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

Percentage Accurate: 98.4% → 98.5%

Time: 11.3s

Alternatives: 15

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: 98.4% 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: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. clear-num 98.7%

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

   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%

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

Alternative 2: 82.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_2 \leq 0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (/ (- z t) (- a t))))
   (if (<= t_2 -1e+134)
     (* y (/ z (- a t)))
     (if (<= t_2 -5e-26)
       t_1
       (if (<= t_2 5e-127)
         (- x (* y (/ t a)))
         (if (<= t_2 0.05)
           t_1
           (if (<= t_2 2e+20) (+ x y) (- x (* z (/ y t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -1e+134) {
		tmp = y * (z / (a - t));
	} else if (t_2 <= -5e-26) {
		tmp = t_1;
	} else if (t_2 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_2 <= 0.05) {
		tmp = t_1;
	} else if (t_2 <= 2e+20) {
		tmp = x + y;
	} else {
		tmp = x - (z * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = (z - t) / (a - t)
    if (t_2 <= (-1d+134)) then
        tmp = y * (z / (a - t))
    else if (t_2 <= (-5d-26)) then
        tmp = t_1
    else if (t_2 <= 5d-127) then
        tmp = x - (y * (t / a))
    else if (t_2 <= 0.05d0) then
        tmp = t_1
    else if (t_2 <= 2d+20) then
        tmp = x + y
    else
        tmp = x - (z * (y / t))
    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));
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -1e+134) {
		tmp = y * (z / (a - t));
	} else if (t_2 <= -5e-26) {
		tmp = t_1;
	} else if (t_2 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_2 <= 0.05) {
		tmp = t_1;
	} else if (t_2 <= 2e+20) {
		tmp = x + y;
	} else {
		tmp = x - (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = (z - t) / (a - t)
	tmp = 0
	if t_2 <= -1e+134:
		tmp = y * (z / (a - t))
	elif t_2 <= -5e-26:
		tmp = t_1
	elif t_2 <= 5e-127:
		tmp = x - (y * (t / a))
	elif t_2 <= 0.05:
		tmp = t_1
	elif t_2 <= 2e+20:
		tmp = x + y
	else:
		tmp = x - (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -1e+134)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t_2 <= -5e-26)
		tmp = t_1;
	elseif (t_2 <= 5e-127)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t_2 <= 0.05)
		tmp = t_1;
	elseif (t_2 <= 2e+20)
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_2 <= -1e+134)
		tmp = y * (z / (a - t));
	elseif (t_2 <= -5e-26)
		tmp = t_1;
	elseif (t_2 <= 5e-127)
		tmp = x - (y * (t / a));
	elseif (t_2 <= 0.05)
		tmp = t_1;
	elseif (t_2 <= 2e+20)
		tmp = x + y;
	else
		tmp = x - (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+134], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-26], t$95$1, If[LessEqual[t$95$2, 5e-127], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.05], t$95$1, If[LessEqual[t$95$2, 2e+20], N[(x + y), $MachinePrecision], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -9.99999999999999921e133

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 89.1%

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

      1. associate--l+ 89.1%

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

      2. div-sub 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around inf 83.8%

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

   if -9.99999999999999921e133 < (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26 or 4.9999999999999997e-127 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.050000000000000003

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999997e-127

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

      3. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in t around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.7%

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

   10. Simplified 94.7%

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

   if 0.050000000000000003 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2e20

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 94.4%

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

      1. +-commutative 94.4%

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

   5. Simplified 94.4%

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

   if 2e20 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 91.1%

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

   4. Taylor expanded in a around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in y around 0 71.4%

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

      1. *-rgt-identity 71.4%

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

      2. times-frac 73.8%

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

      3. /-rgt-identity 73.8%

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

      4. associate-/r/ 73.6%

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

   9. Simplified 73.6%

      \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 73.8%

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

   11. Applied egg-rr 73.8%

       \[\leadsto x - \color{blue}{\frac{y}{t} \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -1 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (* z (/ y (- a t))))))
   (if (<= t_1 -5e-26)
     t_2
     (if (<= t_1 5e-127)
       (- x (* y (/ t a)))
       (if (<= t_1 0.05) (+ x (* y (/ z a))) (if (<= t_1 2.0) (+ x y) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + (z * (y / (a - t)));
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = t_2;
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} 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 = (z - t) / (a - t)
    t_2 = x + (z * (y / (a - t)))
    if (t_1 <= (-5d-26)) then
        tmp = t_2
    else if (t_1 <= 5d-127) then
        tmp = x - (y * (t / a))
    else if (t_1 <= 0.05d0) then
        tmp = x + (y * (z / a))
    else if (t_1 <= 2.0d0) then
        tmp = x + y
    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 = (z - t) / (a - t);
	double t_2 = x + (z * (y / (a - t)));
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = t_2;
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = x + (z * (y / (a - t)))
	tmp = 0
	if t_1 <= -5e-26:
		tmp = t_2
	elif t_1 <= 5e-127:
		tmp = x - (y * (t / a))
	elif t_1 <= 0.05:
		tmp = x + (y * (z / a))
	elif t_1 <= 2.0:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (t_1 <= -5e-26)
		tmp = t_2;
	elseif (t_1 <= 5e-127)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t_1 <= 0.05)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = x + (z * (y / (a - t)));
	tmp = 0.0;
	if (t_1 <= -5e-26)
		tmp = t_2;
	elseif (t_1 <= 5e-127)
		tmp = x - (y * (t / a));
	elseif (t_1 <= 0.05)
		tmp = x + (y * (z / a));
	elseif (t_1 <= 2.0)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-26], t$95$2, If[LessEqual[t$95$1, 5e-127], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.05], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26 or 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 86.0%

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

      1. div-inv 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*l* 97.4%

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

      4. div-inv 97.5%

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

   5. Applied egg-rr 97.5%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999997e-127

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

      3. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in t around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.7%

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

   10. Simplified 94.7%

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

   if 4.9999999999999997e-127 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if 0.050000000000000003 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e-26)
     (+ x (/ y (/ (- a t) z)))
     (if (<= t_1 5e-127)
       (- x (* y (/ t a)))
       (if (<= t_1 0.05)
         (+ x (* y (/ z a)))
         (if (<= t_1 2.0) (+ x y) (+ x (* z (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (y / ((a - t) / z));
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d-26)) then
        tmp = x + (y / ((a - t) / z))
    else if (t_1 <= 5d-127) then
        tmp = x - (y * (t / a))
    else if (t_1 <= 0.05d0) then
        tmp = x + (y * (z / a))
    else if (t_1 <= 2.0d0) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (y / ((a - t) / z));
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e-26:
		tmp = x + (y / ((a - t) / z))
	elif t_1 <= 5e-127:
		tmp = x - (y * (t / a))
	elif t_1 <= 0.05:
		tmp = x + (y * (z / a))
	elif t_1 <= 2.0:
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e-26)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (t_1 <= 5e-127)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t_1 <= 0.05)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e-26)
		tmp = x + (y / ((a - t) / z));
	elseif (t_1 <= 5e-127)
		tmp = x - (y * (t / a));
	elseif (t_1 <= 0.05)
		tmp = x + (y * (z / a));
	elseif (t_1 <= 2.0)
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-26], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-127], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.05], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26

   1. Initial program 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 98.2%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999997e-127

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

      3. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in t around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.7%

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

   10. Simplified 94.7%

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

   if 4.9999999999999997e-127 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if 0.050000000000000003 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. div-inv 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 97.0%

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

      4. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e-26)
     (+ x (/ z (/ (- a t) y)))
     (if (<= t_1 5e-127)
       (- x (* y (/ t a)))
       (if (<= t_1 0.05)
         (+ x (* y (/ z a)))
         (if (<= t_1 2.0) (+ x y) (+ x (* z (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d-26)) then
        tmp = x + (z / ((a - t) / y))
    else if (t_1 <= 5d-127) then
        tmp = x - (y * (t / a))
    else if (t_1 <= 0.05d0) then
        tmp = x + (y * (z / a))
    else if (t_1 <= 2.0d0) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 5e-127) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 0.05) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e-26:
		tmp = x + (z / ((a - t) / y))
	elif t_1 <= 5e-127:
		tmp = x - (y * (t / a))
	elif t_1 <= 0.05:
		tmp = x + (y * (z / a))
	elif t_1 <= 2.0:
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e-26)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 5e-127)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t_1 <= 0.05)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e-26)
		tmp = x + (z / ((a - t) / y));
	elseif (t_1 <= 5e-127)
		tmp = x - (y * (t / a));
	elseif (t_1 <= 0.05)
		tmp = x + (y * (z / a));
	elseif (t_1 <= 2.0)
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-26], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-127], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.05], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. div-inv 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l* 97.8%

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

      4. div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.9%

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

   7. Applied egg-rr 98.9%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999997e-127

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

      3. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in t around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 94.7%

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

   10. Simplified 94.7%

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

   if 4.9999999999999997e-127 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.050000000000000003

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if 0.050000000000000003 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. div-inv 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 97.0%

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

      4. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.05:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t\_1 \leq 0.05:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e-26)
     (+ x (/ z (/ (- a t) y)))
     (if (<= t_1 0.05)
       (+ x (/ (* y (- z t)) a))
       (if (<= t_1 2.0) (+ x y) (+ x (* z (/ y (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 0.05) {
		tmp = x + ((y * (z - t)) / a);
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d-26)) then
        tmp = x + (z / ((a - t) / y))
    else if (t_1 <= 0.05d0) then
        tmp = x + ((y * (z - t)) / a)
    else if (t_1 <= 2.0d0) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 0.05) {
		tmp = x + ((y * (z - t)) / a);
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e-26:
		tmp = x + (z / ((a - t) / y))
	elif t_1 <= 0.05:
		tmp = x + ((y * (z - t)) / a)
	elif t_1 <= 2.0:
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e-26)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 0.05)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e-26)
		tmp = x + (z / ((a - t) / y));
	elseif (t_1 <= 0.05)
		tmp = x + ((y * (z - t)) / a);
	elseif (t_1 <= 2.0)
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-26], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.05], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. div-inv 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l* 97.8%

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

      4. div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.9%

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

   7. Applied egg-rr 98.9%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.050000000000000003

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 93.5%

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

   if 0.050000000000000003 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.2%

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

      1. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. div-inv 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 97.0%

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

      4. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.05:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;t\_1 \leq 50000000:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e-26)
     (+ x (/ z (/ (- a t) y)))
     (if (<= t_1 0.4)
       (+ x (/ (* y (- z t)) a))
       (if (<= t_1 50000000.0)
         (- x (* y (+ (/ z t) -1.0)))
         (+ x (* z (/ y (- a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 0.4) {
		tmp = x + ((y * (z - t)) / a);
	} else if (t_1 <= 50000000.0) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d-26)) then
        tmp = x + (z / ((a - t) / y))
    else if (t_1 <= 0.4d0) then
        tmp = x + ((y * (z - t)) / a)
    else if (t_1 <= 50000000.0d0) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e-26) {
		tmp = x + (z / ((a - t) / y));
	} else if (t_1 <= 0.4) {
		tmp = x + ((y * (z - t)) / a);
	} else if (t_1 <= 50000000.0) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e-26:
		tmp = x + (z / ((a - t) / y))
	elif t_1 <= 0.4:
		tmp = x + ((y * (z - t)) / a)
	elif t_1 <= 50000000.0:
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e-26)
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	elseif (t_1 <= 0.4)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	elseif (t_1 <= 50000000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e-26)
		tmp = x + (z / ((a - t) / y));
	elseif (t_1 <= 0.4)
		tmp = x + ((y * (z - t)) / a);
	elseif (t_1 <= 50000000.0)
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-26], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.4], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 50000000.0], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000019e-26

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 83.3%

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

      1. div-inv 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l* 97.8%

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

      4. div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.9%

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

   7. Applied egg-rr 98.9%

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

   if -5.00000000000000019e-26 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.40000000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 93.5%

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

   if 0.40000000000000002 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

      3. associate-/l* 98.1%

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

      4. div-sub 98.1%

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

      5. sub-neg 98.1%

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

      6. *-inverses 98.1%

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

      7. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if 5e7 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 90.1%

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

      1. div-inv 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*l* 97.8%

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

      4. div-inv 97.9%

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

   5. Applied egg-rr 97.9%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.4:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50000000:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{-199}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-253}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+124}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= a -4.7e-199)
     (+ x y)
     (if (<= a -6.6e-221)
       t_1
       (if (<= a -7.4e-253)
         (+ x y)
         (if (<= a 2.7e-276) t_1 (if (<= a 7e+124) (+ x y) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (a <= -4.7e-199) {
		tmp = x + y;
	} else if (a <= -6.6e-221) {
		tmp = t_1;
	} else if (a <= -7.4e-253) {
		tmp = x + y;
	} else if (a <= 2.7e-276) {
		tmp = t_1;
	} else if (a <= 7e+124) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (a <= (-4.7d-199)) then
        tmp = x + y
    else if (a <= (-6.6d-221)) then
        tmp = t_1
    else if (a <= (-7.4d-253)) then
        tmp = x + y
    else if (a <= 2.7d-276) then
        tmp = t_1
    else if (a <= 7d+124) 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 t_1 = y * (z / (a - t));
	double tmp;
	if (a <= -4.7e-199) {
		tmp = x + y;
	} else if (a <= -6.6e-221) {
		tmp = t_1;
	} else if (a <= -7.4e-253) {
		tmp = x + y;
	} else if (a <= 2.7e-276) {
		tmp = t_1;
	} else if (a <= 7e+124) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if a <= -4.7e-199:
		tmp = x + y
	elif a <= -6.6e-221:
		tmp = t_1
	elif a <= -7.4e-253:
		tmp = x + y
	elif a <= 2.7e-276:
		tmp = t_1
	elif a <= 7e+124:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (a <= -4.7e-199)
		tmp = Float64(x + y);
	elseif (a <= -6.6e-221)
		tmp = t_1;
	elseif (a <= -7.4e-253)
		tmp = Float64(x + y);
	elseif (a <= 2.7e-276)
		tmp = t_1;
	elseif (a <= 7e+124)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (a <= -4.7e-199)
		tmp = x + y;
	elseif (a <= -6.6e-221)
		tmp = t_1;
	elseif (a <= -7.4e-253)
		tmp = x + y;
	elseif (a <= 2.7e-276)
		tmp = t_1;
	elseif (a <= 7e+124)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e-199], N[(x + y), $MachinePrecision], If[LessEqual[a, -6.6e-221], t$95$1, If[LessEqual[a, -7.4e-253], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.7e-276], t$95$1, If[LessEqual[a, 7e+124], N[(x + y), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.6999999999999996e-199 or -6.59999999999999979e-221 < a < -7.3999999999999995e-253 or 2.69999999999999985e-276 < a < 7.0000000000000002e124

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 65.1%

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

      1. +-commutative 65.1%

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

   5. Simplified 65.1%

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

   if -4.6999999999999996e-199 < a < -6.59999999999999979e-221 or -7.3999999999999995e-253 < a < 2.69999999999999985e-276

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 92.0%

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

      1. associate--l+ 92.0%

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

      2. div-sub 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in z around inf 73.6%

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

   if 7.0000000000000002e124 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-199}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-221}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-253}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+124}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-36}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 7 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+45)
   (+ x y)
   (if (<= t -5.7e-36)
     (- x (* t (/ y a)))
     (if (or (<= t -1.2e-119) (not (<= t 7e+93)))
       (+ x y)
       (+ x (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+45) {
		tmp = x + y;
	} else if (t <= -5.7e-36) {
		tmp = x - (t * (y / a));
	} else if ((t <= -1.2e-119) || !(t <= 7e+93)) {
		tmp = x + y;
	} 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 <= (-2.6d+45)) then
        tmp = x + y
    else if (t <= (-5.7d-36)) then
        tmp = x - (t * (y / a))
    else if ((t <= (-1.2d-119)) .or. (.not. (t <= 7d+93))) then
        tmp = x + y
    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 <= -2.6e+45) {
		tmp = x + y;
	} else if (t <= -5.7e-36) {
		tmp = x - (t * (y / a));
	} else if ((t <= -1.2e-119) || !(t <= 7e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+45:
		tmp = x + y
	elif t <= -5.7e-36:
		tmp = x - (t * (y / a))
	elif (t <= -1.2e-119) or not (t <= 7e+93):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+45)
		tmp = Float64(x + y);
	elseif (t <= -5.7e-36)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif ((t <= -1.2e-119) || !(t <= 7e+93))
		tmp = Float64(x + y);
	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 <= -2.6e+45)
		tmp = x + y;
	elseif (t <= -5.7e-36)
		tmp = x - (t * (y / a));
	elseif ((t <= -1.2e-119) || ~((t <= 7e+93)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+45], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.7e-36], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 7e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.60000000000000007e45 or -5.6999999999999999e-36 < t < -1.20000000000000004e-119 or 6.99999999999999996e93 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -2.60000000000000007e45 < t < -5.6999999999999999e-36

   1. Initial program 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

      3. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in t around 0 85.5%

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

      1. associate-/l* 85.4%

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

   10. Simplified 85.4%

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

   if -1.20000000000000004e-119 < t < 6.99999999999999996e93

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-36}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 7 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z t)))))
   (if (<= t -8e+101)
     (+ x y)
     (if (<= t -3.5e-137)
       t_1
       (if (<= t 6.8e-49)
         (+ x (* y (/ z a)))
         (if (<= t 1.05e+129) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / t));
	double tmp;
	if (t <= -8e+101) {
		tmp = x + y;
	} else if (t <= -3.5e-137) {
		tmp = t_1;
	} else if (t <= 6.8e-49) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+129) {
		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 / t))
    if (t <= (-8d+101)) then
        tmp = x + y
    else if (t <= (-3.5d-137)) then
        tmp = t_1
    else if (t <= 6.8d-49) then
        tmp = x + (y * (z / a))
    else if (t <= 1.05d+129) 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 / t));
	double tmp;
	if (t <= -8e+101) {
		tmp = x + y;
	} else if (t <= -3.5e-137) {
		tmp = t_1;
	} else if (t <= 6.8e-49) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+129) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / t))
	tmp = 0
	if t <= -8e+101:
		tmp = x + y
	elif t <= -3.5e-137:
		tmp = t_1
	elif t <= 6.8e-49:
		tmp = x + (y * (z / a))
	elif t <= 1.05e+129:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -8e+101)
		tmp = Float64(x + y);
	elseif (t <= -3.5e-137)
		tmp = t_1;
	elseif (t <= 6.8e-49)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.05e+129)
		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 / t));
	tmp = 0.0;
	if (t <= -8e+101)
		tmp = x + y;
	elseif (t <= -3.5e-137)
		tmp = t_1;
	elseif (t <= 6.8e-49)
		tmp = x + (y * (z / a));
	elseif (t <= 1.05e+129)
		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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+101], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.5e-137], t$95$1, If[LessEqual[t, 6.8e-49], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+129], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.9999999999999998e101 or 1.04999999999999998e129 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.0%

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

      1. +-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -7.9999999999999998e101 < t < -3.5000000000000001e-137 or 6.8000000000000001e-49 < t < 1.04999999999999998e129

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 81.7%

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

   4. Taylor expanded in a around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. associate-/l* 73.2%

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

   6. Simplified 73.2%

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

   if -3.5000000000000001e-137 < t < 6.8000000000000001e-49

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-137}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-119) (not (<= t 1.8e+93))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} 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 <= (-1.2d-119)) .or. (.not. (t <= 1.8d+93))) then
        tmp = x + y
    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 <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-119) or not (t <= 1.8e+93):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-119) || !(t <= 1.8e+93))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e-119) || ~((t <= 1.8e+93)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 1.8e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000004e-119 or 1.8e93 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 69.8%

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

      1. +-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -1.20000000000000004e-119 < t < 1.8e93

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 72.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e-119) (not (<= t 1.8e+93))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} 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 <= (-1.2d-119)) .or. (.not. (t <= 1.8d+93))) then
        tmp = x + y
    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 <= -1.2e-119) || !(t <= 1.8e+93)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e-119) or not (t <= 1.8e+93):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e-119) || !(t <= 1.8e+93))
		tmp = Float64(x + y);
	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 <= -1.2e-119) || ~((t <= 1.8e+93)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e-119], N[Not[LessEqual[t, 1.8e+93]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000004e-119 or 1.8e93 < t

   1. Initial program 99.1%

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

   3. Taylor expanded in t around inf 69.8%

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

      1. +-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -1.20000000000000004e-119 < t < 1.8e93

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-119} \lor \neg \left(t \leq 1.8 \cdot 10^{+93}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.4% 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 98.8%

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

3. Final simplification 98.8%

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

Alternative 14: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 4.8e+126) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.8e+126) {
		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 <= 4.8d+126) 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 <= 4.8e+126) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 4.8e+126:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4.8e+126)
		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 <= 4.8e+126)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 4.8e+126], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 4.80000000000000024e126

   1. Initial program 98.6%

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

   3. Taylor expanded in t around inf 60.2%

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

      1. +-commutative 60.2%

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

   5. Simplified 60.2%

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

   if 4.80000000000000024e126 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.9% 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 98.8%

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

3. Taylor expanded in x around inf 50.3%

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

4. Final simplification 50.3%

   \[\leadsto x \]
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 2024066 
(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)))))