_1;
	else
		tmp = y / ((t - a) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+42], t$95$1, If[LessEqual[z, 1.85e-103], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2e-27], N[Not[LessEqual[z, 1.45e+23]], $MachinePrecision]], t$95$1, N[(y / N[(N[(t - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000003e42 or 1.85e-103 < z < 2.0000000000000001e-27 or 1.45000000000000006e23 < z

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 89.1%

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

   if -2.50000000000000003e42 < z < 1.85e-103

   1. Initial program 99.9%

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

      1. associate-*r/ 86.8%

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

   3. Simplified 86.8%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*r/ 92.0%

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

   8. Simplified 92.0%

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

   if 2.0000000000000001e-27 < z < 1.45000000000000006e23

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 62.8%

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

      4. sub-neg 62.8%

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

      5. +-commutative 62.8%

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

      6. neg-sub0 62.8%

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

      7. associate-+l- 62.8%

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

      8. sub0-neg 62.8%

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

      9. neg-mul-1 62.8%

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

      10. times-frac 99.5%

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

      11. fma-def 99.5%

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

      12. sub-neg 99.5%

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

      13. +-commutative 99.5%

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

      14. neg-sub0 99.5%

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

      15. associate-+l- 99.5%

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

      16. sub0-neg 99.5%

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

      17. neg-mul-1 99.5%

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

      18. *-commutative 99.5%

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

      19. associate-/l* 99.5%

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

      20. metadata-eval 99.5%

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

      21. /-rgt-identity 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around -inf 53.6%

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

      1. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-27} \lor \neg \left(z \leq 1.45 \cdot 10^{+23}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - a}{t - z}}\\ \end{array} \]

Alternative 5: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-306} \lor \neg \left(x \leq 2.7 \cdot 10^{-195}\right) \land x \leq 1.36 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.7e-191)
   (+ x y)
   (if (or (<= x -1.9e-306) (and (not (<= x 2.7e-195)) (<= x 1.36e-68)))
     (/ y (/ a z))
     (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.7e-191) {
		tmp = x + y;
	} else if ((x <= -1.9e-306) || (!(x <= 2.7e-195) && (x <= 1.36e-68))) {
		tmp = y / (a / z);
	} else {
		tmp = x + y;
	}
	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 (x <= (-3.7d-191)) then
        tmp = x + y
    else if ((x <= (-1.9d-306)) .or. (.not. (x <= 2.7d-195)) .and. (x <= 1.36d-68)) then
        tmp = y / (a / z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.7e-191) {
		tmp = x + y;
	} else if ((x <= -1.9e-306) || (!(x <= 2.7e-195) && (x <= 1.36e-68))) {
		tmp = y / (a / z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.7e-191:
		tmp = x + y
	elif (x <= -1.9e-306) or (not (x <= 2.7e-195) and (x <= 1.36e-68)):
		tmp = y / (a / z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.7e-191)
		tmp = Float64(x + y);
	elseif ((x <= -1.9e-306) || (!(x <= 2.7e-195) && (x <= 1.36e-68)))
		tmp = Float64(y / Float64(a / z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.7e-191)
		tmp = x + y;
	elseif ((x <= -1.9e-306) || (~((x <= 2.7e-195)) && (x <= 1.36e-68)))
		tmp = y / (a / z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.7e-191], N[(x + y), $MachinePrecision], If[Or[LessEqual[x, -1.9e-306], And[N[Not[LessEqual[x, 2.7e-195]], $MachinePrecision], LessEqual[x, 1.36e-68]]], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999997e-191 or -1.9e-306 < x < 2.7e-195 or 1.36000000000000003e-68 < x

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 66.2%

      \[\leadsto \color{blue}{y + x} \]

   if -3.6999999999999997e-191 < x < -1.9e-306 or 2.7e-195 < x < 1.36000000000000003e-68

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*l/ 92.5%

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

      4. sub-neg 92.5%

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

      5. +-commutative 92.5%

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

      6. neg-sub0 92.5%

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

      7. associate-+l- 92.5%

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

      8. sub0-neg 92.5%

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

      9. neg-mul-1 92.5%

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

      10. times-frac 94.3%

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

      11. fma-def 94.3%

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

      12. sub-neg 94.3%

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

      13. +-commutative 94.3%

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

      14. neg-sub0 94.3%

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

      15. associate-+l- 94.3%

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

      16. sub0-neg 94.3%

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

      17. neg-mul-1 94.3%

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

      18. *-commutative 94.3%

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

      19. associate-/l* 94.3%

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

      20. metadata-eval 94.3%

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

      21. /-rgt-identity 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around -inf 79.8%

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

      1. associate-/l* 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in t around 0 52.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-306} \lor \neg \left(x \leq 2.7 \cdot 10^{-195}\right) \land x \leq 1.36 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;x \leq -2.85 \cdot 10^{-189}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-158}:\\ \;\;\;\;\frac{-z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= x -2.85e-189)
     (+ x y)
     (if (<= x 2.85e-289)
       t_1
       (if (<= x 1.25e-158)
         (/ (- z) (/ t y))
         (if (<= x 3.8e-66) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -2.85e-189) {
		tmp = x + y;
	} else if (x <= 2.85e-289) {
		tmp = t_1;
	} else if (x <= 1.25e-158) {
		tmp = -z / (t / y);
	} else if (x <= 3.8e-66) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	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 = y / (a / z)
    if (x <= (-2.85d-189)) then
        tmp = x + y
    else if (x <= 2.85d-289) then
        tmp = t_1
    else if (x <= 1.25d-158) then
        tmp = -z / (t / y)
    else if (x <= 3.8d-66) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -2.85e-189) {
		tmp = x + y;
	} else if (x <= 2.85e-289) {
		tmp = t_1;
	} else if (x <= 1.25e-158) {
		tmp = -z / (t / y);
	} else if (x <= 3.8e-66) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if x <= -2.85e-189:
		tmp = x + y
	elif x <= 2.85e-289:
		tmp = t_1
	elif x <= 1.25e-158:
		tmp = -z / (t / y)
	elif x <= 3.8e-66:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (x <= -2.85e-189)
		tmp = Float64(x + y);
	elseif (x <= 2.85e-289)
		tmp = t_1;
	elseif (x <= 1.25e-158)
		tmp = Float64(Float64(-z) / Float64(t / y));
	elseif (x <= 3.8e-66)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (x <= -2.85e-189)
		tmp = x + y;
	elseif (x <= 2.85e-289)
		tmp = t_1;
	elseif (x <= 1.25e-158)
		tmp = -z / (t / y);
	elseif (x <= 3.8e-66)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.85e-189], N[(x + y), $MachinePrecision], If[LessEqual[x, 2.85e-289], t$95$1, If[LessEqual[x, 1.25e-158], N[((-z) / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-66], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.85e-189 or 3.7999999999999998e-66 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{y + x} \]

   if -2.85e-189 < x < 2.84999999999999995e-289 or 1.24999999999999993e-158 < x < 3.7999999999999998e-66

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

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

      7. associate-+l- 94.0%

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

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. times-frac 89.2%

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

      11. fma-def 89.2%

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

      12. sub-neg 89.2%

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

      13. +-commutative 89.2%

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

      14. neg-sub0 89.2%

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

      15. associate-+l- 89.2%

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

      16. sub0-neg 89.2%

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

      17. neg-mul-1 89.2%

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

      18. *-commutative 89.2%

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

      19. associate-/l* 89.2%

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

      20. metadata-eval 89.2%

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

      21. /-rgt-identity 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around -inf 79.4%

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

      1. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in t around 0 53.9%

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

   if 2.84999999999999995e-289 < x < 1.24999999999999993e-158

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. associate-/l* 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in z around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. *-commutative 44.6%

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

      3. associate-*r/ 50.6%

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

      4. distribute-rgt-neg-in 50.6%

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

      5. distribute-neg-frac 50.6%

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

   7. Simplified 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*l/ 44.6%

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

      3. distribute-lft-neg-in 44.6%

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

      4. distribute-neg-frac 44.6%

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

      5. *-commutative 44.6%

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

      6. associate-/l* 50.5%

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

   9. Applied egg-rr 50.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{-189}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-158}:\\ \;\;\;\;\frac{-z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{-190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.95 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-158}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= x -8.8e-190)
     (+ x y)
     (if (<= x 3.95e-289)
       t_1
       (if (<= x 1.66e-158)
         (* (- z) (/ y t))
         (if (<= x 6.8e-69) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -8.8e-190) {
		tmp = x + y;
	} else if (x <= 3.95e-289) {
		tmp = t_1;
	} else if (x <= 1.66e-158) {
		tmp = -z * (y / t);
	} else if (x <= 6.8e-69) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	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 = y / (a / z)
    if (x <= (-8.8d-190)) then
        tmp = x + y
    else if (x <= 3.95d-289) then
        tmp = t_1
    else if (x <= 1.66d-158) then
        tmp = -z * (y / t)
    else if (x <= 6.8d-69) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -8.8e-190) {
		tmp = x + y;
	} else if (x <= 3.95e-289) {
		tmp = t_1;
	} else if (x <= 1.66e-158) {
		tmp = -z * (y / t);
	} else if (x <= 6.8e-69) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if x <= -8.8e-190:
		tmp = x + y
	elif x <= 3.95e-289:
		tmp = t_1
	elif x <= 1.66e-158:
		tmp = -z * (y / t)
	elif x <= 6.8e-69:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (x <= -8.8e-190)
		tmp = Float64(x + y);
	elseif (x <= 3.95e-289)
		tmp = t_1;
	elseif (x <= 1.66e-158)
		tmp = Float64(Float64(-z) * Float64(y / t));
	elseif (x <= 6.8e-69)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (x <= -8.8e-190)
		tmp = x + y;
	elseif (x <= 3.95e-289)
		tmp = t_1;
	elseif (x <= 1.66e-158)
		tmp = -z * (y / t);
	elseif (x <= 6.8e-69)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e-190], N[(x + y), $MachinePrecision], If[LessEqual[x, 3.95e-289], t$95$1, If[LessEqual[x, 1.66e-158], N[((-z) * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-69], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.80000000000000017e-190 or 6.80000000000000016e-69 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{y + x} \]

   if -8.80000000000000017e-190 < x < 3.9499999999999999e-289 or 1.66000000000000009e-158 < x < 6.80000000000000016e-69

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

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

      7. associate-+l- 94.0%

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

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. times-frac 89.2%

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

      11. fma-def 89.2%

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

      12. sub-neg 89.2%

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

      13. +-commutative 89.2%

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

      14. neg-sub0 89.2%

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

      15. associate-+l- 89.2%

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

      16. sub0-neg 89.2%

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

      17. neg-mul-1 89.2%

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

      18. *-commutative 89.2%

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

      19. associate-/l* 89.2%

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

      20. metadata-eval 89.2%

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

      21. /-rgt-identity 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around -inf 79.4%

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

      1. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in t around 0 53.9%

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

   if 3.9499999999999999e-289 < x < 1.66000000000000009e-158

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. associate-/l* 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in z around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. *-commutative 44.6%

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

      3. associate-*r/ 50.6%

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

      4. distribute-rgt-neg-in 50.6%

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

      5. distribute-neg-frac 50.6%

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

   7. Simplified 50.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.95 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-158}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= x -4.2e-190)
     (+ x y)
     (if (<= x 3.3e-289)
       t_1
       (if (<= x 7.8e-156)
         (/ y (/ (- t) z))
         (if (<= x 1.14e-67) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -4.2e-190) {
		tmp = x + y;
	} else if (x <= 3.3e-289) {
		tmp = t_1;
	} else if (x <= 7.8e-156) {
		tmp = y / (-t / z);
	} else if (x <= 1.14e-67) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	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 = y / (a / z)
    if (x <= (-4.2d-190)) then
        tmp = x + y
    else if (x <= 3.3d-289) then
        tmp = t_1
    else if (x <= 7.8d-156) then
        tmp = y / (-t / z)
    else if (x <= 1.14d-67) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -4.2e-190) {
		tmp = x + y;
	} else if (x <= 3.3e-289) {
		tmp = t_1;
	} else if (x <= 7.8e-156) {
		tmp = y / (-t / z);
	} else if (x <= 1.14e-67) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if x <= -4.2e-190:
		tmp = x + y
	elif x <= 3.3e-289:
		tmp = t_1
	elif x <= 7.8e-156:
		tmp = y / (-t / z)
	elif x <= 1.14e-67:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (x <= -4.2e-190)
		tmp = Float64(x + y);
	elseif (x <= 3.3e-289)
		tmp = t_1;
	elseif (x <= 7.8e-156)
		tmp = Float64(y / Float64(Float64(-t) / z));
	elseif (x <= 1.14e-67)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (x <= -4.2e-190)
		tmp = x + y;
	elseif (x <= 3.3e-289)
		tmp = t_1;
	elseif (x <= 7.8e-156)
		tmp = y / (-t / z);
	elseif (x <= 1.14e-67)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e-190], N[(x + y), $MachinePrecision], If[LessEqual[x, 3.3e-289], t$95$1, If[LessEqual[x, 7.8e-156], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.14e-67], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.19999999999999983e-190 or 1.14e-67 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{y + x} \]

   if -4.19999999999999983e-190 < x < 3.29999999999999997e-289 or 7.8000000000000002e-156 < x < 1.14e-67

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

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

      7. associate-+l- 94.0%

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

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. times-frac 89.2%

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

      11. fma-def 89.2%

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

      12. sub-neg 89.2%

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

      13. +-commutative 89.2%

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

      14. neg-sub0 89.2%

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

      15. associate-+l- 89.2%

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

      16. sub0-neg 89.2%

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

      17. neg-mul-1 89.2%

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

      18. *-commutative 89.2%

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

      19. associate-/l* 89.2%

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

      20. metadata-eval 89.2%

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

      21. /-rgt-identity 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around -inf 79.4%

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

      1. associate-/l* 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in t around 0 53.9%

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

   if 3.29999999999999997e-289 < x < 7.8000000000000002e-156

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. associate-/l* 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in z around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. *-commutative 44.6%

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

      3. associate-*r/ 50.6%

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

      4. distribute-rgt-neg-in 50.6%

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

      5. distribute-neg-frac 50.6%

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

   7. Simplified 50.6%

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

      1. clear-num 50.6%

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

      2. un-div-inv 50.5%

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

      3. add-sqr-sqrt 29.6%

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

      4. sqrt-unprod 28.6%

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

      5. sqr-neg 28.6%

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

      6. sqrt-unprod 1.1%

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

      7. add-sqr-sqrt 2.4%

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

      8. associate-/l* 2.5%

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

      9. *-commutative 2.5%

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

      10. associate-/l* 2.5%

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

      11. frac-2neg 2.5%

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

      12. add-sqr-sqrt 1.4%

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

      13. sqrt-unprod 18.4%

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

      14. sqr-neg 18.4%

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

      15. sqrt-unprod 20.8%

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

      16. add-sqr-sqrt 50.6%

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

   9. Applied egg-rr 50.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= x -2.3e-191)
     (+ x y)
     (if (<= x -9.5e-303)
       t_1
       (if (<= x 9.5e-154)
         (* y (- 1.0 (/ z t)))
         (if (<= x 6.8e-69) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -2.3e-191) {
		tmp = x + y;
	} else if (x <= -9.5e-303) {
		tmp = t_1;
	} else if (x <= 9.5e-154) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 6.8e-69) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	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 = y / (a / z)
    if (x <= (-2.3d-191)) then
        tmp = x + y
    else if (x <= (-9.5d-303)) then
        tmp = t_1
    else if (x <= 9.5d-154) then
        tmp = y * (1.0d0 - (z / t))
    else if (x <= 6.8d-69) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / z);
	double tmp;
	if (x <= -2.3e-191) {
		tmp = x + y;
	} else if (x <= -9.5e-303) {
		tmp = t_1;
	} else if (x <= 9.5e-154) {
		tmp = y * (1.0 - (z / t));
	} else if (x <= 6.8e-69) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if x <= -2.3e-191:
		tmp = x + y
	elif x <= -9.5e-303:
		tmp = t_1
	elif x <= 9.5e-154:
		tmp = y * (1.0 - (z / t))
	elif x <= 6.8e-69:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (x <= -2.3e-191)
		tmp = Float64(x + y);
	elseif (x <= -9.5e-303)
		tmp = t_1;
	elseif (x <= 9.5e-154)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (x <= 6.8e-69)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / z);
	tmp = 0.0;
	if (x <= -2.3e-191)
		tmp = x + y;
	elseif (x <= -9.5e-303)
		tmp = t_1;
	elseif (x <= 9.5e-154)
		tmp = y * (1.0 - (z / t));
	elseif (x <= 6.8e-69)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e-191], N[(x + y), $MachinePrecision], If[LessEqual[x, -9.5e-303], t$95$1, If[LessEqual[x, 9.5e-154], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-69], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.30000000000000011e-191 or 6.80000000000000016e-69 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{y + x} \]

   if -2.30000000000000011e-191 < x < -9.4999999999999999e-303 or 9.50000000000000057e-154 < x < 6.80000000000000016e-69

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l/ 95.4%

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

      4. sub-neg 95.4%

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

      5. +-commutative 95.4%

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

      6. neg-sub0 95.4%

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

      7. associate-+l- 95.4%

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

      8. sub0-neg 95.4%

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

      9. neg-mul-1 95.4%

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

      10. times-frac 93.1%

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

      11. fma-def 93.1%

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

      12. sub-neg 93.1%

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

      13. +-commutative 93.1%

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

      14. neg-sub0 93.1%

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

      15. associate-+l- 93.1%

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

      16. sub0-neg 93.1%

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

      17. neg-mul-1 93.1%

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

      18. *-commutative 93.1%

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

      19. associate-/l* 93.1%

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

      20. metadata-eval 93.1%

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

      21. /-rgt-identity 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around -inf 80.1%

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

      1. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around 0 56.1%

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

   if -9.4999999999999999e-303 < x < 9.50000000000000057e-154

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. unsub-neg 69.4%

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

      4. associate-/l* 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in y around inf 69.6%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+123}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+123)
   (+ x y)
   (if (<= t 7.4e+148) (+ x (* y (/ z (- a t)))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+123) {
		tmp = x + y;
	} else if (t <= 7.4e+148) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	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 <= (-9.5d+123)) then
        tmp = x + y
    else if (t <= 7.4d+148) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + y
    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 <= -9.5e+123) {
		tmp = x + y;
	} else if (t <= 7.4e+148) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+123:
		tmp = x + y
	elif t <= 7.4e+148:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+123)
		tmp = Float64(x + y);
	elseif (t <= 7.4e+148)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+123)
		tmp = x + y;
	elseif (t <= 7.4e+148)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+123], N[(x + y), $MachinePrecision], If[LessEqual[t, 7.4e+148], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999996e123 or 7.4000000000000005e148 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 88.6%

      \[\leadsto \color{blue}{y + x} \]

   if -9.4999999999999996e123 < t < 7.4000000000000005e148

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 83.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+123}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+119)
   (+ x y)
   (if (<= t 2.15e+79) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+119) {
		tmp = x + y;
	} else if (t <= 2.15e+79) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	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 <= (-5.5d+119)) then
        tmp = x + y
    else if (t <= 2.15d+79) then
        tmp = x + (y * (z / a))
    else
        tmp = x + y
    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 <= -5.5e+119) {
		tmp = x + y;
	} else if (t <= 2.15e+79) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+119:
		tmp = x + y
	elif t <= 2.15e+79:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+119)
		tmp = Float64(x + y);
	elseif (t <= 2.15e+79)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+119)
		tmp = x + y;
	elseif (t <= 2.15e+79)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+119], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.15e+79], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000003e119 or 2.1500000000000002e79 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.4%

      \[\leadsto \color{blue}{y + x} \]

   if -5.5000000000000003e119 < t < 2.1500000000000002e79

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 69.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 62.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -1.04e+144) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.04e+144) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.04d+144)) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.04e+144) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.04e+144:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.04e+144)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.04e+144)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.04e+144], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04e144

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.5%

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

   if -1.04e144 < a

   1. Initial program 97.8%

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

   2. Taylor expanded in t around inf 56.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.04 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 51.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in x around inf 46.7%

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

3. Final simplification 46.7%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	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) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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