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

Percentage Accurate: 85.7% → 98.4%

Time: 10.9s

Alternatives: 11

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: 85.7% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. clear-num 98.1%

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

   2. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Final simplification 98.2%

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

Alternative 2: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-20} \lor \neg \left(t \leq 3.05 \cdot 10^{+103}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e-20) (not (<= t 3.05e+103)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e-20) || !(t <= 3.05e+103)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9d-20)) .or. (.not. (t <= 3.05d+103))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e-20) || !(t <= 3.05e+103)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e-20) or not (t <= 3.05e+103):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e-20) || !(t <= 3.05e+103))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e-20) || ~((t <= 3.05e+103)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e-20], N[Not[LessEqual[t, 3.05e+103]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.0000000000000003e-20 or 3.0500000000000001e103 < t

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-/l* 94.4%

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

      4. fma-define 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in a around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

      3. associate-/l* 85.1%

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

      4. div-sub 85.1%

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

      5. sub-neg 85.1%

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

      6. *-inverses 85.1%

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

      7. metadata-eval 85.1%

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

   7. Simplified 85.1%

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

   if -9.0000000000000003e-20 < t < 3.0500000000000001e103

   1. Initial program 91.9%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

      1. clear-num 96.9%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around inf 87.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-20} \lor \neg \left(t \leq 3.05 \cdot 10^{+103}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111} \lor \neg \left(t \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.2e+111) (not (<= t 3.5e+113)))
   (+ x y)
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.2e+111) || !(t <= 3.5e+113)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.2d+111)) .or. (.not. (t <= 3.5d+113))) then
        tmp = x + y
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.2e+111) || !(t <= 3.5e+113)) {
		tmp = x + y;
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.2e+111) or not (t <= 3.5e+113):
		tmp = x + y
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.2e+111) || !(t <= 3.5e+113))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.2e+111) || ~((t <= 3.5e+113)))
		tmp = x + y;
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.2e+111], N[Not[LessEqual[t, 3.5e+113]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.20000000000000008e111 or 3.5000000000000001e113 < t

   1. Initial program 62.8%

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

      1. +-commutative 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-/l* 92.3%

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

      4. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. +-commutative 82.0%

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

   7. Simplified 82.0%

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

   if -9.20000000000000008e111 < t < 3.5000000000000001e113

   1. Initial program 92.6%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.3%

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

      2. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around inf 85.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+111} \lor \neg \left(t \leq 3.5 \cdot 10^{+113}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+108} \lor \neg \left(t \leq 3.3 \cdot 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e+108) (not (<= t 3.3e+111)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e+108) || !(t <= 3.3e+111)) {
		tmp = x + y;
	} 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 <= (-2.9d+108)) .or. (.not. (t <= 3.3d+111))) then
        tmp = x + y
    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 <= -2.9e+108) || !(t <= 3.3e+111)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9e+108) or not (t <= 3.3e+111):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e+108) || !(t <= 3.3e+111))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9e+108) || ~((t <= 3.3e+111)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e+108], N[Not[LessEqual[t, 3.3e+111]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000007e108 or 3.3000000000000001e111 < t

   1. Initial program 62.8%

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

      1. +-commutative 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-/l* 92.3%

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

      4. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. +-commutative 82.0%

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

   7. Simplified 82.0%

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

   if -2.90000000000000007e108 < t < 3.3000000000000001e111

   1. Initial program 92.6%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+108} \lor \neg \left(t \leq 3.3 \cdot 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+20)
   (+ x (/ z (/ (- a t) y)))
   (if (<= z 1.7e-68) (+ x (* y (/ t (- t a)))) (+ x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+20) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.7e-68) {
		tmp = x + (y * (t / (t - a)));
	} 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 (z <= (-8d+20)) then
        tmp = x + (z / ((a - t) / y))
    else if (z <= 1.7d-68) then
        tmp = x + (y * (t / (t - a)))
    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 (z <= -8e+20) {
		tmp = x + (z / ((a - t) / y));
	} else if (z <= 1.7e-68) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+20:
		tmp = x + (z / ((a - t) / y))
	elif z <= 1.7e-68:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+20)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (z <= 1.7e-68)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+20)
		tmp = x + (z / ((a - t) / y));
	elseif (z <= 1.7e-68)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+20], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-68], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e20

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-/l* 94.4%

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

      4. fma-define 94.4%

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

   3. Simplified 94.4%

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

      1. fma-undefine 94.4%

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

      2. clear-num 92.6%

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

      3. un-div-inv 92.7%

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

   6. Applied egg-rr 92.7%

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

   7. Taylor expanded in z around inf 83.3%

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

   if -8e20 < z < 1.70000000000000009e-68

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. *-commutative 81.1%

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

      4. *-lft-identity 81.1%

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

      5. times-frac 90.4%

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

      6. /-rgt-identity 90.4%

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

   7. Simplified 90.4%

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

   if 1.70000000000000009e-68 < z

   1. Initial program 81.2%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-68}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-22} \lor \neg \left(t \leq 8.6 \cdot 10^{+64}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.4e-22) (not (<= t 8.6e+64))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.4e-22) || !(t <= 8.6e+64)) {
		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 <= (-7.4d-22)) .or. (.not. (t <= 8.6d+64))) 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 <= -7.4e-22) || !(t <= 8.6e+64)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.4e-22) or not (t <= 8.6e+64):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.4e-22) || !(t <= 8.6e+64))
		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 <= -7.4e-22) || ~((t <= 8.6e+64)))
		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, -7.4e-22], N[Not[LessEqual[t, 8.6e+64]], $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 < -7.4e-22 or 8.5999999999999995e64 < t

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-/l* 94.0%

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

      4. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around inf 75.8%

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

      1. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -7.4e-22 < t < 8.5999999999999995e64

   1. Initial program 91.9%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}} \]
   4. Add Preprocessing
   5. 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 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in t around 0 78.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-22} \lor \neg \left(t \leq 8.6 \cdot 10^{+64}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+152} \lor \neg \left(y \leq 4.5 \cdot 10^{+239}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.1e+152) (not (<= y 4.5e+239)))
   (* y (- 1.0 (/ z t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e+152) || !(y <= 4.5e+239)) {
		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 <= (-1.1d+152)) .or. (.not. (y <= 4.5d+239))) 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 <= -1.1e+152) || !(y <= 4.5e+239)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.1e+152) or not (y <= 4.5e+239):
		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 <= -1.1e+152) || !(y <= 4.5e+239))
		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 <= -1.1e+152) || ~((y <= 4.5e+239)))
		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, -1.1e+152], N[Not[LessEqual[y, 4.5e+239]], $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 < -1.0999999999999999e152 or 4.4999999999999998e239 < y

   1. Initial program 68.9%

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

      1. clear-num 98.0%

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

      2. un-div-inv 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in a around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. unsub-neg 37.9%

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

      3. associate-/l* 61.0%

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

      4. div-sub 61.0%

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

      5. *-inverses 61.0%

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

   9. Simplified 61.0%

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

   10. Taylor expanded in x around 0 57.7%

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

       1. sub-neg 57.7%

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

       2. metadata-eval 57.7%

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

       3. neg-mul-1 57.7%

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

       4. distribute-rgt-neg-in 57.7%

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

       5. +-commutative 57.7%

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

       6. distribute-neg-in 57.7%

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

       7. metadata-eval 57.7%

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

       8. sub-neg 57.7%

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

   12. Simplified 57.7%

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

   if -1.0999999999999999e152 < y < 4.4999999999999998e239

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-/l* 94.5%

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

      4. fma-define 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in t around inf 66.4%

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

      1. +-commutative 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+152} \lor \neg \left(y \leq 4.5 \cdot 10^{+239}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+241}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.1e+241) (/ t (/ (- a) y)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.1e+241) {
		tmp = t / (-a / y);
	} 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 <= (-5.1d+241)) then
        tmp = t / (-a / y)
    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 <= -5.1e+241) {
		tmp = t / (-a / y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.1e+241:
		tmp = t / (-a / y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.1e+241)
		tmp = Float64(t / Float64(Float64(-a) / y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.1e+241)
		tmp = t / (-a / y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.1e+241], N[(t / N[((-a) / y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1000000000000002e241

   1. Initial program 76.2%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf 63.7%

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

   6. Taylor expanded in z around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

      3. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in x around 0 38.0%

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

       1. neg-mul-1 38.0%

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

       2. associate-/l* 41.6%

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

       3. distribute-lft-neg-out 41.6%

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

       4. *-commutative 41.6%

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

   11. Simplified 41.6%

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

       1. *-commutative 41.6%

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

       2. distribute-lft-neg-in 41.6%

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

       3. clear-num 41.6%

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

       4. un-div-inv 42.6%

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

   13. Applied egg-rr 42.6%

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

   if -5.1000000000000002e241 < y

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-/l* 94.9%

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

      4. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around inf 62.3%

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

      1. +-commutative 62.3%

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

   7. Simplified 62.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+241}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

   \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
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. Final simplification 98.1%

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

Alternative 10: 59.9% 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 83.7%

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

   1. +-commutative 83.7%

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

   2. *-commutative 83.7%

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

   3. associate-/l* 93.9%

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

   4. fma-define 93.9%

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

3. Simplified 93.9%

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

5. Taylor expanded in t around inf 58.7%

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

   1. +-commutative 58.7%

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

7. Simplified 58.7%

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

8. Final simplification 58.7%

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

Alternative 11: 50.3% 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 83.7%

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

   1. +-commutative 83.7%

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

   2. *-commutative 83.7%

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

   3. associate-/l* 93.9%

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

   4. fma-define 93.9%

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

3. Simplified 93.9%

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

5. Taylor expanded in y around 0 51.2%

   \[\leadsto \color{blue}{x} \]
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 2024186 
(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))))