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

Percentage Accurate: 85.5% → 98.2%

Time: 9.0s

Alternatives: 10

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: 85.5% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. associate-/l* 95.0%

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

3. Simplified 95.0%

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

5. Taylor expanded in y around 0 88.8%

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

   1. associate-*r/ 88.8%

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

   2. mul-1-neg 88.8%

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

   3. distribute-rgt-neg-out 88.8%

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

   4. associate-*l/ 91.2%

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

   5. associate-*l/ 94.1%

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

   6. distribute-lft-in 95.0%

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

   7. +-commutative 95.0%

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

   8. sub-neg 95.0%

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

   9. associate-*l/ 89.3%

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

   10. associate-*r/ 98.8%

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

7. Simplified 98.8%

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

Alternative 2: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-32} \lor \neg \left(a \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-32) (not (<= a 2.9e+49)))
   (- x (* t (/ (- z y) a)))
   (+ x (* t (/ (- z y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-32) || !(a <= 2.9e+49)) {
		tmp = x - (t * ((z - y) / a));
	} else {
		tmp = x + (t * ((z - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.7d-32)) .or. (.not. (a <= 2.9d+49))) then
        tmp = x - (t * ((z - y) / a))
    else
        tmp = x + (t * ((z - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-32) || !(a <= 2.9e+49)) {
		tmp = x - (t * ((z - y) / a));
	} else {
		tmp = x + (t * ((z - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-32) or not (a <= 2.9e+49):
		tmp = x - (t * ((z - y) / a))
	else:
		tmp = x + (t * ((z - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-32) || !(a <= 2.9e+49))
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-32) || ~((a <= 2.9e+49)))
		tmp = x - (t * ((z - y) / a));
	else
		tmp = x + (t * ((z - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-32], N[Not[LessEqual[a, 2.9e+49]], $MachinePrecision]], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.70000000000000019e-32 or 2.9e49 < a

   1. Initial program 85.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 85.2%

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

      1. associate-*r/ 85.2%

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

      2. mul-1-neg 85.2%

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

      3. distribute-rgt-neg-out 85.2%

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

      4. associate-*l/ 89.6%

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

      5. associate-*l/ 95.9%

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

      6. distribute-lft-in 95.9%

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

      7. +-commutative 95.9%

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

      8. sub-neg 95.9%

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

      9. associate-*l/ 85.4%

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

      10. associate-*r/ 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in a around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. associate-/l* 87.9%

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

   10. Simplified 87.9%

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

   if -4.70000000000000019e-32 < a < 2.9e49

   1. Initial program 92.9%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in a around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. associate-/l* 88.3%

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

   7. Simplified 88.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-32} \lor \neg \left(a \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -58 \lor \neg \left(y \leq 2.4 \cdot 10^{-150}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -58.0) (not (<= y 2.4e-150)))
   (+ x (* t (/ y (- a z))))
   (- x (* z (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -58.0) || !(y <= 2.4e-150)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (z * (t / (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 ((y <= (-58.0d0)) .or. (.not. (y <= 2.4d-150))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (z * (t / (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 ((y <= -58.0) || !(y <= 2.4e-150)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (z * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -58.0) or not (y <= 2.4e-150):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (z * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -58.0) || !(y <= 2.4e-150))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -58.0) || ~((y <= 2.4e-150)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (z * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -58.0], N[Not[LessEqual[y, 2.4e-150]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -58 or 2.4e-150 < y

   1. Initial program 88.5%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 83.1%

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

      1. associate-/l* 86.5%

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

   7. Simplified 86.5%

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

   if -58 < y < 2.4e-150

   1. Initial program 90.6%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 85.0%

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

      1. associate-*r/ 85.0%

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

      2. mul-1-neg 85.0%

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

      3. distribute-rgt-neg-out 85.0%

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

      4. associate-*l/ 90.5%

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

      5. *-commutative 90.5%

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

      6. distribute-lft-neg-out 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. distribute-frac-neg2 90.5%

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

      9. neg-sub0 90.5%

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

      10. sub-neg 90.5%

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

      11. +-commutative 90.5%

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

      12. associate--r+ 90.5%

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

      13. neg-sub0 90.5%

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

      14. remove-double-neg 90.5%

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

   7. Simplified 90.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -58 \lor \neg \left(y \leq 2.4 \cdot 10^{-150}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-53} \lor \neg \left(y \leq 4.2 \cdot 10^{-150}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1e-53) (not (<= y 4.2e-150)))
   (+ x (* t (/ y (- a z))))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1e-53) || !(y <= 4.2e-150)) {
		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 <= (-1d-53)) .or. (.not. (y <= 4.2d-150))) 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 <= -1e-53) || !(y <= 4.2e-150)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1e-53) or not (y <= 4.2e-150):
		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 <= -1e-53) || !(y <= 4.2e-150))
		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 <= -1e-53) || ~((y <= 4.2e-150)))
		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, -1e-53], N[Not[LessEqual[y, 4.2e-150]], $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 < -1.00000000000000003e-53 or 4.2000000000000002e-150 < y

   1. Initial program 89.2%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 81.9%

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

      1. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if -1.00000000000000003e-53 < y < 4.2000000000000002e-150

   1. Initial program 89.5%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 80.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-53} \lor \neg \left(y \leq 4.2 \cdot 10^{-150}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 2.9 \cdot 10^{-87}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e-11) (not (<= z 2.9e-87))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-11) || !(z <= 2.9e-87)) {
		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 <= (-9d-11)) .or. (.not. (z <= 2.9d-87))) 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 <= -9e-11) || !(z <= 2.9e-87)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e-11) or not (z <= 2.9e-87):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e-11) || !(z <= 2.9e-87))
		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 <= -9e-11) || ~((z <= 2.9e-87)))
		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, -9e-11], N[Not[LessEqual[z, 2.9e-87]], $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 < -8.9999999999999999e-11 or 2.8999999999999999e-87 < z

   1. Initial program 83.0%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 69.7%

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

   if -8.9999999999999999e-11 < z < 2.8999999999999999e-87

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-11} \lor \neg \left(z \leq 2.9 \cdot 10^{-87}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+171}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.85e+228) x (if (<= a 3.7e+171) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+228) {
		tmp = x;
	} else if (a <= 3.7e+171) {
		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 (a <= (-2.85d+228)) then
        tmp = x
    else if (a <= 3.7d+171) 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 (a <= -2.85e+228) {
		tmp = x;
	} else if (a <= 3.7e+171) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.85e+228:
		tmp = x
	elif a <= 3.7e+171:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.85e+228)
		tmp = x;
	elseif (a <= 3.7e+171)
		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 (a <= -2.85e+228)
		tmp = x;
	elseif (a <= 3.7e+171)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.85e+228], x, If[LessEqual[a, 3.7e+171], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8500000000000001e228 or 3.69999999999999998e171 < a

   1. Initial program 80.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 76.6%

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

   if -2.8500000000000001e228 < a < 3.69999999999999998e171

   1. Initial program 91.4%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 60.5%

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

Alternative 7: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.6e+154) (* t (- 1.0 (/ y z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+154) {
		tmp = t * (1.0 - (y / 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 <= (-2.6d+154)) then
        tmp = t * (1.0d0 - (y / 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 <= -2.6e+154) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.6e+154:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.6e+154)
		tmp = Float64(t * Float64(1.0 - Float64(y / 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 <= -2.6e+154)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.6e+154], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999989e154

   1. Initial program 81.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

      3. associate-/l* 64.6%

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

   7. Simplified 64.6%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.5%

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

   9. Applied egg-rr 64.5%

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

       1. associate-/r/ 64.6%

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

   11. Simplified 64.6%

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

   12. Taylor expanded in t around inf 57.0%

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

   if -2.59999999999999989e154 < y

   1. Initial program 90.2%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 63.6%

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

Alternative 8: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-267}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.5e-106) x (if (<= x 2.1e-267) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.5e-106) {
		tmp = x;
	} else if (x <= 2.1e-267) {
		tmp = 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 (x <= (-6.5d-106)) then
        tmp = x
    else if (x <= 2.1d-267) then
        tmp = 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 (x <= -6.5e-106) {
		tmp = x;
	} else if (x <= 2.1e-267) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.5e-106:
		tmp = x
	elif x <= 2.1e-267:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.5e-106)
		tmp = x;
	elseif (x <= 2.1e-267)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.5e-106)
		tmp = x;
	elseif (x <= 2.1e-267)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.5e-106], x, If[LessEqual[x, 2.1e-267], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999997e-106 or 2.1000000000000001e-267 < x

   1. Initial program 89.6%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf 59.7%

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

   if -6.4999999999999997e-106 < x < 2.1000000000000001e-267

   1. Initial program 88.0%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in z around inf 40.9%

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

   6. Taylor expanded in x around inf 33.7%

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

   7. Taylor expanded in x around 0 36.8%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3e+157) (* t (/ y (- z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3e+157) {
		tmp = t * (y / -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 <= (-3d+157)) then
        tmp = t * (y / -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 <= -3e+157) {
		tmp = t * (y / -z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3e+157:
		tmp = t * (y / -z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3e+157)
		tmp = Float64(t * Float64(y / Float64(-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 <= -3e+157)
		tmp = t * (y / -z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3e+157], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000001e157

   1. Initial program 81.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

      3. associate-/l* 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in y around inf 57.2%

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

      1. associate-/l* 62.9%

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

   10. Simplified 62.9%

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

   11. Taylor expanded in x around 0 49.7%

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

       1. mul-1-neg 49.7%

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

       2. associate-*r/ 55.4%

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

       3. distribute-rgt-neg-out 55.4%

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

       4. distribute-frac-neg 55.4%

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

   13. Simplified 55.4%

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

   if -3.0000000000000001e157 < y

   1. Initial program 90.2%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 63.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 18.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. associate-/l* 95.0%

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

3. Simplified 95.0%

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

5. Taylor expanded in z around inf 58.6%

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

6. Taylor expanded in x around inf 56.6%

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

7. Taylor expanded in x around 0 18.3%

   \[\leadsto \color{blue}{t} \]
8. Add Preprocessing

Developer Target 1: 99.2% 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 2024165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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