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

Percentage Accurate: 85.2% → 95.9%

Time: 8.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) / ((z - a) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. *-commutative 87.0%

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

   2. associate-/l* 96.8%

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

3. Simplified 96.8%

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

5. Final simplification 96.8%

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

Alternative 2: 92.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (<= t_1 (- INFINITY))
     (- x (* t (/ y (- z a))))
     (if (<= t_1 2e+287) (+ x t_1) (+ x (* y (- 1.0 (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (t * (y / (z - a)));
	} else if (t_1 <= 2e+287) {
		tmp = x + t_1;
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (t * (y / (z - a)));
	} else if (t_1 <= 2e+287) {
		tmp = x + t_1;
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (t * (y / (z - a)))
	elif t_1 <= 2e+287:
		tmp = x + t_1
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	elseif (t_1 <= 2e+287)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (t * (y / (z - a)));
	elseif (t_1 <= 2e+287)
		tmp = x + t_1;
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], N[(x + t$95$1), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 44.3%

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

   3. Taylor expanded in t around inf 48.2%

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

      1. associate-*r/ 75.9%

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

      2. neg-mul-1 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

      4. distribute-neg-frac 75.9%

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

   5. Simplified 75.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000002e287

   1. Initial program 99.8%

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

   if 2.0000000000000002e287 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.2%

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

   6. Taylor expanded in y around 0 38.4%

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

      1. *-commutative 38.4%

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

      2. associate-*l/ 83.2%

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

      3. div-sub 83.2%

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

      4. *-inverses 83.2%

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

      5. *-commutative 83.2%

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

   8. Simplified 83.2%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y}}\\ t_2 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-171}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ (- a z) y)))) (t_2 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -8.8e+83)
     t_2
     (if (<= z -2.3e-247)
       t_1
       (if (<= z 1.7e-171) (+ x (/ y (/ a t))) (if (<= z 6.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / ((a - z) / y));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_2;
	} else if (z <= -2.3e-247) {
		tmp = t_1;
	} else if (z <= 1.7e-171) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t / ((a - z) / y))
    t_2 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-8.8d+83)) then
        tmp = t_2
    else if (z <= (-2.3d-247)) then
        tmp = t_1
    else if (z <= 1.7d-171) then
        tmp = x + (y / (a / t))
    else if (z <= 6.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / ((a - z) / y));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -8.8e+83) {
		tmp = t_2;
	} else if (z <= -2.3e-247) {
		tmp = t_1;
	} else if (z <= 1.7e-171) {
		tmp = x + (y / (a / t));
	} else if (z <= 6.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / ((a - z) / y))
	t_2 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -8.8e+83:
		tmp = t_2
	elif z <= -2.3e-247:
		tmp = t_1
	elif z <= 1.7e-171:
		tmp = x + (y / (a / t))
	elif z <= 6.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(Float64(a - z) / y)))
	t_2 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = t_2;
	elseif (z <= -2.3e-247)
		tmp = t_1;
	elseif (z <= 1.7e-171)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 6.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / ((a - z) / y));
	t_2 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = t_2;
	elseif (z <= -2.3e-247)
		tmp = t_1;
	elseif (z <= 1.7e-171)
		tmp = x + (y / (a / t));
	elseif (z <= 6.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+83], t$95$2, If[LessEqual[z, -2.3e-247], t$95$1, If[LessEqual[z, 1.7e-171], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999995e83 or 6 < z

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 88.8%

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

   6. Taylor expanded in y around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*l/ 91.3%

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

      3. div-sub 91.3%

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

      4. *-inverses 91.3%

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

      5. *-commutative 91.3%

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

   8. Simplified 91.3%

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

   if -8.79999999999999995e83 < z < -2.3e-247 or 1.69999999999999993e-171 < z < 6

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-/l* 99.6%

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

      3. frac-2neg 99.6%

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

      4. div-inv 99.5%

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

      5. distribute-neg-frac 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in t around inf 85.1%

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

      1. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

   if -2.3e-247 < z < 1.69999999999999993e-171

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

      1. associate-/r/ 99.0%

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

   7. Applied egg-rr 99.0%

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

      1. *-commutative 99.0%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.1%

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

   9. Applied egg-rr 99.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-171}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-75} \lor \neg \left(z \leq 3.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.55e-75) (not (<= z 3.7e-6)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.55e-75) || !(z <= 3.7e-6)) {
		tmp = x + (y * (1.0 - (t / z)));
	} 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 <= (-3.55d-75)) .or. (.not. (z <= 3.7d-6))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    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 <= -3.55e-75) || !(z <= 3.7e-6)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.55e-75) or not (z <= 3.7e-6):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.55e-75) || !(z <= 3.7e-6))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	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 <= -3.55e-75) || ~((z <= 3.7e-6)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.55e-75], N[Not[LessEqual[z, 3.7e-6]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5500000000000002e-75 or 3.7000000000000002e-6 < z

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 86.2%

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

   6. Taylor expanded in y around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l/ 88.2%

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

      3. div-sub 88.2%

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

      4. *-inverses 88.2%

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

      5. *-commutative 88.2%

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

   8. Simplified 88.2%

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

   if -3.5500000000000002e-75 < z < 3.7000000000000002e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-/l* 85.0%

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

   5. Simplified 85.0%

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

      1. associate-/r/ 90.3%

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

   7. Applied egg-rr 90.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-75} \lor \neg \left(z \leq 3.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+15} \lor \neg \left(t \leq 3.1 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+15) (not (<= t 3.1e-6)))
   (+ x (/ t (/ (- a z) y)))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+15) || !(t <= 3.1e-6)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y / ((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 ((t <= (-1.05d+15)) .or. (.not. (t <= 3.1d-6))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x + (y / ((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 ((t <= -1.05e+15) || !(t <= 3.1e-6)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+15) or not (t <= 3.1e-6):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+15) || !(t <= 3.1e-6))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+15) || ~((t <= 3.1e-6)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+15], N[Not[LessEqual[t, 3.1e-6]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e15 or 3.1e-6 < t

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 98.2%

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

      3. frac-2neg 98.2%

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

      4. div-inv 98.1%

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

      5. distribute-neg-frac 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in t around inf 83.2%

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

      1. associate-/l* 91.8%

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

   7. Simplified 91.8%

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

   if -1.05e15 < t < 3.1e-6

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 79.5%

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

      1. associate-/l* 90.7%

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

   5. Simplified 90.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+15} \lor \neg \left(t \leq 3.1 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.9e+15)
   (+ x (/ t (/ (- a z) y)))
   (if (<= t 3.1e-9) (+ x (/ y (/ (- z a) z))) (- x (* t (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+15) {
		tmp = x + (t / ((a - z) / y));
	} else if (t <= 3.1e-9) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.9d+15)) then
        tmp = x + (t / ((a - z) / y))
    else if (t <= 3.1d-9) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - (t * (y / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.9e+15) {
		tmp = x + (t / ((a - z) / y));
	} else if (t <= 3.1e-9) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.9e+15:
		tmp = x + (t / ((a - z) / y))
	elif t <= 3.1e-9:
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.9e+15)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	elseif (t <= 3.1e-9)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.9e+15)
		tmp = x + (t / ((a - z) / y));
	elseif (t <= 3.1e-9)
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.9e+15], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-9], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9e15

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/l* 97.7%

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

      3. frac-2neg 97.7%

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

      4. div-inv 97.6%

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

      5. distribute-neg-frac 97.6%

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in t around inf 80.4%

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

      1. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

   if -3.9e15 < t < 3.10000000000000005e-9

   1. Initial program 88.8%

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

   3. Taylor expanded in t around 0 79.5%

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

      1. associate-/l* 90.7%

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

   5. Simplified 90.7%

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

   if 3.10000000000000005e-9 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 87.2%

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

      1. associate-*r/ 92.8%

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

      2. neg-mul-1 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. distribute-neg-frac 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 0.00195\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+83) (not (<= z 0.00195))) (+ x y) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 0.00195)) {
		tmp = x + y;
	} 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 <= (-8.8d+83)) .or. (.not. (z <= 0.00195d0))) then
        tmp = x + y
    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 <= -8.8e+83) || !(z <= 0.00195)) {
		tmp = x + y;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+83) or not (z <= 0.00195):
		tmp = x + y
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+83) || !(z <= 0.00195))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+83) || ~((z <= 0.00195)))
		tmp = x + y;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+83], N[Not[LessEqual[z, 0.00195]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999995e83 or 0.0019499999999999999 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

   if -8.79999999999999995e83 < z < 0.0019499999999999999

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 81.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 0.00195\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+83) (not (<= z 2.2))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 2.2)) {
		tmp = x + y;
	} 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 <= (-8.8d+83)) .or. (.not. (z <= 2.2d0))) then
        tmp = x + y
    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 <= -8.8e+83) || !(z <= 2.2)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+83) or not (z <= 2.2):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+83) || !(z <= 2.2))
		tmp = Float64(x + y);
	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 <= -8.8e+83) || ~((z <= 2.2)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+83], N[Not[LessEqual[z, 2.2]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999995e83 or 2.2000000000000002 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

   if -8.79999999999999995e83 < z < 2.2000000000000002

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

      1. associate-/r/ 84.1%

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

   7. Applied egg-rr 84.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 2.2\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 1.32 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+83) (not (<= z 1.32e-5))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 1.32e-5)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d+83)) .or. (.not. (z <= 1.32d-5))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+83) || !(z <= 1.32e-5)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+83) or not (z <= 1.32e-5):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+83) || !(z <= 1.32e-5))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+83) || ~((z <= 1.32e-5)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+83], N[Not[LessEqual[z, 1.32e-5]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999995e83 or 1.32000000000000007e-5 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

   if -8.79999999999999995e83 < z < 1.32000000000000007e-5

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

      1. associate-/r/ 84.1%

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

   7. Applied egg-rr 84.1%

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

      1. *-commutative 84.1%

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

      2. clear-num 83.9%

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

      3. un-div-inv 84.6%

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

   9. Applied egg-rr 84.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83} \lor \neg \left(z \leq 1.32 \cdot 10^{-5}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 2.2e+91) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.2e+91) {
		tmp = x + y;
	} 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 <= 2.2d+91) then
        tmp = x + y
    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 <= 2.2e+91) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.2e+91:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.2e+91)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 2.2e+91)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.2e+91], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 2.19999999999999999e91

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 64.3%

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

      1. +-commutative 64.3%

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

   5. Simplified 64.3%

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

   if 2.19999999999999999e91 < a

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 67.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

3. Taylor expanded in x around inf 56.7%

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

4. Final simplification 56.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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