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

Percentage Accurate: 98.2% → 98.3%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

Specification

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]

Initial Program: 98.2% 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]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. clear-num 98.4%

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

   2. un-div-inv 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

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

Alternative 2: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-98}:\\ \;\;\;\;x - z \cdot \left(y \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+15)
   (+ x y)
   (if (<= t 1.8e-98)
     (- x (* z (* y (/ -1.0 a))))
     (if (<= t 3.6e+171) (- x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+15) {
		tmp = x + y;
	} else if (t <= 1.8e-98) {
		tmp = x - (z * (y * (-1.0 / a)));
	} else if (t <= 3.6e+171) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + 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 <= (-3d+15)) then
        tmp = x + y
    else if (t <= 1.8d-98) then
        tmp = x - (z * (y * ((-1.0d0) / a)))
    else if (t <= 3.6d+171) then
        tmp = x - (z * (y / t))
    else
        tmp = x + 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 <= -3e+15) {
		tmp = x + y;
	} else if (t <= 1.8e-98) {
		tmp = x - (z * (y * (-1.0 / a)));
	} else if (t <= 3.6e+171) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+15:
		tmp = x + y
	elif t <= 1.8e-98:
		tmp = x - (z * (y * (-1.0 / a)))
	elif t <= 3.6e+171:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+15)
		tmp = Float64(x + y);
	elseif (t <= 1.8e-98)
		tmp = Float64(x - Float64(z * Float64(y * Float64(-1.0 / a))));
	elseif (t <= 3.6e+171)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+15)
		tmp = x + y;
	elseif (t <= 1.8e-98)
		tmp = x - (z * (y * (-1.0 / a)));
	elseif (t <= 3.6e+171)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+15], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.8e-98], N[(x - N[(z * N[(y * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+171], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e15 or 3.60000000000000018e171 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

   5. Simplified 87.9%

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

   if -3e15 < t < 1.8000000000000001e-98

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 80.0%

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

      1. div-inv 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*l* 83.7%

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

   5. Applied egg-rr 83.7%

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

   if 1.8000000000000001e-98 < t < 3.60000000000000018e171

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 83.3%

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

      4. div-sub 83.3%

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

      5. sub-neg 83.3%

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

      6. *-inverses 83.3%

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

      7. metadata-eval 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 75.9%

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

   8. Applied egg-rr 75.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-98}:\\ \;\;\;\;x - z \cdot \left(y \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+171}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+18)
   (+ x y)
   (if (<= t 1.55e-98)
     (+ x (/ y (/ a z)))
     (if (<= t 3.5e+171) (- x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+18) {
		tmp = x + y;
	} else if (t <= 1.55e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.5e+171) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + 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 <= (-7.6d+18)) then
        tmp = x + y
    else if (t <= 1.55d-98) then
        tmp = x + (y / (a / z))
    else if (t <= 3.5d+171) then
        tmp = x - (z * (y / t))
    else
        tmp = x + 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 <= -7.6e+18) {
		tmp = x + y;
	} else if (t <= 1.55e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.5e+171) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.6e+18:
		tmp = x + y
	elif t <= 1.55e-98:
		tmp = x + (y / (a / z))
	elif t <= 3.5e+171:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+18)
		tmp = Float64(x + y);
	elseif (t <= 1.55e-98)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 3.5e+171)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.6e+18)
		tmp = x + y;
	elseif (t <= 1.55e-98)
		tmp = x + (y / (a / z));
	elseif (t <= 3.5e+171)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+18], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.55e-98], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+171], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.6e18 or 3.4999999999999999e171 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

   5. Simplified 87.9%

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

   if -7.6e18 < t < 1.55e-98

   1. Initial program 96.4%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in t around 0 83.1%

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

   if 1.55e-98 < t < 3.4999999999999999e171

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

      3. associate-/l* 83.3%

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

      4. div-sub 83.3%

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

      5. sub-neg 83.3%

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

      6. *-inverses 83.3%

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

      7. metadata-eval 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 75.9%

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

   8. Applied egg-rr 75.9%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+171}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6800:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+16)
   (+ x y)
   (if (<= t 1.55e-98)
     (+ x (/ y (/ a z)))
     (if (<= t 6800.0) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+16) {
		tmp = x + y;
	} else if (t <= 1.55e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 6800.0) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + 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 <= (-1.95d+16)) then
        tmp = x + y
    else if (t <= 1.55d-98) then
        tmp = x + (y / (a / z))
    else if (t <= 6800.0d0) then
        tmp = x - (y * (z / t))
    else
        tmp = x + 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 <= -1.95e+16) {
		tmp = x + y;
	} else if (t <= 1.55e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 6800.0) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+16:
		tmp = x + y
	elif t <= 1.55e-98:
		tmp = x + (y / (a / z))
	elif t <= 6800.0:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+16)
		tmp = Float64(x + y);
	elseif (t <= 1.55e-98)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 6800.0)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+16)
		tmp = x + y;
	elseif (t <= 1.55e-98)
		tmp = x + (y / (a / z));
	elseif (t <= 6800.0)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+16], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.55e-98], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6800.0], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.95e16 or 6800 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.7%

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

      1. +-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -1.95e16 < t < 1.55e-98

   1. Initial program 96.4%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in t around 0 83.1%

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

   if 1.55e-98 < t < 6800

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 96.4%

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

   4. Taylor expanded in a around 0 87.1%

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

      1. mul-1-neg 87.1%

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

      2. associate-/l* 87.1%

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

      3. *-commutative 87.1%

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

      4. unsub-neg 87.1%

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

      5. *-commutative 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+16}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6800:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+54} \lor \neg \left(t \leq 9 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e+54) (not (<= t 9e+61)))
   (+ x (/ y (/ t (- t z))))
   (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+54) || !(t <= 9e+61)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + ((y * z) / (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 ((t <= (-7.5d+54)) .or. (.not. (t <= 9d+61))) then
        tmp = x + (y / (t / (t - z)))
    else
        tmp = x + ((y * z) / (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 ((t <= -7.5e+54) || !(t <= 9e+61)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e+54) or not (t <= 9e+61):
		tmp = x + (y / (t / (t - z)))
	else:
		tmp = x + ((y * z) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e+54) || !(t <= 9e+61))
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e+54) || ~((t <= 9e+61)))
		tmp = x + (y / (t / (t - z)));
	else
		tmp = x + ((y * z) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e+54], N[Not[LessEqual[t, 9e+61]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000042e54 or 9e61 < t

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 91.1%

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

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac2 91.1%

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

   7. Simplified 91.1%

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

      1. distribute-frac-neg2 91.1%

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

      2. neg-sub0 91.1%

         \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]

   9. Applied egg-rr 91.1%

      \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]
   10. Step-by-step derivation

       1. neg-sub0 91.1%

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

       2. distribute-neg-frac2 91.1%

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

       3. sub-neg 91.1%

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

       4. distribute-neg-in 91.1%

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

       5. remove-double-neg 91.1%

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

       6. +-commutative 91.1%

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

       7. sub-neg 91.1%

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

   11. Simplified 91.1%

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

   if -7.50000000000000042e54 < t < 9e61

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 88.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+54} \lor \neg \left(t \leq 9 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-109} \lor \neg \left(t \leq 1.6 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(y \cdot \frac{-1}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e-109) (not (<= t 1.6e-98)))
   (+ x (/ y (/ t (- t z))))
   (- x (* z (* y (/ -1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e-109) || !(t <= 1.6e-98)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x - (z * (y * (-1.0 / 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 <= (-2.7d-109)) .or. (.not. (t <= 1.6d-98))) then
        tmp = x + (y / (t / (t - z)))
    else
        tmp = x - (z * (y * ((-1.0d0) / 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 <= -2.7e-109) || !(t <= 1.6e-98)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x - (z * (y * (-1.0 / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e-109) or not (t <= 1.6e-98):
		tmp = x + (y / (t / (t - z)))
	else:
		tmp = x - (z * (y * (-1.0 / a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e-109) || !(t <= 1.6e-98))
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	else
		tmp = Float64(x - Float64(z * Float64(y * Float64(-1.0 / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.7e-109) || ~((t <= 1.6e-98)))
		tmp = x + (y / (t / (t - z)));
	else
		tmp = x - (z * (y * (-1.0 / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e-109], N[Not[LessEqual[t, 1.6e-98]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e-109 or 1.6e-98 < t

   1. Initial program 99.0%

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

      1. clear-num 98.9%

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

      2. un-div-inv 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in a around 0 85.4%

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

      1. neg-mul-1 85.4%

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

      2. distribute-neg-frac2 85.4%

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

   7. Simplified 85.4%

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

      1. distribute-frac-neg2 85.4%

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

      2. neg-sub0 85.4%

         \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]

   9. Applied egg-rr 85.4%

      \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]
   10. Step-by-step derivation

       1. neg-sub0 85.4%

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

       2. distribute-neg-frac2 85.4%

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

       3. sub-neg 85.4%

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

       4. distribute-neg-in 85.4%

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

       5. remove-double-neg 85.4%

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

       6. +-commutative 85.4%

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

       7. sub-neg 85.4%

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

   11. Simplified 85.4%

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

   if -2.7e-109 < t < 1.6e-98

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. div-inv 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*l* 89.9%

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

   5. Applied egg-rr 89.9%

      \[\leadsto x + \color{blue}{z \cdot \left(y \cdot \frac{1}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-109} \lor \neg \left(t \leq 1.6 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(y \cdot \frac{-1}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7800000:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7800000.0)
   (+ x (* y (/ t (- t a))))
   (if (<= t 1.32e+62) (+ x (/ (* y z) (- a t))) (+ x (- y (* z (/ y t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7800000.0) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 1.32e+62) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y - (z * (y / 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 (t <= (-7800000.0d0)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 1.32d+62) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y - (z * (y / 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 (t <= -7800000.0) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 1.32e+62) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y - (z * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7800000.0:
		tmp = x + (y * (t / (t - a)))
	elif t <= 1.32e+62:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y - (z * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7800000.0)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 1.32e+62)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7800000.0)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 1.32e+62)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y - (z * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7800000.0], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+62], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

   if -7.8e6 < t < 1.3199999999999999e62

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 89.4%

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

   if 1.3199999999999999e62 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

      3. associate-/l* 90.0%

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

      4. div-sub 90.0%

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

      5. sub-neg 90.0%

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

      6. *-inverses 90.0%

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

      7. metadata-eval 90.0%

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

   5. Simplified 90.0%

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

      1. distribute-lft-in 90.0%

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

      2. clear-num 90.0%

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

      3. un-div-inv 90.1%

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

   7. Applied egg-rr 90.1%

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

      1. *-commutative 90.1%

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

      2. neg-mul-1 90.1%

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

      3. unsub-neg 90.1%

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

      4. associate-/r/ 91.9%

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

   9. Simplified 91.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7800000:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1020000:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1020000.0)
   (+ x (* y (/ t (- t a))))
   (if (<= t 9e+61) (+ x (/ (* y z) (- a t))) (+ x (/ y (/ t (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1020000.0) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9e+61) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y / (t / (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 <= (-1020000.0d0)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 9d+61) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y / (t / (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 <= -1020000.0) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 9e+61) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y / (t / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1020000.0:
		tmp = x + (y * (t / (t - a)))
	elif t <= 9e+61:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y / (t / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1020000.0)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 9e+61)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1020000.0)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 9e+61)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y / (t / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1020000.0], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+61], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 92.7%

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

   5. Simplified 92.7%

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

   if -1.02e6 < t < 9e61

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 89.4%

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

   if 9e61 < t

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 90.1%

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

      1. neg-mul-1 90.1%

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

      2. distribute-neg-frac2 90.1%

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

   7. Simplified 90.1%

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

      1. distribute-frac-neg2 90.1%

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

      2. neg-sub0 90.1%

         \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]

   9. Applied egg-rr 90.1%

      \[\leadsto x + \frac{y}{\color{blue}{0 - \frac{t}{z - t}}} \]
   10. Step-by-step derivation

       1. neg-sub0 90.1%

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

       2. distribute-neg-frac2 90.1%

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

       3. sub-neg 90.1%

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

       4. distribute-neg-in 90.1%

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

       5. remove-double-neg 90.1%

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

       6. +-commutative 90.1%

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

       7. sub-neg 90.1%

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

   11. Simplified 90.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1020000:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+61}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+15} \lor \neg \left(t \leq 2.4 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.65e+15) (not (<= t 2.4e-15))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.65e+15) || !(t <= 2.4e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (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 <= (-2.65d+15)) .or. (.not. (t <= 2.4d-15))) then
        tmp = x + y
    else
        tmp = x + (y / (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 <= -2.65e+15) || !(t <= 2.4e-15)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.65e+15) or not (t <= 2.4e-15):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.65e+15) || !(t <= 2.4e-15))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.65e+15) || ~((t <= 2.4e-15)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.65e+15], N[Not[LessEqual[t, 2.4e-15]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.65e15 or 2.39999999999999995e-15 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t 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 -2.65e15 < t < 2.39999999999999995e-15

   1. Initial program 96.9%

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

      1. clear-num 96.7%

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

      2. un-div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around 0 79.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+15} \lor \neg \left(t \leq 2.4 \cdot 10^{-15}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.2% 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 98.5%

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

Alternative 11: 61.4% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

3. Taylor expanded in t around inf 64.4%

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

   1. +-commutative 64.4%

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

5. Simplified 64.4%

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

6. Final simplification 64.4%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 12: 50.8% 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 98.5%

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

3. Taylor expanded in x around inf 52.8%

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

Developer target: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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