Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.3% → 97.9%

Time: 10.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

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(x + Float64(Float64(Float64(y - z) * 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[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

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(x + Float64(Float64(Float64(y - z) * 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[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{y - z}{a - z}}{\frac{1}{t}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (/ (/ (- y z) (- a z)) (/ 1.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) / (a - z)) / (1.0 / 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) / (a - z)) / (1.0d0 / t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) / (a - z)) / (1.0 / t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - z) / (a - z)) / (1.0 / t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) / Float64(1.0 / t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - z) / (a - z)) / (1.0 / t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] / N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.7%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-inv 82.6%

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

   2. *-commutative 82.6%

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

   3. associate-*l* 97.5%

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

4. Applied egg-rr 97.5%

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

   1. *-commutative 97.5%

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

   2. un-div-inv 97.6%

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

   3. associate-/r/ 97.3%

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

   4. div-inv 97.2%

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

   5. associate-/r* 97.6%

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

6. Applied egg-rr 97.6%

   \[\leadsto x + \color{blue}{\frac{\frac{y - z}{a - z}}{\frac{1}{t}}} \]
7. Add Preprocessing

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -3.85 \cdot 10^{+87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+117} \lor \neg \left(z \leq 2.05 \cdot 10^{+156}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ t a)))))
   (if (<= z -3.85e+87)
     (+ x t)
     (if (<= z -5.4e-75)
       t_1
       (if (<= z 5.9e-62)
         (+ x (/ t (/ a y)))
         (if (or (<= z 4.4e+117) (not (<= z 2.05e+156))) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (t / a));
	double tmp;
	if (z <= -3.85e+87) {
		tmp = x + t;
	} else if (z <= -5.4e-75) {
		tmp = t_1;
	} else if (z <= 5.9e-62) {
		tmp = x + (t / (a / y));
	} else if ((z <= 4.4e+117) || !(z <= 2.05e+156)) {
		tmp = x + 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 - (z * (t / a))
    if (z <= (-3.85d+87)) then
        tmp = x + t
    else if (z <= (-5.4d-75)) then
        tmp = t_1
    else if (z <= 5.9d-62) then
        tmp = x + (t / (a / y))
    else if ((z <= 4.4d+117) .or. (.not. (z <= 2.05d+156))) then
        tmp = x + 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 - (z * (t / a));
	double tmp;
	if (z <= -3.85e+87) {
		tmp = x + t;
	} else if (z <= -5.4e-75) {
		tmp = t_1;
	} else if (z <= 5.9e-62) {
		tmp = x + (t / (a / y));
	} else if ((z <= 4.4e+117) || !(z <= 2.05e+156)) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (t / a))
	tmp = 0
	if z <= -3.85e+87:
		tmp = x + t
	elif z <= -5.4e-75:
		tmp = t_1
	elif z <= 5.9e-62:
		tmp = x + (t / (a / y))
	elif (z <= 4.4e+117) or not (z <= 2.05e+156):
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(t / a)))
	tmp = 0.0
	if (z <= -3.85e+87)
		tmp = Float64(x + t);
	elseif (z <= -5.4e-75)
		tmp = t_1;
	elseif (z <= 5.9e-62)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif ((z <= 4.4e+117) || !(z <= 2.05e+156))
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * (t / a));
	tmp = 0.0;
	if (z <= -3.85e+87)
		tmp = x + t;
	elseif (z <= -5.4e-75)
		tmp = t_1;
	elseif (z <= 5.9e-62)
		tmp = x + (t / (a / y));
	elseif ((z <= 4.4e+117) || ~((z <= 2.05e+156)))
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.85e+87], N[(x + t), $MachinePrecision], If[LessEqual[z, -5.4e-75], t$95$1, If[LessEqual[z, 5.9e-62], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.4e+117], N[Not[LessEqual[z, 2.05e+156]], $MachinePrecision]], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.85000000000000015e87 or 5.9000000000000004e-62 < z < 4.40000000000000028e117 or 2.0500000000000001e156 < z

   1. Initial program 73.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.0%

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

   if -3.85000000000000015e87 < z < -5.3999999999999996e-75 or 4.40000000000000028e117 < z < 2.0500000000000001e156

   1. Initial program 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

      3. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in z around 0 64.8%

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

      1. *-commutative 64.8%

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

      2. associate-/l* 75.2%

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

   10. Applied egg-rr 75.2%

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

   if -5.3999999999999996e-75 < z < 5.9000000000000004e-62

   1. Initial program 95.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*l* 95.4%

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

   4. Applied egg-rr 95.4%

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

      1. *-commutative 95.4%

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

      2. un-div-inv 95.6%

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

      3. associate-/r/ 97.4%

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

      4. div-inv 97.4%

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

      5. associate-/r* 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in z around 0 75.2%

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

      1. associate-/l* 78.4%

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

   9. Simplified 78.4%

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

       1. clear-num 78.3%

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

       2. un-div-inv 79.4%

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

   11. Applied egg-rr 79.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+87}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-75}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+117} \lor \neg \left(z \leq 2.05 \cdot 10^{+156}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-72}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= z -2.3e-72)
     (+ x t)
     (if (<= z -1.35e-293)
       t_1
       (if (<= z 1e-251) x (if (<= z 8e-63) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -2.3e-72) {
		tmp = x + t;
	} else if (z <= -1.35e-293) {
		tmp = t_1;
	} else if (z <= 1e-251) {
		tmp = x;
	} else if (z <= 8e-63) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (z <= (-2.3d-72)) then
        tmp = x + t
    else if (z <= (-1.35d-293)) then
        tmp = t_1
    else if (z <= 1d-251) then
        tmp = x
    else if (z <= 8d-63) then
        tmp = t_1
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (z <= -2.3e-72) {
		tmp = x + t;
	} else if (z <= -1.35e-293) {
		tmp = t_1;
	} else if (z <= 1e-251) {
		tmp = x;
	} else if (z <= 8e-63) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if z <= -2.3e-72:
		tmp = x + t
	elif z <= -1.35e-293:
		tmp = t_1
	elif z <= 1e-251:
		tmp = x
	elif z <= 8e-63:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.3e-72)
		tmp = Float64(x + t);
	elseif (z <= -1.35e-293)
		tmp = t_1;
	elseif (z <= 1e-251)
		tmp = x;
	elseif (z <= 8e-63)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (z <= -2.3e-72)
		tmp = x + t;
	elseif (z <= -1.35e-293)
		tmp = t_1;
	elseif (z <= 1e-251)
		tmp = x;
	elseif (z <= 8e-63)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-72], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.35e-293], t$95$1, If[LessEqual[z, 1e-251], x, If[LessEqual[z, 8e-63], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999995e-72 or 8.00000000000000053e-63 < z

   1. Initial program 76.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.2%

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

   if -2.29999999999999995e-72 < z < -1.35000000000000001e-293 or 1.00000000000000002e-251 < z < 8.00000000000000053e-63

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-/l* 61.9%

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

   7. Applied egg-rr 61.9%

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

   if -1.35000000000000001e-293 < z < 1.00000000000000002e-251

   1. Initial program 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+64)
   (+ x (* (/ t z) (- z y)))
   (if (<= z 1.26e+98)
     (+ x (/ (* (- y z) t) (- a z)))
     (+ x (/ t (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+64) {
		tmp = x + ((t / z) * (z - y));
	} else if (z <= 1.26e+98) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+64)) then
        tmp = x + ((t / z) * (z - y))
    else if (z <= 1.26d+98) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = x + (t / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+64) {
		tmp = x + ((t / z) * (z - y));
	} else if (z <= 1.26e+98) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+64:
		tmp = x + ((t / z) * (z - y))
	elif z <= 1.26e+98:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = x + (t / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+64)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(z - y)));
	elseif (z <= 1.26e+98)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+64)
		tmp = x + ((t / z) * (z - y));
	elseif (z <= 1.26e+98)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = x + (t / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+64], N[(x + N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e+98], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.29999999999999998e64

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 98.1%

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

      3. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in a around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. *-commutative 68.7%

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

      4. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

   if -1.29999999999999998e64 < z < 1.25999999999999999e98

   1. Initial program 93.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   if 1.25999999999999999e98 < z

   1. Initial program 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 95.8%

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

      3. fma-define 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

      3. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.1%

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

   9. Applied egg-rr 91.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-50}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e-50)
   (+ x t)
   (if (<= z 6e-251) x (if (<= z 1.72e-63) (* y (/ t a)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e-50) {
		tmp = x + t;
	} else if (z <= 6e-251) {
		tmp = x;
	} else if (z <= 1.72e-63) {
		tmp = y * (t / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d-50)) then
        tmp = x + t
    else if (z <= 6d-251) then
        tmp = x
    else if (z <= 1.72d-63) then
        tmp = y * (t / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e-50) {
		tmp = x + t;
	} else if (z <= 6e-251) {
		tmp = x;
	} else if (z <= 1.72e-63) {
		tmp = y * (t / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e-50:
		tmp = x + t
	elif z <= 6e-251:
		tmp = x
	elif z <= 1.72e-63:
		tmp = y * (t / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e-50)
		tmp = Float64(x + t);
	elseif (z <= 6e-251)
		tmp = x;
	elseif (z <= 1.72e-63)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e-50)
		tmp = x + t;
	elseif (z <= 6e-251)
		tmp = x;
	elseif (z <= 1.72e-63)
		tmp = y * (t / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e-50], N[(x + t), $MachinePrecision], If[LessEqual[z, 6e-251], x, If[LessEqual[z, 1.72e-63], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0999999999999999e-50 or 1.71999999999999989e-63 < z

   1. Initial program 75.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.9%

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

   if -1.0999999999999999e-50 < z < 5.9999999999999997e-251

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-/l* 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 49.2%

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

   if 5.9999999999999997e-251 < z < 1.71999999999999989e-63

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-/l* 96.3%

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

      3. fma-define 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 74.5%

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

   7. Applied egg-rr 74.5%

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

   8. Taylor expanded in a around inf 54.0%

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

Alternative 6: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-55}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e-55)
   (+ x t)
   (if (<= z 5.5e-251) x (if (<= z 4.1e-64) (* t (/ y a)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e-55) {
		tmp = x + t;
	} else if (z <= 5.5e-251) {
		tmp = x;
	} else if (z <= 4.1e-64) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d-55)) then
        tmp = x + t
    else if (z <= 5.5d-251) then
        tmp = x
    else if (z <= 4.1d-64) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e-55) {
		tmp = x + t;
	} else if (z <= 5.5e-251) {
		tmp = x;
	} else if (z <= 4.1e-64) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e-55:
		tmp = x + t
	elif z <= 5.5e-251:
		tmp = x
	elif z <= 4.1e-64:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e-55)
		tmp = Float64(x + t);
	elseif (z <= 5.5e-251)
		tmp = x;
	elseif (z <= 4.1e-64)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e-55)
		tmp = x + t;
	elseif (z <= 5.5e-251)
		tmp = x;
	elseif (z <= 4.1e-64)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e-55], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.5e-251], x, If[LessEqual[z, 4.1e-64], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e-55 or 4.1e-64 < z

   1. Initial program 75.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.9%

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

   if -1.2999999999999999e-55 < z < 5.5e-251

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-/l* 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 49.2%

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

   if 5.5e-251 < z < 4.1e-64

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-/l* 96.3%

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

      3. fma-define 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 74.5%

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

   7. Applied egg-rr 74.5%

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

   8. Taylor expanded in a around inf 54.0%

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

   9. Taylor expanded in y around 0 47.3%

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

       1. associate-*r/ 54.0%

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

   11. Simplified 54.0%

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

Alternative 7: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-60} \lor \neg \left(y \leq 950000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.15e-60) (not (<= y 950000.0)))
   (+ x (* t (/ y (- a z))))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.15e-60) || !(y <= 950000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.15d-60)) .or. (.not. (y <= 950000.0d0))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (t * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.15e-60) || !(y <= 950000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.15e-60) or not (y <= 950000.0):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.15e-60) || !(y <= 950000.0))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.15e-60) || ~((y <= 950000.0)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.15e-60], N[Not[LessEqual[y, 950000.0]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1500000000000001e-60 or 9.5e5 < y

   1. Initial program 80.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   if -1.1500000000000001e-60 < y < 9.5e5

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

      3. associate-/l* 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-60} \lor \neg \left(y \leq 950000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-202} \lor \neg \left(y \leq 2450\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.1e-202) (not (<= y 2450.0)))
   (+ x (* t (/ y (- a z))))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.1e-202) || !(y <= 2450.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.1d-202)) .or. (.not. (y <= 2450.0d0))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.1e-202) || !(y <= 2450.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.1e-202) or not (y <= 2450.0):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.1e-202) || !(y <= 2450.0))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.1e-202) || ~((y <= 2450.0)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.1e-202], N[Not[LessEqual[y, 2450.0]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.10000000000000045e-202 or 2450 < y

   1. Initial program 81.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.4%

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

      1. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

   if -6.10000000000000045e-202 < y < 2450

   1. Initial program 85.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-202} \lor \neg \left(y \leq 2450\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4500000 \lor \neg \left(z \leq 1.26 \cdot 10^{-61}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4500000.0) (not (<= z 1.26e-61))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4500000.0) || !(z <= 1.26e-61)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / 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 ((z <= (-4500000.0d0)) .or. (.not. (z <= 1.26d-61))) then
        tmp = x + t
    else
        tmp = x + (t / (a / 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 ((z <= -4500000.0) || !(z <= 1.26e-61)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4500000.0) or not (z <= 1.26e-61):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4500000.0) || !(z <= 1.26e-61))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4500000.0) || ~((z <= 1.26e-61)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4500000.0], N[Not[LessEqual[z, 1.26e-61]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e6 or 1.2599999999999999e-61 < z

   1. Initial program 73.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.5%

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

   if -4.5e6 < z < 1.2599999999999999e-61

   1. Initial program 96.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. *-commutative 95.1%

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

      2. un-div-inv 95.2%

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

      3. associate-/r/ 97.8%

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

      4. div-inv 97.7%

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

      5. associate-/r* 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around 0 73.3%

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

      1. associate-/l* 75.2%

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

   9. Simplified 75.2%

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

       1. clear-num 75.1%

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

       2. un-div-inv 76.0%

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

   11. Applied egg-rr 76.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4500000 \lor \neg \left(z \leq 1.26 \cdot 10^{-61}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -520000 \lor \neg \left(z \leq 7.1 \cdot 10^{-62}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -520000.0) (not (<= z 7.1e-62))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -520000.0) || !(z <= 7.1e-62)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / 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 <= (-520000.0d0)) .or. (.not. (z <= 7.1d-62))) then
        tmp = x + t
    else
        tmp = x + (y * (t / 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 <= -520000.0) || !(z <= 7.1e-62)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -520000.0) or not (z <= 7.1e-62):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -520000.0) || !(z <= 7.1e-62))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -520000.0) || ~((z <= 7.1e-62)))
		tmp = x + t;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -520000.0], N[Not[LessEqual[z, 7.1e-62]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e5 or 7.1000000000000001e-62 < z

   1. Initial program 73.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.5%

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

   if -5.2e5 < z < 7.1000000000000001e-62

   1. Initial program 96.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -520000 \lor \neg \left(z \leq 7.1 \cdot 10^{-62}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -24500000 \lor \neg \left(z \leq 1.26 \cdot 10^{-61}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -24500000.0) (not (<= z 1.26e-61)))
   (+ x t)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -24500000.0) || !(z <= 1.26e-61)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (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 <= (-24500000.0d0)) .or. (.not. (z <= 1.26d-61))) then
        tmp = x + t
    else
        tmp = x + (t * (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 <= -24500000.0) || !(z <= 1.26e-61)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -24500000.0) or not (z <= 1.26e-61):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -24500000.0) || !(z <= 1.26e-61))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -24500000.0) || ~((z <= 1.26e-61)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -24500000.0], N[Not[LessEqual[z, 1.26e-61]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e7 or 1.2599999999999999e-61 < z

   1. Initial program 73.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.5%

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

   if -2.45e7 < z < 1.2599999999999999e-61

   1. Initial program 96.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*l* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. *-commutative 95.1%

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

      2. un-div-inv 95.2%

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

      3. associate-/r/ 97.8%

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

      4. div-inv 97.7%

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

      5. associate-/r* 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around 0 73.3%

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

      1. associate-/l* 75.2%

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

   9. Simplified 75.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24500000 \lor \neg \left(z \leq 1.26 \cdot 10^{-61}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-56} \lor \neg \left(z \leq 6.4 \cdot 10^{-173}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e-56) (not (<= z 6.4e-173))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e-56) || !(z <= 6.4e-173)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d-56)) .or. (.not. (z <= 6.4d-173))) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e-56) || !(z <= 6.4e-173)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e-56) or not (z <= 6.4e-173):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e-56) || !(z <= 6.4e-173))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e-56) || ~((z <= 6.4e-173)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e-56], N[Not[LessEqual[z, 6.4e-173]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999997e-56 or 6.4e-173 < z

   1. Initial program 77.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.0%

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

   if -1.39999999999999997e-56 < z < 6.4e-173

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 97.2%

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

      3. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 43.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-56} \lor \neg \left(z \leq 6.4 \cdot 10^{-173}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + t \cdot \left(\left(y - z\right) \cdot \frac{-1}{z - a}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* t (* (- y z) (/ -1.0 (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t * ((y - z) * (-1.0 / (z - a))));
}

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 * ((y - z) * ((-1.0d0) / (z - a))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t * ((y - z) * (-1.0 / (z - a))));
}

Python

def code(x, y, z, t, a):
	return x + (t * ((y - z) * (-1.0 / (z - a))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t * Float64(Float64(y - z) * Float64(-1.0 / Float64(z - a)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t * ((y - z) * (-1.0 / (z - a))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t * N[(N[(y - z), $MachinePrecision] * N[(-1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.7%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-inv 82.6%

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

   2. *-commutative 82.6%

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

   3. associate-*l* 97.5%

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

4. Applied egg-rr 97.5%

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

5. Final simplification 97.5%

   \[\leadsto x + t \cdot \left(\left(y - z\right) \cdot \frac{-1}{z - a}\right) \]
6. Add Preprocessing

Alternative 14: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) / ((a - z) / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.7%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/l* 97.1%

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

   2. clear-num 96.8%

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

   3. un-div-inv 97.3%

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

4. Applied egg-rr 97.3%

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

Alternative 15: 50.0% 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 82.7%

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

   1. +-commutative 82.7%

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

   2. associate-/l* 97.1%

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

   3. fma-define 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in t around 0 48.8%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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