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

Percentage Accurate: 76.2% → 90.4%

Time: 11.0s

Alternatives: 13

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+109} \lor \neg \left(t \leq 7.5 \cdot 10^{+95}\right):\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+109) (not (<= t 7.5e+95)))
   (- (+ x (* y (/ z t))) (* a (/ y t)))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+109) || !(t <= 7.5e+95)) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.5d+109)) .or. (.not. (t <= 7.5d+95))) then
        tmp = (x + (y * (z / t))) - (a * (y / t))
    else
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+109) || !(t <= 7.5e+95)) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+109) or not (t <= 7.5e+95):
		tmp = (x + (y * (z / t))) - (a * (y / t))
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+109) || !(t <= 7.5e+95))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) - Float64(a * Float64(y / t)));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e+109) || ~((t <= 7.5e+95)))
		tmp = (x + (y * (z / t))) - (a * (y / t));
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+109], N[Not[LessEqual[t, 7.5e+95]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999996e109 or 7.5000000000000001e95 < t

   1. Initial program 42.0%

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

      1. sub-neg 42.0%

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

      2. +-commutative 42.0%

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

      3. distribute-frac-neg 42.0%

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

      4. distribute-rgt-neg-out 42.0%

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

      5. associate-/l* 57.8%

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

      6. fma-define 58.1%

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

      7. distribute-frac-neg 58.1%

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

      8. distribute-neg-frac2 58.1%

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

      9. sub-neg 58.1%

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

      10. distribute-neg-in 58.1%

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

      11. remove-double-neg 58.1%

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

      12. +-commutative 58.1%

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

      13. sub-neg 58.1%

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

   3. Simplified 58.1%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. associate-+r+ 77.0%

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

      2. distribute-rgt1-in 77.0%

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

      3. metadata-eval 77.0%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. mul0-lft 77.0%

         \[\leadsto \left(x + \left(\color{blue}{0} + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-+r+ 77.0%

         \[\leadsto \color{blue}{\left(\left(x + 0\right) + \frac{y \cdot z}{t}\right)} - \frac{a \cdot y}{t} \]

      6. associate-/l* 82.7%

         \[\leadsto \left(\left(x + 0\right) + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t} \]

      7. associate-/l* 89.5%

         \[\leadsto \left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 89.5%

      \[\leadsto \color{blue}{\left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}} \]

   if -4.4999999999999996e109 < t < 7.5000000000000001e95

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 90.5%

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

      1. associate-*l/ 94.1%

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

   5. Simplified 94.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+109} \lor \neg \left(t \leq 7.5 \cdot 10^{+95}\right):\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq -1.6 \cdot 10^{-51} \lor \neg \left(z \leq -3.15 \cdot 10^{-55}\right) \land z \leq 9.6 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+140)
         (not
          (or (<= z -1.6e-51) (and (not (<= z -3.15e-55)) (<= z 9.6e+96)))))
   (* y (/ z (- t a)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+140) || !((z <= -1.6e-51) || (!(z <= -3.15e-55) && (z <= 9.6e+96)))) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+140)) .or. (.not. (z <= (-1.6d-51)) .or. (.not. (z <= (-3.15d-55))) .and. (z <= 9.6d+96))) then
        tmp = y * (z / (t - a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+140) || !((z <= -1.6e-51) || (!(z <= -3.15e-55) && (z <= 9.6e+96)))) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+140) or not ((z <= -1.6e-51) or (not (z <= -3.15e-55) and (z <= 9.6e+96))):
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+140) || !((z <= -1.6e-51) || (!(z <= -3.15e-55) && (z <= 9.6e+96))))
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+140) || ~(((z <= -1.6e-51) || (~((z <= -3.15e-55)) && (z <= 9.6e+96)))))
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+140], N[Not[Or[LessEqual[z, -1.6e-51], And[N[Not[LessEqual[z, -3.15e-55]], $MachinePrecision], LessEqual[z, 9.6e+96]]]], $MachinePrecision]], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e140 or -1.6e-51 < z < -3.1499999999999999e-55 or 9.59999999999999972e96 < z

   1. Initial program 76.4%

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

      1. sub-neg 76.4%

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

      2. +-commutative 76.4%

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

      3. distribute-frac-neg 76.4%

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

      4. distribute-rgt-neg-out 76.4%

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

      5. associate-/l* 90.7%

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

      6. fma-define 90.8%

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

      7. distribute-frac-neg 90.8%

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

      8. distribute-neg-frac2 90.8%

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

      9. sub-neg 90.8%

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

      10. distribute-neg-in 90.8%

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

      11. remove-double-neg 90.8%

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

      12. +-commutative 90.8%

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

      13. sub-neg 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate-/l* 66.3%

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

   7. Simplified 66.3%

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

   if -8.4999999999999996e140 < z < -1.6e-51 or -3.1499999999999999e-55 < z < 9.59999999999999972e96

   1. Initial program 73.9%

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

   3. Taylor expanded in a around inf 70.0%

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

      1. +-commutative 70.0%

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

   5. Simplified 70.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140} \lor \neg \left(z \leq -1.6 \cdot 10^{-51} \lor \neg \left(z \leq -3.15 \cdot 10^{-55}\right) \land z \leq 9.6 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+198}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \frac{y}{-t}\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-103}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.25e+198)
   (+ x y)
   (if (<= y -4.7e+116)
     (* a (/ y (- t)))
     (if (<= y -1.04e-103)
       (+ x y)
       (if (<= y 1.75e+18) x (* y (- 1.0 (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.25e+198) {
		tmp = x + y;
	} else if (y <= -4.7e+116) {
		tmp = a * (y / -t);
	} else if (y <= -1.04e-103) {
		tmp = x + y;
	} else if (y <= 1.75e+18) {
		tmp = x;
	} else {
		tmp = y * (1.0 - (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 (y <= (-1.25d+198)) then
        tmp = x + y
    else if (y <= (-4.7d+116)) then
        tmp = a * (y / -t)
    else if (y <= (-1.04d-103)) then
        tmp = x + y
    else if (y <= 1.75d+18) then
        tmp = x
    else
        tmp = y * (1.0d0 - (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 (y <= -1.25e+198) {
		tmp = x + y;
	} else if (y <= -4.7e+116) {
		tmp = a * (y / -t);
	} else if (y <= -1.04e-103) {
		tmp = x + y;
	} else if (y <= 1.75e+18) {
		tmp = x;
	} else {
		tmp = y * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.25e+198:
		tmp = x + y
	elif y <= -4.7e+116:
		tmp = a * (y / -t)
	elif y <= -1.04e-103:
		tmp = x + y
	elif y <= 1.75e+18:
		tmp = x
	else:
		tmp = y * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.25e+198)
		tmp = Float64(x + y);
	elseif (y <= -4.7e+116)
		tmp = Float64(a * Float64(y / Float64(-t)));
	elseif (y <= -1.04e-103)
		tmp = Float64(x + y);
	elseif (y <= 1.75e+18)
		tmp = x;
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.25e+198)
		tmp = x + y;
	elseif (y <= -4.7e+116)
		tmp = a * (y / -t);
	elseif (y <= -1.04e-103)
		tmp = x + y;
	elseif (y <= 1.75e+18)
		tmp = x;
	else
		tmp = y * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.25e+198], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.7e+116], N[(a * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.04e-103], N[(x + y), $MachinePrecision], If[LessEqual[y, 1.75e+18], x, N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.25000000000000012e198 or -4.7000000000000003e116 < y < -1.04000000000000001e-103

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -1.25000000000000012e198 < y < -4.7000000000000003e116

   1. Initial program 45.8%

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

      1. sub-neg 45.8%

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

      2. +-commutative 45.8%

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

      3. distribute-frac-neg 45.8%

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

      4. distribute-rgt-neg-out 45.8%

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

      5. associate-/l* 60.0%

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

      6. fma-define 60.2%

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

      7. distribute-frac-neg 60.2%

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

      8. distribute-neg-frac2 60.2%

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

      9. sub-neg 60.2%

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

      10. distribute-neg-in 60.2%

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

      11. remove-double-neg 60.2%

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

      12. +-commutative 60.2%

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

      13. sub-neg 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in t around inf 72.4%

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

      1. associate-+r+ 72.4%

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

      2. distribute-rgt1-in 72.4%

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

      3. metadata-eval 72.4%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. mul0-lft 72.4%

         \[\leadsto \left(x + \left(\color{blue}{0} + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-+r+ 72.4%

         \[\leadsto \color{blue}{\left(\left(x + 0\right) + \frac{y \cdot z}{t}\right)} - \frac{a \cdot y}{t} \]

      6. associate-/l* 81.5%

         \[\leadsto \left(\left(x + 0\right) + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t} \]

      7. associate-/l* 81.5%

         \[\leadsto \left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 81.5%

      \[\leadsto \color{blue}{\left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in a around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. associate-*r/ 49.0%

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

      3. distribute-rgt-neg-in 49.0%

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

      4. distribute-neg-frac2 49.0%

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

   10. Simplified 49.0%

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

   if -1.04000000000000001e-103 < y < 1.75e18

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf 78.2%

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

   if 1.75e18 < y

   1. Initial program 59.7%

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

   3. Taylor expanded in t around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around inf 58.6%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+198}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \frac{y}{-t}\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-103}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-278}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e-14)
   (+ x y)
   (if (<= a -2.55e-278)
     x
     (if (<= a 2.35e-278) (/ (* y z) t) (if (<= a 5.5e-26) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-14) {
		tmp = x + y;
	} else if (a <= -2.55e-278) {
		tmp = x;
	} else if (a <= 2.35e-278) {
		tmp = (y * z) / t;
	} else if (a <= 5.5e-26) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d-14)) then
        tmp = x + y
    else if (a <= (-2.55d-278)) then
        tmp = x
    else if (a <= 2.35d-278) then
        tmp = (y * z) / t
    else if (a <= 5.5d-26) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e-14) {
		tmp = x + y;
	} else if (a <= -2.55e-278) {
		tmp = x;
	} else if (a <= 2.35e-278) {
		tmp = (y * z) / t;
	} else if (a <= 5.5e-26) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e-14:
		tmp = x + y
	elif a <= -2.55e-278:
		tmp = x
	elif a <= 2.35e-278:
		tmp = (y * z) / t
	elif a <= 5.5e-26:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e-14)
		tmp = Float64(x + y);
	elseif (a <= -2.55e-278)
		tmp = x;
	elseif (a <= 2.35e-278)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 5.5e-26)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e-14)
		tmp = x + y;
	elseif (a <= -2.55e-278)
		tmp = x;
	elseif (a <= 2.35e-278)
		tmp = (y * z) / t;
	elseif (a <= 5.5e-26)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e-14], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.55e-278], x, If[LessEqual[a, 2.35e-278], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 5.5e-26], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9000000000000003e-14 or 5.5000000000000005e-26 < a

   1. Initial program 77.2%

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

   3. Taylor expanded in a around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -2.9000000000000003e-14 < a < -2.55000000000000005e-278 or 2.3499999999999998e-278 < a < 5.5000000000000005e-26

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf 56.6%

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

   if -2.55000000000000005e-278 < a < 2.3499999999999998e-278

   1. Initial program 67.8%

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

      1. sub-neg 67.8%

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

      2. +-commutative 67.8%

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

      3. distribute-frac-neg 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

      5. associate-/l* 68.2%

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

      6. fma-define 68.1%

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

      7. distribute-frac-neg 68.1%

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

      8. distribute-neg-frac2 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-neg-in 68.1%

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

      11. remove-double-neg 68.1%

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

      12. +-commutative 68.1%

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

      13. sub-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 77.3%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in t around inf 77.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-278}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-276}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-13)
   (+ x y)
   (if (<= a -2.25e-278)
     x
     (if (<= a 1e-276) (* y (/ z t)) (if (<= a 5.8e-35) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-13) {
		tmp = x + y;
	} else if (a <= -2.25e-278) {
		tmp = x;
	} else if (a <= 1e-276) {
		tmp = y * (z / t);
	} else if (a <= 5.8e-35) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d-13)) then
        tmp = x + y
    else if (a <= (-2.25d-278)) then
        tmp = x
    else if (a <= 1d-276) then
        tmp = y * (z / t)
    else if (a <= 5.8d-35) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-13) {
		tmp = x + y;
	} else if (a <= -2.25e-278) {
		tmp = x;
	} else if (a <= 1e-276) {
		tmp = y * (z / t);
	} else if (a <= 5.8e-35) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-13:
		tmp = x + y
	elif a <= -2.25e-278:
		tmp = x
	elif a <= 1e-276:
		tmp = y * (z / t)
	elif a <= 5.8e-35:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-13)
		tmp = Float64(x + y);
	elseif (a <= -2.25e-278)
		tmp = x;
	elseif (a <= 1e-276)
		tmp = Float64(y * Float64(z / t));
	elseif (a <= 5.8e-35)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e-13)
		tmp = x + y;
	elseif (a <= -2.25e-278)
		tmp = x;
	elseif (a <= 1e-276)
		tmp = y * (z / t);
	elseif (a <= 5.8e-35)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-13], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.25e-278], x, If[LessEqual[a, 1e-276], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-35], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.09999999999999998e-13 or 5.8000000000000004e-35 < a

   1. Initial program 77.2%

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

   3. Taylor expanded in a around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.09999999999999998e-13 < a < -2.2499999999999999e-278 or 1e-276 < a < 5.8000000000000004e-35

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf 56.6%

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

   if -2.2499999999999999e-278 < a < 1e-276

   1. Initial program 67.8%

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

      1. sub-neg 67.8%

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

      2. +-commutative 67.8%

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

      3. distribute-frac-neg 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

      5. associate-/l* 68.2%

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

      6. fma-define 68.1%

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

      7. distribute-frac-neg 68.1%

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

      8. distribute-neg-frac2 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-neg-in 68.1%

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

      11. remove-double-neg 68.1%

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

      12. +-commutative 68.1%

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

      13. sub-neg 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around inf 77.3%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in t around inf 77.3%

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

      1. associate-/l* 69.7%

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

   10. Simplified 69.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-276}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+201} \lor \neg \left(t \leq 1.55 \cdot 10^{+98}\right):\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+201) (not (<= t 1.55e+98)))
   (- x (/ (* y (- a z)) t))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+201) || !(t <= 1.55e+98)) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.8d+201)) .or. (.not. (t <= 1.55d+98))) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+201) || !(t <= 1.55e+98)) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+201) or not (t <= 1.55e+98):
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+201) || !(t <= 1.55e+98))
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+201) || ~((t <= 1.55e+98)))
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+201], N[Not[LessEqual[t, 1.55e+98]], $MachinePrecision]], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000005e201 or 1.5500000000000001e98 < t

   1. Initial program 38.6%

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

   3. Taylor expanded in t around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. distribute-lft-out-- 79.3%

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

      3. div-sub 79.3%

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

      4. mul-1-neg 79.3%

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

      5. unsub-neg 79.3%

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

      6. *-commutative 79.3%

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

      7. distribute-lft-out-- 79.4%

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

   5. Simplified 79.4%

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

   if -2.80000000000000005e201 < t < 1.5500000000000001e98

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 88.2%

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

      1. associate-*l/ 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+201} \lor \neg \left(t \leq 1.55 \cdot 10^{+98}\right):\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e+116)
   (* y (/ (- z a) t))
   (if (<= y -1.06e-101) (+ x y) (if (<= y 2.9e+19) x (* y (- 1.0 (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e+116) {
		tmp = y * ((z - a) / t);
	} else if (y <= -1.06e-101) {
		tmp = x + y;
	} else if (y <= 2.9e+19) {
		tmp = x;
	} else {
		tmp = y * (1.0 - (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 (y <= (-2.7d+116)) then
        tmp = y * ((z - a) / t)
    else if (y <= (-1.06d-101)) then
        tmp = x + y
    else if (y <= 2.9d+19) then
        tmp = x
    else
        tmp = y * (1.0d0 - (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 (y <= -2.7e+116) {
		tmp = y * ((z - a) / t);
	} else if (y <= -1.06e-101) {
		tmp = x + y;
	} else if (y <= 2.9e+19) {
		tmp = x;
	} else {
		tmp = y * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e+116:
		tmp = y * ((z - a) / t)
	elif y <= -1.06e-101:
		tmp = x + y
	elif y <= 2.9e+19:
		tmp = x
	else:
		tmp = y * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.7e+116)
		tmp = Float64(y * Float64(Float64(z - a) / t));
	elseif (y <= -1.06e-101)
		tmp = Float64(x + y);
	elseif (y <= 2.9e+19)
		tmp = x;
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.7e+116)
		tmp = y * ((z - a) / t);
	elseif (y <= -1.06e-101)
		tmp = x + y;
	elseif (y <= 2.9e+19)
		tmp = x;
	else
		tmp = y * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.7e+116], N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.06e-101], N[(x + y), $MachinePrecision], If[LessEqual[y, 2.9e+19], x, N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e116

   1. Initial program 55.5%

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

      1. sub-neg 55.5%

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

      2. +-commutative 55.5%

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

      3. distribute-frac-neg 55.5%

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

      4. distribute-rgt-neg-out 55.5%

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

      5. associate-/l* 70.5%

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

      6. fma-define 70.5%

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

      7. distribute-frac-neg 70.5%

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

      8. distribute-neg-frac2 70.5%

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

      9. sub-neg 70.5%

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

      10. distribute-neg-in 70.5%

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

      11. remove-double-neg 70.5%

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

      12. +-commutative 70.5%

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

      13. sub-neg 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in t around inf 60.5%

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

      1. associate-+r+ 63.3%

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

      2. distribute-rgt1-in 63.3%

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

      3. metadata-eval 63.3%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. mul0-lft 63.3%

         \[\leadsto \left(x + \left(\color{blue}{0} + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-+r+ 63.3%

         \[\leadsto \color{blue}{\left(\left(x + 0\right) + \frac{y \cdot z}{t}\right)} - \frac{a \cdot y}{t} \]

      6. associate-/l* 67.5%

         \[\leadsto \left(\left(x + 0\right) + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t} \]

      7. associate-/l* 67.5%

         \[\leadsto \left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{\left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in y around inf 56.7%

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

      1. div-sub 56.7%

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

   10. Simplified 56.7%

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

   if -2.7e116 < y < -1.0600000000000001e-101

   1. Initial program 84.8%

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

   3. Taylor expanded in a around inf 76.6%

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

      1. +-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -1.0600000000000001e-101 < y < 2.9e19

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf 78.2%

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

   if 2.9e19 < y

   1. Initial program 59.7%

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

   3. Taylor expanded in t around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around inf 58.6%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+14} \lor \neg \left(a \leq 4.5 \cdot 10^{-25}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e+14) (not (<= a 4.5e-25)))
   (- (+ x y) (* y (/ z a)))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e+14) || !(a <= 4.5e-25)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / 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 ((a <= (-1.3d+14)) .or. (.not. (a <= 4.5d-25))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - ((y * (a - z)) / 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 ((a <= -1.3e+14) || !(a <= 4.5e-25)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e+14) or not (a <= 4.5e-25):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e+14) || !(a <= 4.5e-25))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e+14) || ~((a <= 4.5e-25)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e+14], N[Not[LessEqual[a, 4.5e-25]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e14 or 4.5000000000000001e-25 < a

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 84.3%

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

   5. Simplified 84.3%

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

   if -1.3e14 < a < 4.5000000000000001e-25

   1. Initial program 71.6%

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

   3. Taylor expanded in t around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. distribute-lft-out-- 82.8%

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

      3. div-sub 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. *-commutative 82.8%

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

      7. distribute-lft-out-- 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+14} \lor \neg \left(a \leq 4.5 \cdot 10^{-25}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+14} \lor \neg \left(a \leq 1.48 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.1e+14) (not (<= a 1.48e+57)))
   (+ x y)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.1e+14) || !(a <= 1.48e+57)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / 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 ((a <= (-4.1d+14)) .or. (.not. (a <= 1.48d+57))) then
        tmp = x + y
    else
        tmp = x - ((y * (a - z)) / 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 ((a <= -4.1e+14) || !(a <= 1.48e+57)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.1e+14) or not (a <= 1.48e+57):
		tmp = x + y
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.1e+14) || !(a <= 1.48e+57))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.1e+14) || ~((a <= 1.48e+57)))
		tmp = x + y;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.1e+14], N[Not[LessEqual[a, 1.48e+57]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1e14 or 1.47999999999999999e57 < a

   1. Initial program 78.4%

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

   3. Taylor expanded in a around inf 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if -4.1e14 < a < 1.47999999999999999e57

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 81.8%

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

      4. mul-1-neg 81.8%

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

      5. unsub-neg 81.8%

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

      6. *-commutative 81.8%

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

      7. distribute-lft-out-- 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+14} \lor \neg \left(a \leq 1.48 \cdot 10^{+57}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+19} \lor \neg \left(a \leq 1.95 \cdot 10^{+26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e+19) (not (<= a 1.95e+26))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e+19) || !(a <= 1.95e+26)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / 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 ((a <= (-3.3d+19)) .or. (.not. (a <= 1.95d+26))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / 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 ((a <= -3.3e+19) || !(a <= 1.95e+26)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e+19) or not (a <= 1.95e+26):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e+19) || !(a <= 1.95e+26))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e+19) || ~((a <= 1.95e+26)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e+19], N[Not[LessEqual[a, 1.95e+26]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3e19 or 1.95e26 < a

   1. Initial program 76.6%

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

   3. Taylor expanded in a around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -3.3e19 < a < 1.95e26

   1. Initial program 72.6%

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

      1. sub-neg 72.6%

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

      2. +-commutative 72.6%

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

      3. distribute-frac-neg 72.6%

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

      4. distribute-rgt-neg-out 72.6%

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

      5. associate-/l* 77.6%

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

      6. fma-define 77.6%

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

      7. distribute-frac-neg 77.6%

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

      8. distribute-neg-frac2 77.6%

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

      9. sub-neg 77.6%

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

      10. distribute-neg-in 77.6%

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

      11. remove-double-neg 77.6%

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

      12. +-commutative 77.6%

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

      13. sub-neg 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around inf 75.2%

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

      1. associate-+r+ 81.5%

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

      2. distribute-rgt1-in 81.5%

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

      3. metadata-eval 81.5%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. mul0-lft 81.5%

         \[\leadsto \left(x + \left(\color{blue}{0} + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-+r+ 81.5%

         \[\leadsto \color{blue}{\left(\left(x + 0\right) + \frac{y \cdot z}{t}\right)} - \frac{a \cdot y}{t} \]

      6. associate-/l* 80.1%

         \[\leadsto \left(\left(x + 0\right) + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t} \]

      7. associate-/l* 75.3%

         \[\leadsto \left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{\left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}} \]

   8. Taylor expanded in a around 0 80.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+19} \lor \neg \left(a \leq 1.95 \cdot 10^{+26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-13} \lor \neg \left(a \leq 1.75 \cdot 10^{-28}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-13) (not (<= a 1.75e-28))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-13) || !(a <= 1.75e-28)) {
		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 <= (-5.5d-13)) .or. (.not. (a <= 1.75d-28))) 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 <= -5.5e-13) || !(a <= 1.75e-28)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e-13) or not (a <= 1.75e-28):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e-13) || !(a <= 1.75e-28))
		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 <= -5.5e-13) || ~((a <= 1.75e-28)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e-13], N[Not[LessEqual[a, 1.75e-28]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999979e-13 or 1.75e-28 < a

   1. Initial program 77.2%

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

   3. Taylor expanded in a around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -5.49999999999999979e-13 < a < 1.75e-28

   1. Initial program 71.4%

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

   3. Taylor expanded in x around inf 52.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-13} \lor \neg \left(a \leq 1.75 \cdot 10^{-28}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 1.45e+100) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.45e+100) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.45d+100) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.45e+100) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.45e+100:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.45e+100)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.45e+100)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.45e+100], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.45e100

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf 57.4%

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

   if 1.45e100 < y

   1. Initial program 58.5%

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

   3. Taylor expanded in x around 0 56.0%

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

      1. sub-neg 56.0%

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

      2. *-rgt-identity 56.0%

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

      3. associate-*r/ 74.8%

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

      4. distribute-rgt-neg-in 74.8%

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

      5. mul-1-neg 74.8%

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

      6. distribute-lft-in 74.8%

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

      7. mul-1-neg 74.8%

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

      8. unsub-neg 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in a around inf 30.1%

      \[\leadsto y \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 13.0× 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 74.6%

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

3. Taylor expanded in x around inf 51.0%

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

Developer target: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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