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

Percentage Accurate: 98.1% → 98.3%

Time: 8.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. clear-num 98.4%

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

   2. un-div-inv 98.8%

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

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 82.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a - t}\\ \mathbf{if}\;t \leq -0.92:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) (- a t)))))
   (if (<= t -0.92)
     (+ x y)
     (if (<= t 1.5e-129)
       t_1
       (if (<= t 9e-97)
         (+ x (/ (* y t) (- t a)))
         (if (<= t 9.6e+23) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / (a - t));
	double tmp;
	if (t <= -0.92) {
		tmp = x + y;
	} else if (t <= 1.5e-129) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = x + ((y * t) / (t - a));
	} else if (t <= 9.6e+23) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / (a - t))
    if (t <= (-0.92d0)) then
        tmp = x + y
    else if (t <= 1.5d-129) then
        tmp = t_1
    else if (t <= 9d-97) then
        tmp = x + ((y * t) / (t - a))
    else if (t <= 9.6d+23) then
        tmp = t_1
    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 t_1 = x + ((y * z) / (a - t));
	double tmp;
	if (t <= -0.92) {
		tmp = x + y;
	} else if (t <= 1.5e-129) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = x + ((y * t) / (t - a));
	} else if (t <= 9.6e+23) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / (a - t))
	tmp = 0
	if t <= -0.92:
		tmp = x + y
	elif t <= 1.5e-129:
		tmp = t_1
	elif t <= 9e-97:
		tmp = x + ((y * t) / (t - a))
	elif t <= 9.6e+23:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / Float64(a - t)))
	tmp = 0.0
	if (t <= -0.92)
		tmp = Float64(x + y);
	elseif (t <= 1.5e-129)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(t - a)));
	elseif (t <= 9.6e+23)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / (a - t));
	tmp = 0.0;
	if (t <= -0.92)
		tmp = x + y;
	elseif (t <= 1.5e-129)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = x + ((y * t) / (t - a));
	elseif (t <= 9.6e+23)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.92], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.5e-129], t$95$1, If[LessEqual[t, 9e-97], N[(x + N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+23], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.92000000000000004 or 9.6e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -0.92000000000000004 < t < 1.4999999999999999e-129 or 9.0000000000000002e-97 < t < 9.6e23

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 89.5%

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

   if 1.4999999999999999e-129 < t < 9.0000000000000002e-97

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-*r/ 91.0%

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

      3. mul-1-neg 91.0%

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

      4. distribute-lft-neg-out 91.0%

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

      5. *-commutative 91.0%

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

   5. Simplified 91.0%

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

      1. frac-2neg 91.0%

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

      2. div-inv 91.0%

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

      3. distribute-rgt-neg-out 91.0%

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

      4. remove-double-neg 91.0%

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

      5. *-commutative 91.0%

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

      6. sub-neg 91.0%

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

      7. distribute-neg-in 91.0%

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

      8. add-sqr-sqrt 0.0%

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

      9. sqrt-unprod 59.3%

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

      10. sqr-neg 59.3%

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

      11. sqrt-unprod 59.3%

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

      12. add-sqr-sqrt 59.3%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 91.0%

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

      15. sqr-neg 91.0%

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

      16. sqrt-unprod 91.0%

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

      17. add-sqr-sqrt 91.0%

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

   7. Applied egg-rr 91.0%

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

      1. associate-*r/ 91.0%

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

      2. *-rgt-identity 91.0%

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

      3. +-commutative 91.0%

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

      4. unsub-neg 91.0%

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

   9. Simplified 91.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.92:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a - t}\\ t_2 := x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{if}\;t \leq -0.05:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) (- a t)))) (t_2 (- x (* y (+ (/ z t) -1.0)))))
   (if (<= t -0.05)
     t_2
     (if (<= t 3.2e-128)
       t_1
       (if (<= t 9e-97)
         (+ x (/ (* y t) (- t a)))
         (if (<= t 9e+23) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / (a - t));
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -0.05) {
		tmp = t_2;
	} else if (t <= 3.2e-128) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = x + ((y * t) / (t - a));
	} else if (t <= 9e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 + ((y * z) / (a - t))
    t_2 = x - (y * ((z / t) + (-1.0d0)))
    if (t <= (-0.05d0)) then
        tmp = t_2
    else if (t <= 3.2d-128) then
        tmp = t_1
    else if (t <= 9d-97) then
        tmp = x + ((y * t) / (t - a))
    else if (t <= 9d+23) then
        tmp = t_1
    else
        tmp = t_2
    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) / (a - t));
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -0.05) {
		tmp = t_2;
	} else if (t <= 3.2e-128) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = x + ((y * t) / (t - a));
	} else if (t <= 9e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / (a - t))
	t_2 = x - (y * ((z / t) + -1.0))
	tmp = 0
	if t <= -0.05:
		tmp = t_2
	elif t <= 3.2e-128:
		tmp = t_1
	elif t <= 9e-97:
		tmp = x + ((y * t) / (t - a))
	elif t <= 9e+23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / Float64(a - t)))
	t_2 = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)))
	tmp = 0.0
	if (t <= -0.05)
		tmp = t_2;
	elseif (t <= 3.2e-128)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(t - a)));
	elseif (t <= 9e+23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / (a - t));
	t_2 = x - (y * ((z / t) + -1.0));
	tmp = 0.0;
	if (t <= -0.05)
		tmp = t_2;
	elseif (t <= 3.2e-128)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = x + ((y * t) / (t - a));
	elseif (t <= 9e+23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.05], t$95$2, If[LessEqual[t, 3.2e-128], t$95$1, If[LessEqual[t, 9e-97], N[(x + N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.050000000000000003 or 8.99999999999999958e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

      3. associate-/l* 90.0%

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

      4. div-sub 90.0%

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

      5. sub-neg 90.0%

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

      6. *-inverses 90.0%

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

      7. metadata-eval 90.0%

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

   5. Simplified 90.0%

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

   if -0.050000000000000003 < t < 3.1999999999999998e-128 or 9.0000000000000002e-97 < t < 8.99999999999999958e23

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 89.5%

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

   if 3.1999999999999998e-128 < t < 9.0000000000000002e-97

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-*r/ 91.0%

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

      3. mul-1-neg 91.0%

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

      4. distribute-lft-neg-out 91.0%

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

      5. *-commutative 91.0%

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

   5. Simplified 91.0%

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

      1. frac-2neg 91.0%

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

      2. div-inv 91.0%

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

      3. distribute-rgt-neg-out 91.0%

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

      4. remove-double-neg 91.0%

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

      5. *-commutative 91.0%

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

      6. sub-neg 91.0%

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

      7. distribute-neg-in 91.0%

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

      8. add-sqr-sqrt 0.0%

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

      9. sqrt-unprod 59.3%

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

      10. sqr-neg 59.3%

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

      11. sqrt-unprod 59.3%

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

      12. add-sqr-sqrt 59.3%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 91.0%

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

      15. sqr-neg 91.0%

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

      16. sqrt-unprod 91.0%

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

      17. add-sqr-sqrt 91.0%

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

   7. Applied egg-rr 91.0%

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

      1. associate-*r/ 91.0%

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

      2. *-rgt-identity 91.0%

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

      3. +-commutative 91.0%

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

      4. unsub-neg 91.0%

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

   9. Simplified 91.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.05:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a - t}\\ t_2 := x + y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) (- a t)))) (t_2 (+ x (* y (/ t (- t a))))))
   (if (<= t -4.1e-95)
     t_2
     (if (<= t 3.2e-128)
       t_1
       (if (<= t 9e-97)
         t_2
         (if (<= t 8.4e+23) t_1 (- x (* y (+ (/ z t) -1.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / (a - t));
	double t_2 = x + (y * (t / (t - a)));
	double tmp;
	if (t <= -4.1e-95) {
		tmp = t_2;
	} else if (t <= 3.2e-128) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = t_2;
	} else if (t <= 8.4e+23) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	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 + ((y * z) / (a - t))
    t_2 = x + (y * (t / (t - a)))
    if (t <= (-4.1d-95)) then
        tmp = t_2
    else if (t <= 3.2d-128) then
        tmp = t_1
    else if (t <= 9d-97) then
        tmp = t_2
    else if (t <= 8.4d+23) then
        tmp = t_1
    else
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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) / (a - t));
	double t_2 = x + (y * (t / (t - a)));
	double tmp;
	if (t <= -4.1e-95) {
		tmp = t_2;
	} else if (t <= 3.2e-128) {
		tmp = t_1;
	} else if (t <= 9e-97) {
		tmp = t_2;
	} else if (t <= 8.4e+23) {
		tmp = t_1;
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / (a - t))
	t_2 = x + (y * (t / (t - a)))
	tmp = 0
	if t <= -4.1e-95:
		tmp = t_2
	elif t <= 3.2e-128:
		tmp = t_1
	elif t <= 9e-97:
		tmp = t_2
	elif t <= 8.4e+23:
		tmp = t_1
	else:
		tmp = x - (y * ((z / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(t / Float64(t - a))))
	tmp = 0.0
	if (t <= -4.1e-95)
		tmp = t_2;
	elseif (t <= 3.2e-128)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = t_2;
	elseif (t <= 8.4e+23)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / (a - t));
	t_2 = x + (y * (t / (t - a)));
	tmp = 0.0;
	if (t <= -4.1e-95)
		tmp = t_2;
	elseif (t <= 3.2e-128)
		tmp = t_1;
	elseif (t <= 9e-97)
		tmp = t_2;
	elseif (t <= 8.4e+23)
		tmp = t_1;
	else
		tmp = x - (y * ((z / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e-95], t$95$2, If[LessEqual[t, 3.2e-128], t$95$1, If[LessEqual[t, 9e-97], t$95$2, If[LessEqual[t, 8.4e+23], t$95$1, N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0999999999999997e-95 or 3.1999999999999998e-128 < t < 9.0000000000000002e-97

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. *-commutative 63.8%

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

      4. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

   if -4.0999999999999997e-95 < t < 3.1999999999999998e-128 or 9.0000000000000002e-97 < t < 8.4000000000000005e23

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 93.1%

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

   if 8.4000000000000005e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. associate-/l* 94.6%

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

      4. div-sub 94.6%

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

      5. sub-neg 94.6%

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

      6. *-inverses 94.6%

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

      7. metadata-eval 94.6%

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

   5. Simplified 94.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-95}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-97}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1300000 \lor \neg \left(t \leq 5.3 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1300000.0) (not (<= t 5.3e+23)))
   (+ x y)
   (- x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1300000.0) || !(t <= 5.3e+23)) {
		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 <= (-1300000.0d0)) .or. (.not. (t <= 5.3d+23))) 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 <= -1300000.0) || !(t <= 5.3e+23)) {
		tmp = x + y;
	} else {
		tmp = x - ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1300000.0) or not (t <= 5.3e+23):
		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 <= -1300000.0) || !(t <= 5.3e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1300000.0) || ~((t <= 5.3e+23)))
		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, -1300000.0], N[Not[LessEqual[t, 5.3e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e6 or 5.3000000000000001e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. +-commutative 82.8%

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

   5. Simplified 82.8%

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

   if -1.3e6 < t < 5.3000000000000001e23

   1. Initial program 97.3%

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

      1. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in a around inf 79.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1300000 \lor \neg \left(t \leq 5.3 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \lor \neg \left(t \leq 10^{+24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35) (not (<= t 1e+24))) (+ x y) (+ x (/ (* y z) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35) || !(t <= 1e+24)) {
		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 <= (-1.35d0)) .or. (.not. (t <= 1d+24))) 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 <= -1.35) || !(t <= 1e+24)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35) or not (t <= 1e+24):
		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 <= -1.35) || !(t <= 1e+24))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35) || ~((t <= 1e+24)))
		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, -1.35], N[Not[LessEqual[t, 1e+24]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3500000000000001 or 9.9999999999999998e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -1.3500000000000001 < t < 9.9999999999999998e23

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 86.3%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \lor \neg \left(t \leq 10^{+24}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -900000 \lor \neg \left(t \leq 6.2 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -900000.0) (not (<= t 6.2e+23))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -900000.0) || !(t <= 6.2e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-900000.0d0)) .or. (.not. (t <= 6.2d+23))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -900000.0) || !(t <= 6.2e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -900000.0) or not (t <= 6.2e+23):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -900000.0) || !(t <= 6.2e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -900000.0) || ~((t <= 6.2e+23)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -900000.0], N[Not[LessEqual[t, 6.2e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9e5 or 6.19999999999999941e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. +-commutative 82.8%

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

   5. Simplified 82.8%

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

   if -9e5 < t < 6.19999999999999941e23

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 77.4%

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

   5. Applied egg-rr 77.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -900000 \lor \neg \left(t \leq 6.2 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1200000 \lor \neg \left(t \leq 5.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1200000.0) (not (<= t 5.5e+23))) (+ x y) (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1200000.0) || !(t <= 5.5e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (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 ((t <= (-1200000.0d0)) .or. (.not. (t <= 5.5d+23))) then
        tmp = x + y
    else
        tmp = x + (z / (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 ((t <= -1200000.0) || !(t <= 5.5e+23)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1200000.0) or not (t <= 5.5e+23):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1200000.0) || !(t <= 5.5e+23))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1200000.0) || ~((t <= 5.5e+23)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1200000.0], N[Not[LessEqual[t, 5.5e+23]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e6 or 5.50000000000000004e23 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. +-commutative 82.8%

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

   5. Simplified 82.8%

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

   if -1.2e6 < t < 5.50000000000000004e23

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 77.4%

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

   5. Applied egg-rr 77.4%

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

      1. clear-num 77.4%

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

      2. div-inv 77.5%

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

   7. Applied egg-rr 77.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1200000 \lor \neg \left(t \leq 5.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 10: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 9.5e+56) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 9.5e+56) {
		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 (a <= 9.5d+56) 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 (a <= 9.5e+56) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 9.5e+56:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 9.5e+56)
		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 (a <= 9.5e+56)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 9.5e+56], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 9.4999999999999997e56

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 59.1%

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

      1. +-commutative 59.1%

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

   5. Simplified 59.1%

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

   if 9.4999999999999997e56 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 69.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in x around inf 49.5%

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

4. Final simplification 49.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024115 
(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)))))