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

Percentage Accurate: 85.4% → 98.2%

Time: 11.0s

Alternatives: 12

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: 85.4% 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: 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 85.8%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

Alternative 2: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+134}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+117)
   (+ x y)
   (if (<= t 1.05e-88)
     (+ x (* z (/ y a)))
     (if (<= t 3.1e+134) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+117) {
		tmp = x + y;
	} else if (t <= 1.05e-88) {
		tmp = x + (z * (y / a));
	} else if (t <= 3.1e+134) {
		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 <= (-6.5d+117)) then
        tmp = x + y
    else if (t <= 1.05d-88) then
        tmp = x + (z * (y / a))
    else if (t <= 3.1d+134) 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 <= -6.5e+117) {
		tmp = x + y;
	} else if (t <= 1.05e-88) {
		tmp = x + (z * (y / a));
	} else if (t <= 3.1e+134) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+117:
		tmp = x + y
	elif t <= 1.05e-88:
		tmp = x + (z * (y / a))
	elif t <= 3.1e+134:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+117)
		tmp = Float64(x + y);
	elseif (t <= 1.05e-88)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 3.1e+134)
		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 <= -6.5e+117)
		tmp = x + y;
	elseif (t <= 1.05e-88)
		tmp = x + (z * (y / a));
	elseif (t <= 3.1e+134)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+117], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.05e-88], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+134], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000004e117 or 3.09999999999999982e134 < t

   1. Initial program 63.7%

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

      1. +-commutative 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-/l* 90.1%

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

      4. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in t around inf 81.8%

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

      1. +-commutative 81.8%

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

   7. Simplified 81.8%

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

   if -6.5000000000000004e117 < t < 1.05e-88

   1. Initial program 93.9%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around 0 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if 1.05e-88 < t < 3.09999999999999982e134

   1. Initial program 97.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 90.2%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. associate-/l* 83.5%

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

   8. Simplified 83.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+134}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+128} \lor \neg \left(t \leq 1.4 \cdot 10^{+38}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+128) (not (<= t 1.4e+38)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+128) || !(t <= 1.4e+38)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.3d+128)) .or. (.not. (t <= 1.4d+38))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+128) || !(t <= 1.4e+38)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+128) or not (t <= 1.4e+38):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+128) || !(t <= 1.4e+38))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+128) || ~((t <= 1.4e+38)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+128], N[Not[LessEqual[t, 1.4e+38]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3000000000000001e128 or 1.4e38 < t

   1. Initial program 69.6%

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

      1. +-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 91.4%

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

      4. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. unsub-neg 66.2%

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

      3. associate-/l* 93.8%

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

      4. div-sub 93.8%

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

      5. sub-neg 93.8%

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

      6. *-inverses 93.8%

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

      7. metadata-eval 93.8%

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

   7. Simplified 93.8%

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

   if -3.3000000000000001e128 < t < 1.4e38

   1. Initial program 93.8%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-/l* 90.9%

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

   7. Applied egg-rr 90.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+128} \lor \neg \left(t \leq 1.4 \cdot 10^{+38}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+193} \lor \neg \left(t \leq 5.7 \cdot 10^{+134}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+193) (not (<= t 5.7e+134)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+193) || !(t <= 5.7e+134)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d+193)) .or. (.not. (t <= 5.7d+134))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+193) || !(t <= 5.7e+134)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+193) or not (t <= 5.7e+134):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+193) || !(t <= 5.7e+134))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+193) || ~((t <= 5.7e+134)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+193], N[Not[LessEqual[t, 5.7e+134]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8e193 or 5.70000000000000038e134 < t

   1. Initial program 61.5%

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

      1. +-commutative 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-/l* 91.0%

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

      4. fma-define 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   if -4.8e193 < t < 5.70000000000000038e134

   1. Initial program 93.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/l* 88.2%

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

   7. Applied egg-rr 88.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+193} \lor \neg \left(t \leq 5.7 \cdot 10^{+134}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+123)
   (+ x (* y (/ t (- t a))))
   (if (<= t 2.95e+38) (+ x (* z (/ y (- a t)))) (+ x (* y (- 1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+123) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 2.95e+38) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (1.0 - (z / 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 <= (-9d+123)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 2.95d+38) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y * (1.0d0 - (z / 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 <= -9e+123) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 2.95e+38) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (1.0 - (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+123:
		tmp = x + (y * (t / (t - a)))
	elif t <= 2.95e+38:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y * (1.0 - (z / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+123)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 2.95e+38)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+123)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 2.95e+38)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y * (1.0 - (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+123], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+38], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999965e123

   1. Initial program 62.3%

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

      1. +-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-/l* 93.5%

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

      4. fma-define 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

      3. *-commutative 59.2%

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

      4. *-lft-identity 59.2%

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

      5. times-frac 88.0%

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

      6. /-rgt-identity 88.0%

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

   7. Simplified 88.0%

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

   if -8.99999999999999965e123 < t < 2.94999999999999991e38

   1. Initial program 94.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-/l* 91.4%

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

   7. Applied egg-rr 91.4%

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

   if 2.94999999999999991e38 < t

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 90.3%

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

      4. fma-define 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in a around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

      3. associate-/l* 96.3%

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

      4. div-sub 96.3%

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

      5. sub-neg 96.3%

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

      6. *-inverses 96.3%

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

      7. metadata-eval 96.3%

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

   7. Simplified 96.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+117} \lor \neg \left(t \leq 9.5 \cdot 10^{+36}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.45e+117) (not (<= t 9.5e+36))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+117) || !(t <= 9.5e+36)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.45d+117)) .or. (.not. (t <= 9.5d+36))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+117) || !(t <= 9.5e+36)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.45e+117) or not (t <= 9.5e+36):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.45e+117) || !(t <= 9.5e+36))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.45e+117) || ~((t <= 9.5e+36)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.45e+117], N[Not[LessEqual[t, 9.5e+36]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.45e117 or 9.49999999999999974e36 < t

   1. Initial program 68.1%

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

      1. +-commutative 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-/l* 91.6%

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

      4. fma-define 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around inf 79.0%

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

      1. +-commutative 79.0%

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

   7. Simplified 79.0%

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

   if -2.45e117 < t < 9.49999999999999974e36

   1. Initial program 94.8%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-/l* 74.8%

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

   7. Applied egg-rr 74.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+117} \lor \neg \left(t \leq 9.5 \cdot 10^{+36}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+56} \lor \neg \left(y \leq 1.15 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.4e+56) (not (<= y 1.15e+121)))
   (* y (- 1.0 (/ z t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.4e+56) || !(y <= 1.15e+121)) {
		tmp = y * (1.0 - (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 ((y <= (-3.4d+56)) .or. (.not. (y <= 1.15d+121))) then
        tmp = y * (1.0d0 - (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 ((y <= -3.4e+56) || !(y <= 1.15e+121)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.4e+56) or not (y <= 1.15e+121):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.4e+56) || !(y <= 1.15e+121))
		tmp = Float64(y * Float64(1.0 - 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 ((y <= -3.4e+56) || ~((y <= 1.15e+121)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.4e+56], N[Not[LessEqual[y, 1.15e+121]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000001e56 or 1.1499999999999999e121 < y

   1. Initial program 69.8%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in a around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. unsub-neg 41.2%

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

      3. associate-/l* 60.5%

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

      4. div-sub 60.5%

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

      5. *-inverses 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in x around 0 52.0%

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

       1. sub-neg 52.0%

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

       2. metadata-eval 52.0%

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

       3. neg-mul-1 52.0%

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

       4. distribute-rgt-neg-out 52.0%

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

       5. +-commutative 52.0%

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

       6. distribute-neg-in 52.0%

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

       7. metadata-eval 52.0%

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

       8. sub-neg 52.0%

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

   12. Simplified 52.0%

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

   if -3.40000000000000001e56 < y < 1.1499999999999999e121

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-/l* 94.1%

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

      4. fma-define 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 69.4%

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

      1. +-commutative 69.4%

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

   7. Simplified 69.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+56} \lor \neg \left(y \leq 1.15 \cdot 10^{+121}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+121) (not (<= z 5e+223))) (/ (* y (- z)) t) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+121) || !(z <= 5e+223)) {
		tmp = (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 ((z <= (-1.35d+121)) .or. (.not. (z <= 5d+223))) then
        tmp = (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 ((z <= -1.35e+121) || !(z <= 5e+223)) {
		tmp = (y * -z) / t;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+121) or not (z <= 5e+223):
		tmp = (y * -z) / t
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+121) || !(z <= 5e+223))
		tmp = Float64(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 ((z <= -1.35e+121) || ~((z <= 5e+223)))
		tmp = (y * -z) / t;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+121], N[Not[LessEqual[z, 5e+223]], $MachinePrecision]], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e121 or 4.99999999999999985e223 < z

   1. Initial program 84.2%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   9. Simplified 62.0%

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

   10. Taylor expanded in z around inf 49.5%

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

       1. associate-*r/ 49.5%

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

       2. neg-mul-1 49.5%

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

       3. distribute-rgt-neg-in 49.5%

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

   12. Simplified 49.5%

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

   if -1.3500000000000001e121 < z < 4.99999999999999985e223

   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. *-commutative 86.3%

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

      3. associate-/l* 96.2%

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

      4. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

   7. Simplified 63.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 1.95 \cdot 10^{+226}\right):\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+121) (not (<= z 1.95e+226))) (* y (/ z (- t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+121) || !(z <= 1.95e+226)) {
		tmp = 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 ((z <= (-1.35d+121)) .or. (.not. (z <= 1.95d+226))) then
        tmp = 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 ((z <= -1.35e+121) || !(z <= 1.95e+226)) {
		tmp = y * (z / -t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+121) or not (z <= 1.95e+226):
		tmp = y * (z / -t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+121) || !(z <= 1.95e+226))
		tmp = Float64(y * Float64(z / Float64(-t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+121) || ~((z <= 1.95e+226)))
		tmp = y * (z / -t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+121], N[Not[LessEqual[z, 1.95e+226]], $MachinePrecision]], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e121 or 1.94999999999999992e226 < z

   1. Initial program 84.2%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   9. Simplified 62.0%

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

   10. Taylor expanded in z around inf 49.5%

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

       1. mul-1-neg 49.5%

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

       2. associate-*r/ 49.4%

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

       3. distribute-rgt-neg-in 49.4%

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

       4. distribute-frac-neg2 49.4%

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

   12. Simplified 49.4%

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

   if -1.3500000000000001e121 < z < 1.94999999999999992e226

   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. *-commutative 86.3%

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

      3. associate-/l* 96.2%

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

      4. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

   7. Simplified 63.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 1.95 \cdot 10^{+226}\right):\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -5.6e+95) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+95) {
		tmp = x;
	} 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 (a <= (-5.6d+95)) then
        tmp = x
    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 (a <= -5.6e+95) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e+95:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e+95)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e+95)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e+95], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5999999999999995e95

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-/l* 95.9%

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

      4. fma-define 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 61.1%

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

   if -5.5999999999999995e95 < a

   1. Initial program 86.6%

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

      1. +-commutative 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-/l* 95.1%

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

      4. fma-define 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around inf 55.2%

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

      1. +-commutative 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.15 \cdot 10^{+268}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 1.15e+268) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.15e+268) {
		tmp = x;
	} else {
		tmp = 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+268) then
        tmp = x
    else
        tmp = 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+268) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.15e+268:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.15e+268)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.15e+268)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.15e+268], x, y]

Derivation

1. Split input into 2 regimes

2. if t < 1.15000000000000006e268

   1. Initial program 87.4%

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

      1. +-commutative 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 47.1%

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

   if 1.15000000000000006e268 < t

   1. Initial program 20.7%

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

      1. +-commutative 20.7%

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

      2. *-commutative 20.7%

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

      3. associate-/l* 86.4%

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

      4. fma-define 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

Alternative 12: 50.5% 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 85.8%

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

   1. +-commutative 85.8%

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

   2. *-commutative 85.8%

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

   3. associate-/l* 95.2%

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

   4. fma-define 95.2%

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

3. Simplified 95.2%

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

5. Taylor expanded in y around 0 46.1%

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

Developer Target 1: 98.4% 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 2024185 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- a t) (- z t)))))

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