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

Percentage Accurate: 85.2% → 99.4%

Time: 11.4s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+198}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+198)))
     (+ x (* y (/ (- z t) (- a t))))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+198)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+198)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+198):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+198))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+198)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+198]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 2.00000000000000004e198 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 38.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 2.00000000000000004e198

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+198}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. +-commutative 86.3%

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

   2. associate-*l/ 97.2%

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

   3. fma-def 97.2%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 3: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := x - \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-57}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1250000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (- x (/ y (/ t z)))))
   (if (<= t -9e+138)
     (+ y x)
     (if (<= t -5.1e-52)
       t_2
       (if (<= t -1.15e-57)
         (+ y x)
         (if (<= t 3.6e-100)
           (+ x (* z (/ y a)))
           (if (<= t 5.4e-60)
             t_2
             (if (<= t 1250000000.0)
               t_1
               (if (<= t 8.4e+160)
                 t_2
                 (if (<= t 8.5e+160) t_1 (+ y x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = x - (y / (t / z));
	double tmp;
	if (t <= -9e+138) {
		tmp = y + x;
	} else if (t <= -5.1e-52) {
		tmp = t_2;
	} else if (t <= -1.15e-57) {
		tmp = y + x;
	} else if (t <= 3.6e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.4e-60) {
		tmp = t_2;
	} else if (t <= 1250000000.0) {
		tmp = t_1;
	} else if (t <= 8.4e+160) {
		tmp = t_2;
	} else if (t <= 8.5e+160) {
		tmp = t_1;
	} else {
		tmp = y + 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = x - (y / (t / z))
    if (t <= (-9d+138)) then
        tmp = y + x
    else if (t <= (-5.1d-52)) then
        tmp = t_2
    else if (t <= (-1.15d-57)) then
        tmp = y + x
    else if (t <= 3.6d-100) then
        tmp = x + (z * (y / a))
    else if (t <= 5.4d-60) then
        tmp = t_2
    else if (t <= 1250000000.0d0) then
        tmp = t_1
    else if (t <= 8.4d+160) then
        tmp = t_2
    else if (t <= 8.5d+160) then
        tmp = t_1
    else
        tmp = y + x
    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));
	double t_2 = x - (y / (t / z));
	double tmp;
	if (t <= -9e+138) {
		tmp = y + x;
	} else if (t <= -5.1e-52) {
		tmp = t_2;
	} else if (t <= -1.15e-57) {
		tmp = y + x;
	} else if (t <= 3.6e-100) {
		tmp = x + (z * (y / a));
	} else if (t <= 5.4e-60) {
		tmp = t_2;
	} else if (t <= 1250000000.0) {
		tmp = t_1;
	} else if (t <= 8.4e+160) {
		tmp = t_2;
	} else if (t <= 8.5e+160) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = x - (y / (t / z))
	tmp = 0
	if t <= -9e+138:
		tmp = y + x
	elif t <= -5.1e-52:
		tmp = t_2
	elif t <= -1.15e-57:
		tmp = y + x
	elif t <= 3.6e-100:
		tmp = x + (z * (y / a))
	elif t <= 5.4e-60:
		tmp = t_2
	elif t <= 1250000000.0:
		tmp = t_1
	elif t <= 8.4e+160:
		tmp = t_2
	elif t <= 8.5e+160:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(x - Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -9e+138)
		tmp = Float64(y + x);
	elseif (t <= -5.1e-52)
		tmp = t_2;
	elseif (t <= -1.15e-57)
		tmp = Float64(y + x);
	elseif (t <= 3.6e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 5.4e-60)
		tmp = t_2;
	elseif (t <= 1250000000.0)
		tmp = t_1;
	elseif (t <= 8.4e+160)
		tmp = t_2;
	elseif (t <= 8.5e+160)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = x - (y / (t / z));
	tmp = 0.0;
	if (t <= -9e+138)
		tmp = y + x;
	elseif (t <= -5.1e-52)
		tmp = t_2;
	elseif (t <= -1.15e-57)
		tmp = y + x;
	elseif (t <= 3.6e-100)
		tmp = x + (z * (y / a));
	elseif (t <= 5.4e-60)
		tmp = t_2;
	elseif (t <= 1250000000.0)
		tmp = t_1;
	elseif (t <= 8.4e+160)
		tmp = t_2;
	elseif (t <= 8.5e+160)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+138], N[(y + x), $MachinePrecision], If[LessEqual[t, -5.1e-52], t$95$2, If[LessEqual[t, -1.15e-57], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.6e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-60], t$95$2, If[LessEqual[t, 1250000000.0], t$95$1, If[LessEqual[t, 8.4e+160], t$95$2, If[LessEqual[t, 8.5e+160], t$95$1, N[(y + x), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.99999999999999963e138 or -5.09999999999999989e-52 < t < -1.15e-57 or 8.49999999999999982e160 < t

   1. Initial program 63.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 85.9%

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

      1. +-commutative 85.9%

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

   7. Simplified 85.9%

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

   if -8.99999999999999963e138 < t < -5.09999999999999989e-52 or 3.5999999999999999e-100 < t < 5.40000000000000001e-60 or 1.25e9 < t < 8.39999999999999987e160

   1. Initial program 90.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 80.4%

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

   8. Taylor expanded in a around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

      3. associate-/l* 72.9%

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

   10. Simplified 72.9%

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

   if -1.15e-57 < t < 3.5999999999999999e-100

   1. Initial program 94.4%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 90.5%

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

      3. clear-num 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r/ 84.6%

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

   9. Simplified 84.6%

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

   if 5.40000000000000001e-60 < t < 1.25e9 or 8.39999999999999987e160 < t < 8.49999999999999982e160

   1. Initial program 91.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 74.0%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+138}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-57}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1250000000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+160}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+160}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-54} \lor \neg \left(t \leq 4.4 \cdot 10^{-100} \lor \neg \left(t \leq 1.25 \cdot 10^{-27}\right) \land t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.6e-54)
         (not
          (or (<= t 4.4e-100) (and (not (<= t 1.25e-27)) (<= t 7.5e+122)))))
   (+ y x)
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e-54) || !((t <= 4.4e-100) || (!(t <= 1.25e-27) && (t <= 7.5e+122)))) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.6d-54)) .or. (.not. (t <= 4.4d-100) .or. (.not. (t <= 1.25d-27)) .and. (t <= 7.5d+122))) then
        tmp = y + x
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e-54) || !((t <= 4.4e-100) || (!(t <= 1.25e-27) && (t <= 7.5e+122)))) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.6e-54) or not ((t <= 4.4e-100) or (not (t <= 1.25e-27) and (t <= 7.5e+122))):
		tmp = y + x
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.6e-54) || !((t <= 4.4e-100) || (!(t <= 1.25e-27) && (t <= 7.5e+122))))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.6e-54) || ~(((t <= 4.4e-100) || (~((t <= 1.25e-27)) && (t <= 7.5e+122)))))
		tmp = y + x;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.6e-54], N[Not[Or[LessEqual[t, 4.4e-100], And[N[Not[LessEqual[t, 1.25e-27]], $MachinePrecision], LessEqual[t, 7.5e+122]]]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.59999999999999999e-54 or 4.39999999999999978e-100 < t < 1.25e-27 or 7.5000000000000002e122 < t

   1. Initial program 79.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.6%

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

      1. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -1.59999999999999999e-54 < t < 4.39999999999999978e-100 or 1.25e-27 < t < 7.5000000000000002e122

   1. Initial program 92.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. clear-num 93.3%

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

      2. associate-/r/ 92.6%

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

      3. clear-num 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in t around 0 78.8%

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

      1. associate-/r/ 80.7%

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

   9. Applied egg-rr 80.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-54} \lor \neg \left(t \leq 4.4 \cdot 10^{-100} \lor \neg \left(t \leq 1.25 \cdot 10^{-27}\right) \land t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-27} \lor \neg \left(t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-53)
   (+ y x)
   (if (<= t 4.4e-100)
     (+ x (* z (/ y a)))
     (if (or (<= t 1.12e-27) (not (<= t 7.5e+122)))
       (+ y x)
       (+ x (/ z (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y + x;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1.12e-27) || !(t <= 7.5e+122)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-53)) then
        tmp = y + x
    else if (t <= 4.4d-100) then
        tmp = x + (z * (y / a))
    else if ((t <= 1.12d-27) .or. (.not. (t <= 7.5d+122))) then
        tmp = y + x
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-53) {
		tmp = y + x;
	} else if (t <= 4.4e-100) {
		tmp = x + (z * (y / a));
	} else if ((t <= 1.12e-27) || !(t <= 7.5e+122)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-53:
		tmp = y + x
	elif t <= 4.4e-100:
		tmp = x + (z * (y / a))
	elif (t <= 1.12e-27) or not (t <= 7.5e+122):
		tmp = y + x
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-53)
		tmp = Float64(y + x);
	elseif (t <= 4.4e-100)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif ((t <= 1.12e-27) || !(t <= 7.5e+122))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-53)
		tmp = y + x;
	elseif (t <= 4.4e-100)
		tmp = x + (z * (y / a));
	elseif ((t <= 1.12e-27) || ~((t <= 7.5e+122)))
		tmp = y + x;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-53], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.4e-100], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.12e-27], N[Not[LessEqual[t, 7.5e+122]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e-53 or 4.39999999999999978e-100 < t < 1.1199999999999999e-27 or 7.5000000000000002e122 < t

   1. Initial program 79.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.6%

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

      1. +-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -1.1500000000000001e-53 < t < 4.39999999999999978e-100

   1. Initial program 94.4%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.4%

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

      2. associate-/r/ 90.5%

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

      3. clear-num 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in t around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r/ 84.6%

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

   9. Simplified 84.6%

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

   if 1.1199999999999999e-27 < t < 7.5000000000000002e122

   1. Initial program 87.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.6%

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

      3. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 64.0%

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

      1. associate-/r/ 67.4%

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

   9. Applied egg-rr 67.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-27} \lor \neg \left(t \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-113}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.75e-33)
   (+ x (/ z (/ a y)))
   (if (<= a -2.6e-113)
     (+ y x)
     (if (<= a 1.45e-41) (- x (/ z (/ t y))) (+ x (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.75e-33) {
		tmp = x + (z / (a / y));
	} else if (a <= -2.6e-113) {
		tmp = y + x;
	} else if (a <= 1.45e-41) {
		tmp = x - (z / (t / y));
	} else {
		tmp = x + (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 (a <= (-1.75d-33)) then
        tmp = x + (z / (a / y))
    else if (a <= (-2.6d-113)) then
        tmp = y + x
    else if (a <= 1.45d-41) then
        tmp = x - (z / (t / y))
    else
        tmp = x + (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 (a <= -1.75e-33) {
		tmp = x + (z / (a / y));
	} else if (a <= -2.6e-113) {
		tmp = y + x;
	} else if (a <= 1.45e-41) {
		tmp = x - (z / (t / y));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.75e-33:
		tmp = x + (z / (a / y))
	elif a <= -2.6e-113:
		tmp = y + x
	elif a <= 1.45e-41:
		tmp = x - (z / (t / y))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.75e-33)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (a <= -2.6e-113)
		tmp = Float64(y + x);
	elseif (a <= 1.45e-41)
		tmp = Float64(x - Float64(z / Float64(t / y)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.75e-33)
		tmp = x + (z / (a / y));
	elseif (a <= -2.6e-113)
		tmp = y + x;
	elseif (a <= 1.45e-41)
		tmp = x - (z / (t / y));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.75e-33], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-113], N[(y + x), $MachinePrecision], If[LessEqual[a, 1.45e-41], N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7499999999999999e-33

   1. Initial program 83.2%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.5%

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

      2. associate-/r/ 95.6%

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

      3. clear-num 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in t around 0 70.1%

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

      1. associate-/r/ 71.8%

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

   9. Applied egg-rr 71.8%

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

   if -1.7499999999999999e-33 < a < -2.5999999999999999e-113

   1. Initial program 85.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 66.2%

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

      1. +-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -2.5999999999999999e-113 < a < 1.44999999999999989e-41

   1. Initial program 90.6%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around inf 82.0%

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

      1. associate-*l/ 81.1%

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

      2. *-commutative 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in a around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/l* 73.7%

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

   10. Simplified 73.7%

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

   if 1.44999999999999989e-41 < a

   1. Initial program 83.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.7%

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

      3. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 76.4%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-113}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+139} \lor \neg \left(t \leq 8.1 \cdot 10^{+192}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7e+139) (not (<= t 8.1e+192)))
   (+ y x)
   (+ x (* (/ y (- a t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+139) || !(t <= 8.1e+192)) {
		tmp = y + x;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7d+139)) .or. (.not. (t <= 8.1d+192))) then
        tmp = y + x
    else
        tmp = x + ((y / (a - t)) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7e+139) || !(t <= 8.1e+192)) {
		tmp = y + x;
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7e+139) or not (t <= 8.1e+192):
		tmp = y + x
	else:
		tmp = x + ((y / (a - t)) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7e+139) || !(t <= 8.1e+192))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7e+139) || ~((t <= 8.1e+192)))
		tmp = y + x;
	else
		tmp = x + ((y / (a - t)) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7e+139], N[Not[LessEqual[t, 8.1e+192]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999957e139 or 8.10000000000000019e192 < t

   1. Initial program 59.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 88.1%

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

      1. +-commutative 88.1%

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

   7. Simplified 88.1%

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

   if -6.99999999999999957e139 < t < 8.10000000000000019e192

   1. Initial program 92.3%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+139} \lor \neg \left(t \leq 8.1 \cdot 10^{+192}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56} \lor \neg \left(t \leq 6 \cdot 10^{+75}\right):\\ \;\;\;\;y + \left(x - \frac{z}{\frac{t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e-56) (not (<= t 6e+75)))
   (+ y (- x (/ z (/ t y))))
   (+ x (* (/ y (- a t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-56) || !(t <= 6e+75)) {
		tmp = y + (x - (z / (t / y)));
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.5d-56)) .or. (.not. (t <= 6d+75))) then
        tmp = y + (x - (z / (t / y)))
    else
        tmp = x + ((y / (a - t)) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-56) || !(t <= 6e+75)) {
		tmp = y + (x - (z / (t / y)));
	} else {
		tmp = x + ((y / (a - t)) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e-56) or not (t <= 6e+75):
		tmp = y + (x - (z / (t / y)))
	else:
		tmp = x + ((y / (a - t)) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e-56) || !(t <= 6e+75))
		tmp = Float64(y + Float64(x - Float64(z / Float64(t / y))));
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e-56) || ~((t <= 6e+75)))
		tmp = y + (x - (z / (t / y)));
	else
		tmp = x + ((y / (a - t)) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e-56], N[Not[LessEqual[t, 6e+75]], $MachinePrecision]], N[(y + N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999991e-56 or 6e75 < t

   1. Initial program 76.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-/l* 84.0%

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

   9. Simplified 84.0%

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

   10. Taylor expanded in z around 0 80.5%

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

       1. cancel-sign-sub-inv 80.5%

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

       2. associate-*r/ 80.5%

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

       3. *-commutative 80.5%

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

       4. neg-mul-1 80.5%

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

       5. distribute-neg-frac 80.5%

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

       6. sub-neg 80.5%

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

       7. associate-/l* 85.1%

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

       8. metadata-eval 85.1%

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

       9. *-lft-identity 85.1%

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

   12. Simplified 85.1%

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

   if -9.4999999999999991e-56 < t < 6e75

   1. Initial program 93.6%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 89.0%

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

      2. *-commutative 89.0%

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

   7. Simplified 89.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-56} \lor \neg \left(t \leq 6 \cdot 10^{+75}\right):\\ \;\;\;\;y + \left(x - \frac{z}{\frac{t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.098 \lor \neg \left(z \leq 7.5 \cdot 10^{-74}\right):\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.098) (not (<= z 7.5e-74)))
   (+ x (* (/ y (- a t)) z))
   (- x (/ y (+ (/ a t) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.098) || !(z <= 7.5e-74)) {
		tmp = x + ((y / (a - t)) * z);
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.098d0)) .or. (.not. (z <= 7.5d-74))) then
        tmp = x + ((y / (a - t)) * z)
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.098) || !(z <= 7.5e-74)) {
		tmp = x + ((y / (a - t)) * z);
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.098) or not (z <= 7.5e-74):
		tmp = x + ((y / (a - t)) * z)
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.098) || !(z <= 7.5e-74))
		tmp = Float64(x + Float64(Float64(y / Float64(a - t)) * z));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.098) || ~((z <= 7.5e-74)))
		tmp = x + ((y / (a - t)) * z);
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.098], N[Not[LessEqual[z, 7.5e-74]], $MachinePrecision]], N[(x + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.098000000000000004 or 7.5e-74 < z

   1. Initial program 82.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 81.5%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   7. Simplified 88.8%

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

   if -0.098000000000000004 < z < 7.5e-74

   1. Initial program 90.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 97.3%

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

      3. clear-num 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. *-commutative 86.2%

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

      4. associate-/l* 93.7%

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

   9. Simplified 93.7%

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

   10. Taylor expanded in a around 0 93.7%

       \[\leadsto x - \frac{y}{\color{blue}{\frac{a}{t} - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.098 \lor \neg \left(z \leq 7.5 \cdot 10^{-74}\right):\\ \;\;\;\;x + \frac{y}{a - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-53} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e-53) (not (<= t 8.5e+160))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e-53) || !(t <= 8.5e+160)) {
		tmp = y + x;
	} else {
		tmp = x + (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 <= (-1.1d-53)) .or. (.not. (t <= 8.5d+160))) then
        tmp = y + x
    else
        tmp = x + (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 <= -1.1e-53) || !(t <= 8.5e+160)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e-53) or not (t <= 8.5e+160):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e-53) || !(t <= 8.5e+160))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e-53) || ~((t <= 8.5e+160)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e-53], N[Not[LessEqual[t, 8.5e+160]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000009e-53 or 8.49999999999999982e160 < t

   1. Initial program 75.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. +-commutative 73.2%

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

   7. Simplified 73.2%

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

   if -1.10000000000000009e-53 < t < 8.49999999999999982e160

   1. Initial program 92.9%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 93.9%

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

      3. clear-num 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in t around 0 75.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-53} \lor \neg \left(t \leq 8.5 \cdot 10^{+160}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-92} \lor \neg \left(t \leq 1.15 \cdot 10^{-89}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-92) (not (<= t 1.15e-89))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-92) || !(t <= 1.15e-89)) {
		tmp = y + 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 ((t <= (-1.45d-92)) .or. (.not. (t <= 1.15d-89))) then
        tmp = y + 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 ((t <= -1.45e-92) || !(t <= 1.15e-89)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-92) or not (t <= 1.15e-89):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-92) || !(t <= 1.15e-89))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e-92) || ~((t <= 1.15e-89)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-92], N[Not[LessEqual[t, 1.15e-89]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999992e-92 or 1.15e-89 < t

   1. Initial program 81.2%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

   7. Simplified 66.6%

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

   if -1.44999999999999992e-92 < t < 1.15e-89

   1. Initial program 95.0%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 57.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-92} \lor \neg \left(t \leq 1.15 \cdot 10^{-89}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

   1. clear-num 96.4%

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

   2. associate-/r/ 96.1%

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

   3. clear-num 96.2%

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

6. Applied egg-rr 96.2%

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

7. Final simplification 96.2%

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

Alternative 13: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 14: 51.6% 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 86.3%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in x around inf 52.2%

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

6. Final simplification 52.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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