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

Percentage Accurate: 86.0% → 98.2%

Time: 7.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. clear-num 83.7%

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

   2. inv-pow 83.7%

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

4. Applied egg-rr 83.7%

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

   1. unpow-1 83.7%

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

   2. *-commutative 83.7%

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

   3. associate-/r* 97.4%

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

6. Simplified 97.4%

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

   1. clear-num 97.5%

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

   2. add-cube-cbrt 96.8%

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{z - a}{z - t}} \]

   3. associate-/l* 96.8%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{\frac{z - a}{z - t}}} \]

   4. pow2 96.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{z - a}{z - t}} \]

8. Applied egg-rr 96.8%

   \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y}\right)}^{2} \cdot \frac{\sqrt[3]{y}}{\frac{z - a}{z - t}}} \]
9. Step-by-step derivation

   1. associate-*r/ 96.8%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{z - a}{z - t}}} \]

   2. unpow2 96.8%

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{z - a}{z - t}} \]

   3. rem-3cbrt-lft 97.5%

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

10. Simplified 97.5%

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

Alternative 2: 83.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+145} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -5e+145) (not (<= t_1 2e-17)))
     (* (- z t) (/ y (- z a)))
     (+ x (/ y (- 1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+145) || !(t_1 <= 2e-17)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x + (y / (1.0 - (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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (z - a)
    if ((t_1 <= (-5d+145)) .or. (.not. (t_1 <= 2d-17))) then
        tmp = (z - t) * (y / (z - a))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -5e+145) || !(t_1 <= 2e-17)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (z - a)
	tmp = 0
	if (t_1 <= -5e+145) or not (t_1 <= 2e-17):
		tmp = (z - t) * (y / (z - a))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -5e+145) || !(t_1 <= 2e-17))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -5e+145) || ~((t_1 <= 2e-17)))
		tmp = (z - t) * (y / (z - a));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+145], N[Not[LessEqual[t$95$1, 2e-17]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -4.99999999999999967e145 or 2.00000000000000014e-17 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around inf 81.2%

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

      1. div-sub 81.2%

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

      2. associate-*r/ 54.5%

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

      3. associate-*l/ 84.6%

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

   7. Simplified 84.6%

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

   if -4.99999999999999967e145 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.00000000000000014e-17

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-/r* 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in t around 0 87.3%

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

      1. *-rgt-identity 87.3%

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

      2. times-frac 82.6%

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

      3. /-rgt-identity 82.6%

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

      4. associate-/r/ 86.7%

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

      5. div-sub 86.7%

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

      6. *-inverses 86.7%

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

   9. Simplified 86.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -5 \cdot 10^{+145} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-15} \lor \neg \left(z \leq 1.35 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e-15) (not (<= z 1.35e-34)))
   (+ x (* y (/ z (- z a))))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-15) || !(z <= 1.35e-34)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d-15)) .or. (.not. (z <= 1.35d-34))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e-15) || !(z <= 1.35e-34)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e-15) or not (z <= 1.35e-34):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e-15) || !(z <= 1.35e-34))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e-15) || ~((z <= 1.35e-34)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e-15], N[Not[LessEqual[z, 1.35e-34]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999991e-15 or 1.35000000000000008e-34 < z

   1. Initial program 74.5%

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

   3. Taylor expanded in t around 0 64.5%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

   if -6.49999999999999991e-15 < z < 1.35000000000000008e-34

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

      1. clear-num 81.7%

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

      2. un-div-inv 82.4%

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

   9. Applied egg-rr 82.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-15} \lor \neg \left(z \leq 1.35 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+46} \lor \neg \left(z \leq 6 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+46) (not (<= z 6e-10)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+46) || !(z <= 6e-10)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d+46)) .or. (.not. (z <= 6d-10))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+46) || !(z <= 6e-10)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+46) or not (z <= 6e-10):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+46) || !(z <= 6e-10))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+46) || ~((z <= 6e-10)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+46], N[Not[LessEqual[z, 6e-10]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e46 or 6e-10 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in a around 0 62.6%

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

      1. associate-/l* 87.2%

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

      2. div-sub 87.2%

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

      3. *-inverses 87.2%

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

   5. Simplified 87.2%

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

   if -2.3000000000000001e46 < z < 6e-10

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-/l* 94.5%

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

      3. fma-define 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

      1. clear-num 79.8%

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

      2. un-div-inv 80.4%

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

   9. Applied egg-rr 80.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+46} \lor \neg \left(z \leq 6 \cdot 10^{-10}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 3.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+153) (not (<= z 3.5e-7))) (+ x y) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 3.5e-7)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.9d+153)) .or. (.not. (z <= 3.5d-7))) then
        tmp = x + y
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 3.5e-7)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+153) or not (z <= 3.5e-7):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+153) || !(z <= 3.5e-7))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+153) || ~((z <= 3.5e-7)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+153], N[Not[LessEqual[z, 3.5e-7]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999983e153 or 3.49999999999999984e-7 < z

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

   if -1.89999999999999983e153 < z < 3.49999999999999984e-7

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-/l* 95.2%

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

      3. fma-define 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. un-div-inv 78.3%

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

   9. Applied egg-rr 78.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 3.5 \cdot 10^{-7}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+153} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e+153) (not (<= z 3.5e-8))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+153) || !(z <= 3.5e-8)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.25d+153)) .or. (.not. (z <= 3.5d-8))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+153) || !(z <= 3.5e-8)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.25e+153) or not (z <= 3.5e-8):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e+153) || !(z <= 3.5e-8))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.25e+153) || ~((z <= 3.5e-8)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e+153], N[Not[LessEqual[z, 3.5e-8]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e153 or 3.50000000000000024e-8 < z

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. +-commutative 81.9%

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

   7. Simplified 81.9%

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

   if -2.25e153 < z < 3.50000000000000024e-8

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-/l* 95.2%

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

      3. fma-define 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+153} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+91} \lor \neg \left(z \leq 3 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+91) (not (<= z 3e-9))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+91) || !(z <= 3e-9)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d+91)) .or. (.not. (z <= 3d-9))) then
        tmp = x + y
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+91) || !(z <= 3e-9)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+91) or not (z <= 3e-9):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+91) || !(z <= 3e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e+91) || ~((z <= 3e-9)))
		tmp = x + y;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+91], N[Not[LessEqual[z, 3e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999999e91 or 2.99999999999999998e-9 < z

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   7. Simplified 80.3%

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

   if -1.54999999999999999e91 < z < 2.99999999999999998e-9

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 72.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+91} \lor \neg \left(z \leq 3 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+226} \lor \neg \left(t \leq 1.15 \cdot 10^{+86}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.8e+226) (not (<= t 1.15e+86))) (* t (/ y a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.8e+226) || !(t <= 1.15e+86)) {
		tmp = t * (y / a);
	} 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 <= (-6.8d+226)) .or. (.not. (t <= 1.15d+86))) then
        tmp = t * (y / a)
    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 <= -6.8e+226) || !(t <= 1.15e+86)) {
		tmp = t * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.8e+226) or not (t <= 1.15e+86):
		tmp = t * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.8e+226) || !(t <= 1.15e+86))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.8e+226) || ~((t <= 1.15e+86)))
		tmp = t * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.8e+226], N[Not[LessEqual[t, 1.15e+86]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.79999999999999958e226 or 1.14999999999999995e86 < t

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-/l* 92.2%

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

      3. fma-define 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around -inf 65.0%

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

   6. Taylor expanded in z around 0 45.4%

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

      1. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

   if -6.79999999999999958e226 < t < 1.14999999999999995e86

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-/l* 98.4%

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

      3. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 69.2%

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

      1. +-commutative 69.2%

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

   7. Simplified 69.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+226} \lor \neg \left(t \leq 1.15 \cdot 10^{+86}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{-34}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e-17) (not (<= z 8e-34))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e-17) || !(z <= 8e-34)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.4d-17)) .or. (.not. (z <= 8d-34))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e-17) || !(z <= 8e-34)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.4e-17) or not (z <= 8e-34):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e-17) || !(z <= 8e-34))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.4e-17) || ~((z <= 8e-34)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.4e-17], N[Not[LessEqual[z, 8e-34]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000002e-17 or 7.99999999999999942e-34 < z

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

   7. Simplified 75.2%

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

   if -5.4000000000000002e-17 < z < 7.99999999999999942e-34

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 48.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-17} \lor \neg \left(z \leq 8 \cdot 10^{-34}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+118}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 455000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.65e+118) y (if (<= y 455000.0) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.65e+118) {
		tmp = y;
	} else if (y <= 455000.0) {
		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 (y <= (-3.65d+118)) then
        tmp = y
    else if (y <= 455000.0d0) 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 (y <= -3.65e+118) {
		tmp = y;
	} else if (y <= 455000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.65e+118:
		tmp = y
	elif y <= 455000.0:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.65e+118)
		tmp = y;
	elseif (y <= 455000.0)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.65e+118)
		tmp = y;
	elseif (y <= 455000.0)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.65e+118], y, If[LessEqual[y, 455000.0], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6500000000000002e118 or 455000 < y

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-/l* 98.9%

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

      3. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around -inf 48.8%

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

   6. Taylor expanded in z around inf 33.7%

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

   if -3.6500000000000002e118 < y < 455000

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-/l* 95.7%

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

      3. fma-define 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around 0 65.9%

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

Alternative 11: 50.4% 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%

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

   1. +-commutative 83.7%

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

   2. associate-/l* 96.9%

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

   3. fma-define 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in y around 0 47.5%

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

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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