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

Percentage Accurate: 86.4% → 99.6%

Time: 8.5s

Alternatives: 12

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: 86.4% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+266}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+266)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+266)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+266)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+266):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+266))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+266)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+266]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1e266 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 42.3%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1e266

   1. Initial program 99.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+266}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-51}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1150000000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.18e-51)
   (+ t x)
   (if (<= z 1.65e-87)
     (+ x (* y (/ t a)))
     (if (<= z 1150000000.0) (- x (* t (/ y z))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.18e-51) {
		tmp = t + x;
	} else if (z <= 1.65e-87) {
		tmp = x + (y * (t / a));
	} else if (z <= 1150000000.0) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t + 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 <= (-1.18d-51)) then
        tmp = t + x
    else if (z <= 1.65d-87) then
        tmp = x + (y * (t / a))
    else if (z <= 1150000000.0d0) then
        tmp = x - (t * (y / z))
    else
        tmp = t + 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 <= -1.18e-51) {
		tmp = t + x;
	} else if (z <= 1.65e-87) {
		tmp = x + (y * (t / a));
	} else if (z <= 1150000000.0) {
		tmp = x - (t * (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.18e-51:
		tmp = t + x
	elif z <= 1.65e-87:
		tmp = x + (y * (t / a))
	elif z <= 1150000000.0:
		tmp = x - (t * (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.18e-51)
		tmp = Float64(t + x);
	elseif (z <= 1.65e-87)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1150000000.0)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.18e-51)
		tmp = t + x;
	elseif (z <= 1.65e-87)
		tmp = x + (y * (t / a));
	elseif (z <= 1150000000.0)
		tmp = x - (t * (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.18e-51], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.65e-87], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1150000000.0], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18000000000000004e-51 or 1.15e9 < z

   1. Initial program 73.4%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 78.9%

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

   if -1.18000000000000004e-51 < z < 1.65e-87

   1. Initial program 97.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 z around 0 77.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. clear-num 74.5%

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

      2. un-div-inv 75.3%

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

   9. Applied egg-rr 75.3%

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

       1. associate-/r/ 77.8%

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

   11. Simplified 77.8%

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

   if 1.65e-87 < z < 1.15e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.3%

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

   4. Taylor expanded in a around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 68.7%

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

   6. Simplified 68.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{-51}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1150000000:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-18} \lor \neg \left(z \leq 1700000000\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.48e-18) (not (<= z 1700000000.0)))
   (+ x (* t (/ z (- z a))))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.48e-18) || !(z <= 1700000000.0)) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (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 ((z <= (-1.48d-18)) .or. (.not. (z <= 1700000000.0d0))) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x + (y * (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 ((z <= -1.48e-18) || !(z <= 1700000000.0)) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.48e-18) or not (z <= 1700000000.0):
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.48e-18) || !(z <= 1700000000.0))
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.48e-18) || ~((z <= 1700000000.0)))
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.48e-18], N[Not[LessEqual[z, 1700000000.0]], $MachinePrecision]], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48000000000000002e-18 or 1.7e9 < z

   1. Initial program 71.9%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in y around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 91.4%

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

      3. distribute-rgt-neg-in 91.4%

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

      4. distribute-neg-frac2 91.4%

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

      5. neg-sub0 91.4%

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

      6. sub-neg 91.4%

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

      7. +-commutative 91.4%

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

      8. associate--r+ 91.4%

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

      9. neg-sub0 91.4%

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

      10. remove-double-neg 91.4%

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

   7. Simplified 91.4%

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

   if -1.48000000000000002e-18 < z < 1.7e9

   1. Initial program 97.8%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 88.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-18} \lor \neg \left(z \leq 1700000000\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-52} \lor \neg \left(z \leq 2.75 \cdot 10^{-98}\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e-52) (not (<= z 2.75e-98)))
   (+ x (* t (/ z (- z a))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e-52) || !(z <= 2.75e-98)) {
		tmp = x + (t * (z / (z - a)));
	} 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 <= (-4.3d-52)) .or. (.not. (z <= 2.75d-98))) then
        tmp = x + (t * (z / (z - a)))
    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 <= -4.3e-52) || !(z <= 2.75e-98)) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e-52) or not (z <= 2.75e-98):
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e-52) || !(z <= 2.75e-98))
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	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 <= -4.3e-52) || ~((z <= 2.75e-98)))
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e-52], N[Not[LessEqual[z, 2.75e-98]], $MachinePrecision]], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000003e-52 or 2.7499999999999999e-98 < z

   1. Initial program 77.2%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l* 86.4%

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

      3. distribute-rgt-neg-in 86.4%

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

      4. distribute-neg-frac2 86.4%

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

      5. neg-sub0 86.4%

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

      6. sub-neg 86.4%

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

      7. +-commutative 86.4%

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

      8. associate--r+ 86.4%

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

      9. neg-sub0 86.4%

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

      10. remove-double-neg 86.4%

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

   7. Simplified 86.4%

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

   if -4.3000000000000003e-52 < z < 2.7499999999999999e-98

   1. Initial program 97.2%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 76.8%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

      1. clear-num 73.7%

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

      2. un-div-inv 74.6%

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

   9. Applied egg-rr 74.6%

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

       1. associate-/r/ 77.1%

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

   11. Simplified 77.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-52} \lor \neg \left(z \leq 2.75 \cdot 10^{-98}\right):\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-21}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1300000000:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.9e-21)
   (+ x (* t (/ z (- z a))))
   (if (<= z 1300000000.0)
     (+ x (/ (* y 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 <= -5.9e-21) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1300000000.0) {
		tmp = x + ((y * 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 <= (-5.9d-21)) then
        tmp = x + (t * (z / (z - a)))
    else if (z <= 1300000000.0d0) then
        tmp = x + ((y * 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 <= -5.9e-21) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1300000000.0) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.9e-21:
		tmp = x + (t * (z / (z - a)))
	elif z <= 1300000000.0:
		tmp = x + ((y * 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 <= -5.9e-21)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	elseif (z <= 1300000000.0)
		tmp = Float64(x + Float64(Float64(y * 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 <= -5.9e-21)
		tmp = x + (t * (z / (z - a)));
	elseif (z <= 1300000000.0)
		tmp = x + ((y * 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, -5.9e-21], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1300000000.0], N[(x + N[(N[(y * 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 < -5.9000000000000003e-21

   1. Initial program 73.3%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 89.9%

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

      3. distribute-rgt-neg-in 89.9%

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

      4. distribute-neg-frac2 89.9%

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

      5. neg-sub0 89.9%

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

      6. sub-neg 89.9%

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

      7. +-commutative 89.9%

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

      8. associate--r+ 89.9%

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

      9. neg-sub0 89.9%

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

      10. remove-double-neg 89.9%

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

   7. Simplified 89.9%

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

   if -5.9000000000000003e-21 < z < 1.3e9

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 88.8%

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

   if 1.3e9 < z

   1. Initial program 70.7%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. associate-/l* 92.7%

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

      3. distribute-rgt-neg-in 92.7%

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

      4. distribute-neg-frac2 92.7%

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

      5. neg-sub0 92.7%

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

      6. sub-neg 92.7%

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

      7. +-commutative 92.7%

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

      8. associate--r+ 92.7%

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

      9. neg-sub0 92.7%

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

      10. remove-double-neg 92.7%

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

   7. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.7%

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

   9. Applied egg-rr 92.7%

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

Alternative 6: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1550000000:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-18)
   (+ x (* t (/ z (- z a))))
   (if (<= z 1550000000.0)
     (+ x (* y (/ 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 <= -2.4e-18) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1550000000.0) {
		tmp = x + (y * (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 <= (-2.4d-18)) then
        tmp = x + (t * (z / (z - a)))
    else if (z <= 1550000000.0d0) then
        tmp = x + (y * (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 <= -2.4e-18) {
		tmp = x + (t * (z / (z - a)));
	} else if (z <= 1550000000.0) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-18:
		tmp = x + (t * (z / (z - a)))
	elif z <= 1550000000.0:
		tmp = x + (y * (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 <= -2.4e-18)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	elseif (z <= 1550000000.0)
		tmp = Float64(x + Float64(y * Float64(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 <= -2.4e-18)
		tmp = x + (t * (z / (z - a)));
	elseif (z <= 1550000000.0)
		tmp = x + (y * (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, -2.4e-18], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1550000000.0], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $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 < -2.39999999999999994e-18

   1. Initial program 73.3%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 89.9%

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

      3. distribute-rgt-neg-in 89.9%

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

      4. distribute-neg-frac2 89.9%

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

      5. neg-sub0 89.9%

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

      6. sub-neg 89.9%

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

      7. +-commutative 89.9%

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

      8. associate--r+ 89.9%

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

      9. neg-sub0 89.9%

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

      10. remove-double-neg 89.9%

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

   7. Simplified 89.9%

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

   if -2.39999999999999994e-18 < z < 1.55e9

   1. Initial program 97.8%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 88.4%

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

   if 1.55e9 < z

   1. Initial program 70.7%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. associate-/l* 92.7%

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

      3. distribute-rgt-neg-in 92.7%

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

      4. distribute-neg-frac2 92.7%

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

      5. neg-sub0 92.7%

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

      6. sub-neg 92.7%

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

      7. +-commutative 92.7%

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

      8. associate--r+ 92.7%

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

      9. neg-sub0 92.7%

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

      10. remove-double-neg 92.7%

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

   7. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.7%

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

   9. Applied egg-rr 92.7%

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

Alternative 7: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-51} \lor \neg \left(z \leq 5.2 \cdot 10^{-87}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e-51) (not (<= z 5.2e-87))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e-51) || !(z <= 5.2e-87)) {
		tmp = t + x;
	} 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 <= (-6d-51)) .or. (.not. (z <= 5.2d-87))) then
        tmp = t + x
    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 <= -6e-51) || !(z <= 5.2e-87)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e-51) or not (z <= 5.2e-87):
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e-51) || !(z <= 5.2e-87))
		tmp = Float64(t + x);
	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 <= -6e-51) || ~((z <= 5.2e-87)))
		tmp = t + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e-51], N[Not[LessEqual[z, 5.2e-87]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000005e-51 or 5.20000000000000005e-87 < z

   1. Initial program 76.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 74.8%

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

   if -6.00000000000000005e-51 < z < 5.20000000000000005e-87

   1. Initial program 97.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 z around 0 77.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

      1. clear-num 74.5%

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

      2. un-div-inv 75.3%

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

   9. Applied egg-rr 75.3%

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

       1. associate-/r/ 77.8%

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

   11. Simplified 77.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-51} \lor \neg \left(z \leq 5.2 \cdot 10^{-87}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-51} \lor \neg \left(z \leq 5.2 \cdot 10^{-87}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e-51) (not (<= z 5.2e-87))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-51) || !(z <= 5.2e-87)) {
		tmp = t + x;
	} 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 <= (-5d-51)) .or. (.not. (z <= 5.2d-87))) then
        tmp = t + x
    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 <= -5e-51) || !(z <= 5.2e-87)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e-51) or not (z <= 5.2e-87):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e-51) || !(z <= 5.2e-87))
		tmp = Float64(t + x);
	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 <= -5e-51) || ~((z <= 5.2e-87)))
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e-51], N[Not[LessEqual[z, 5.2e-87]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000004e-51 or 5.20000000000000005e-87 < z

   1. Initial program 76.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 74.8%

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

   if -5.00000000000000004e-51 < z < 5.20000000000000005e-87

   1. Initial program 97.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 z around 0 77.4%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-51} \lor \neg \left(z \leq 5.2 \cdot 10^{-87}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.9% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(t / Float64(a - z))))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

Alternative 10: 63.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{+149}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 6e+149) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6e+149) {
		tmp = t + x;
	} 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 <= 6d+149) then
        tmp = t + x
    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 <= 6e+149) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 6e+149:
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 6e+149)
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 6e+149)
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 6e+149], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 6.00000000000000007e149

   1. Initial program 86.6%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 62.3%

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

   if 6.00000000000000007e149 < a

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      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 t around 0 68.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{+149}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+213}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z 2.7e+213) x t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.7e+213) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 2.7d+213) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.7e+213) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2.7e+213:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.7e+213)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2.7e+213)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.7e+213], x, t]

Derivation

1. Split input into 2 regimes

2. if z < 2.7000000000000001e213

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 95.9%

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

      3. fma-define 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 50.6%

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

   if 2.7000000000000001e213 < z

   1. Initial program 45.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 94.8%

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

   6. Taylor expanded in x around 0 68.6%

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

Alternative 12: 18.5% 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 85.5%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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 z around inf 59.3%

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

6. Taylor expanded in x around 0 20.3%

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

Developer Target 1: 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 2024180 
(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))))