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

Percentage Accurate: 97.9% → 95.8%

Time: 9.2s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. *-commutative 97.6%

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

   2. div-inv 97.5%

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

   3. associate-*l* 98.2%

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

4. Applied egg-rr 98.2%

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

   1. +-commutative 98.2%

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

   2. associate-*l/ 98.3%

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

   3. *-un-lft-identity 98.3%

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

6. Applied egg-rr 98.3%

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

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 1350\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (- x (* y (/ z t)))))
   (if (<= t -6.5e+186)
     (+ y x)
     (if (<= t -1.75e+42)
       t_2
       (if (<= t -9e-15)
         t_1
         (if (<= t -4.7e-68)
           t_2
           (if (or (<= t -7.5e-83) (not (<= t 1350.0))) (+ y x) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = y + x;
	} else if (t <= -1.75e+42) {
		tmp = t_2;
	} else if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= -4.7e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 1350.0)) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = x - (y * (z / t))
    if (t <= (-6.5d+186)) then
        tmp = y + x
    else if (t <= (-1.75d+42)) then
        tmp = t_2
    else if (t <= (-9d-15)) then
        tmp = t_1
    else if (t <= (-4.7d-68)) then
        tmp = t_2
    else if ((t <= (-7.5d-83)) .or. (.not. (t <= 1350.0d0))) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = y + x;
	} else if (t <= -1.75e+42) {
		tmp = t_2;
	} else if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= -4.7e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 1350.0)) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = x - (y * (z / t))
	tmp = 0
	if t <= -6.5e+186:
		tmp = y + x
	elif t <= -1.75e+42:
		tmp = t_2
	elif t <= -9e-15:
		tmp = t_1
	elif t <= -4.7e-68:
		tmp = t_2
	elif (t <= -7.5e-83) or not (t <= 1350.0):
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(y + x);
	elseif (t <= -1.75e+42)
		tmp = t_2;
	elseif (t <= -9e-15)
		tmp = t_1;
	elseif (t <= -4.7e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || !(t <= 1350.0))
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = x - (y * (z / t));
	tmp = 0.0;
	if (t <= -6.5e+186)
		tmp = y + x;
	elseif (t <= -1.75e+42)
		tmp = t_2;
	elseif (t <= -9e-15)
		tmp = t_1;
	elseif (t <= -4.7e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || ~((t <= 1350.0)))
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+186], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.75e+42], t$95$2, If[LessEqual[t, -9e-15], t$95$1, If[LessEqual[t, -4.7e-68], t$95$2, If[Or[LessEqual[t, -7.5e-83], N[Not[LessEqual[t, 1350.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186 or -4.69999999999999988e-68 < t < -7.4999999999999997e-83 or 1350 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   if -6.4999999999999997e186 < t < -1.75000000000000012e42 or -8.9999999999999995e-15 < t < -4.69999999999999988e-68

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*l* 94.3%

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

   4. Applied egg-rr 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-*l/ 94.4%

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

      3. *-un-lft-identity 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around inf 81.0%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in a around 0 79.9%

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

       1. mul-1-neg 79.9%

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

       2. distribute-frac-neg2 79.9%

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

   12. Simplified 79.9%

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

   if -1.75000000000000012e42 < t < -8.9999999999999995e-15 or -7.4999999999999997e-83 < t < 1350

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-68}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 1350\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := x - \frac{z \cdot y}{t}\\ \mathbf{if}\;t \leq -7.1 \cdot 10^{+149}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 45\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (- x (/ (* z y) t))))
   (if (<= t -7.1e+149)
     (+ y x)
     (if (<= t -2.05e+42)
       t_2
       (if (<= t -1.12e-14)
         t_1
         (if (<= t -5e-68)
           t_2
           (if (or (<= t -7.5e-83) (not (<= t 45.0))) (+ y x) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - ((z * y) / t);
	double tmp;
	if (t <= -7.1e+149) {
		tmp = y + x;
	} else if (t <= -2.05e+42) {
		tmp = t_2;
	} else if (t <= -1.12e-14) {
		tmp = t_1;
	} else if (t <= -5e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 45.0)) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = x - ((z * y) / t)
    if (t <= (-7.1d+149)) then
        tmp = y + x
    else if (t <= (-2.05d+42)) then
        tmp = t_2
    else if (t <= (-1.12d-14)) then
        tmp = t_1
    else if (t <= (-5d-68)) then
        tmp = t_2
    else if ((t <= (-7.5d-83)) .or. (.not. (t <= 45.0d0))) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - ((z * y) / t);
	double tmp;
	if (t <= -7.1e+149) {
		tmp = y + x;
	} else if (t <= -2.05e+42) {
		tmp = t_2;
	} else if (t <= -1.12e-14) {
		tmp = t_1;
	} else if (t <= -5e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 45.0)) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = x - ((z * y) / t)
	tmp = 0
	if t <= -7.1e+149:
		tmp = y + x
	elif t <= -2.05e+42:
		tmp = t_2
	elif t <= -1.12e-14:
		tmp = t_1
	elif t <= -5e-68:
		tmp = t_2
	elif (t <= -7.5e-83) or not (t <= 45.0):
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(x - Float64(Float64(z * y) / t))
	tmp = 0.0
	if (t <= -7.1e+149)
		tmp = Float64(y + x);
	elseif (t <= -2.05e+42)
		tmp = t_2;
	elseif (t <= -1.12e-14)
		tmp = t_1;
	elseif (t <= -5e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || !(t <= 45.0))
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = x - ((z * y) / t);
	tmp = 0.0;
	if (t <= -7.1e+149)
		tmp = y + x;
	elseif (t <= -2.05e+42)
		tmp = t_2;
	elseif (t <= -1.12e-14)
		tmp = t_1;
	elseif (t <= -5e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || ~((t <= 45.0)))
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.1e+149], N[(y + x), $MachinePrecision], If[LessEqual[t, -2.05e+42], t$95$2, If[LessEqual[t, -1.12e-14], t$95$1, If[LessEqual[t, -5e-68], t$95$2, If[Or[LessEqual[t, -7.5e-83], N[Not[LessEqual[t, 45.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.1000000000000001e149 or -4.99999999999999971e-68 < t < -7.4999999999999997e-83 or 45 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.0%

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

      1. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -7.1000000000000001e149 < t < -2.05e42 or -1.12000000000000006e-14 < t < -4.99999999999999971e-68

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. div-inv 99.7%

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

      3. associate-*l* 92.6%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in a around 0 91.0%

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

      1. mul-1-neg 91.0%

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

      2. unsub-neg 91.0%

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

      3. associate-/l* 91.0%

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

      4. div-sub 91.0%

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

      5. *-inverses 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in z around inf 81.0%

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

   if -2.05e42 < t < -1.12000000000000006e-14 or -7.4999999999999997e-83 < t < 45

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{+149}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 45\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-48} \lor \neg \left(z \leq 230000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-48) (not (<= z 230000.0)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-48) || !(z <= 230000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (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 <= (-2.7d-48)) .or. (.not. (z <= 230000.0d0))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (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 <= -2.7e-48) || !(z <= 230000.0)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-48) or not (z <= 230000.0):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-48) || !(z <= 230000.0))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-48) || ~((z <= 230000.0)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-48], N[Not[LessEqual[z, 230000.0]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000011e-48 or 2.3e5 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if -2.70000000000000011e-48 < z < 2.3e5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. div-inv 90.5%

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

      3. associate-*l* 91.4%

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

      4. associate-*l/ 91.5%

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

      5. *-un-lft-identity 91.5%

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

   7. Applied egg-rr 91.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-48} \lor \neg \left(z \leq 230000\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+186} \lor \neg \left(t \leq 4.2 \cdot 10^{+129}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+186) (not (<= t 4.2e+129)))
   (+ y x)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+186) || !(t <= 4.2e+129)) {
		tmp = y + x;
	} 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 <= (-8.5d+186)) .or. (.not. (t <= 4.2d+129))) then
        tmp = y + x
    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 <= -8.5e+186) || !(t <= 4.2e+129)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+186) or not (t <= 4.2e+129):
		tmp = y + x
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+186) || !(t <= 4.2e+129))
		tmp = Float64(y + x);
	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 <= -8.5e+186) || ~((t <= 4.2e+129)))
		tmp = y + x;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+186], N[Not[LessEqual[t, 4.2e+129]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4999999999999999e186 or 4.19999999999999993e129 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -8.4999999999999999e186 < t < 4.19999999999999993e129

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+186} \lor \neg \left(t \leq 4.2 \cdot 10^{+129}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.022 \lor \neg \left(t \leq 1.45\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.022) (not (<= t 1.45))) (+ y x) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.022) || !(t <= 1.45)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.022d0)) .or. (.not. (t <= 1.45d0))) then
        tmp = y + x
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.022) || !(t <= 1.45)) {
		tmp = y + x;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.022) or not (t <= 1.45):
		tmp = y + x
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.022) || !(t <= 1.45))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.022) || ~((t <= 1.45)))
		tmp = y + x;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.022], N[Not[LessEqual[t, 1.45]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.021999999999999999 or 1.44999999999999996 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -0.021999999999999999 < t < 1.44999999999999996

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.022 \lor \neg \left(t \leq 1.45\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.046 \lor \neg \left(t \leq 1.4\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.046) (not (<= t 1.4))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.046) || !(t <= 1.4)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.046d0)) .or. (.not. (t <= 1.4d0))) then
        tmp = y + x
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.046) || !(t <= 1.4)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.046) or not (t <= 1.4):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.046) || !(t <= 1.4))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.046) || ~((t <= 1.4)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.046], N[Not[LessEqual[t, 1.4]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.045999999999999999 or 1.3999999999999999 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -0.045999999999999999 < t < 1.3999999999999999

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0 79.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.046 \lor \neg \left(t \leq 1.4\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-89} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-89) (not (<= t 2.6e+110))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-89) || !(t <= 2.6e+110)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.3d-89)) .or. (.not. (t <= 2.6d+110))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-89) || !(t <= 2.6e+110)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e-89) or not (t <= 2.6e+110):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-89) || !(t <= 2.6e+110))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e-89) || ~((t <= 2.6e+110)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-89], N[Not[LessEqual[t, 2.6e+110]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.2999999999999999e-89 or 2.6e110 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 73.5%

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

      1. +-commutative 73.5%

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

   5. Simplified 73.5%

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

   if -1.2999999999999999e-89 < t < 2.6e110

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 52.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-89} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

Alternative 10: 50.2% 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 97.6%

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

3. Taylor expanded in x around inf 49.7%

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

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

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

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