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

Percentage Accurate: 76.5% → 93.3%

Time: 11.5s

Alternatives: 15

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: 76.5% 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: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (+ 1.0 (/ (- z t) (- t a))))))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 -1e-247) t_1 (if (<= t_2 0.0) (+ x (/ (* y (- z a)) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 + ((z - t) / (t - a))));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -1e-247) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x + ((y * (z - 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 = x + (y * (1.0d0 + ((z - t) / (t - a))))
    t_2 = (x + y) + ((y * (z - t)) / (t - a))
    if (t_2 <= (-1d-247)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x + ((y * (z - 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 * (1.0 + ((z - t) / (t - a))));
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -1e-247) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 + ((z - t) / (t - a))))
	t_2 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if t_2 <= -1e-247:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a)))))
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= -1e-247)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 + ((z - t) / (t - a))));
	t_2 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if (t_2 <= -1e-247)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x + ((y * (z - 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[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-247], t$95$1, If[LessEqual[t$95$2, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1e-247 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 84.7%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 97.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 97.0%

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

   if -1e-247 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 99.7%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -1 \cdot 10^{-247}:\\ \;\;\;\;x + y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.62 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y a)))))
   (if (<= a -1.15e+147)
     (+ x y)
     (if (<= a -2.62e-11)
       t_1
       (if (<= a 9.8e-92)
         (+ x (* y (/ (- z a) t)))
         (if (<= a 1.65e+79) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / a));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = x + y;
	} else if (a <= -2.62e-11) {
		tmp = t_1;
	} else if (a <= 9.8e-92) {
		tmp = x + (y * ((z - a) / t));
	} else if (a <= 1.65e+79) {
		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 - (z * (y / a))
    if (a <= (-1.15d+147)) then
        tmp = x + y
    else if (a <= (-2.62d-11)) then
        tmp = t_1
    else if (a <= 9.8d-92) then
        tmp = x + (y * ((z - a) / t))
    else if (a <= 1.65d+79) 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 - (z * (y / a));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = x + y;
	} else if (a <= -2.62e-11) {
		tmp = t_1;
	} else if (a <= 9.8e-92) {
		tmp = x + (y * ((z - a) / t));
	} else if (a <= 1.65e+79) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (y / a))
	tmp = 0
	if a <= -1.15e+147:
		tmp = x + y
	elif a <= -2.62e-11:
		tmp = t_1
	elif a <= 9.8e-92:
		tmp = x + (y * ((z - a) / t))
	elif a <= 1.65e+79:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.15e+147)
		tmp = Float64(x + y);
	elseif (a <= -2.62e-11)
		tmp = t_1;
	elseif (a <= 9.8e-92)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	elseif (a <= 1.65e+79)
		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 - (z * (y / a));
	tmp = 0.0;
	if (a <= -1.15e+147)
		tmp = x + y;
	elseif (a <= -2.62e-11)
		tmp = t_1;
	elseif (a <= 9.8e-92)
		tmp = x + (y * ((z - a) / t));
	elseif (a <= 1.65e+79)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+147], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.62e-11], t$95$1, If[LessEqual[a, 9.8e-92], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+79], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e147 or 1.6500000000000001e79 < a

   1. Initial program 77.0%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 95.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 95.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 84.4%

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

   if -1.15e147 < a < -2.62000000000000006e-11 or 9.8e-92 < a < 1.6500000000000001e79

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 89.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 89.1%

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

      1. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{y \cdot z}{\color{blue}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{z \cdot y}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 87.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 87.9%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, a\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 78.8%

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

   if -2.62000000000000006e-11 < a < 9.8e-92

   1. Initial program 75.2%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z + -1 \cdot a\right)}{t}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z + -1 \cdot a}{t}}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z + \left(\mathsf{neg}\left(a\right)\right)}{t}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z - a}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - a\right), \color{blue}{t}\right)\right)\right) \]

      7. --lowering--.f64 87.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, a\right), t\right)\right)\right) \]

   7. Simplified 87.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.62 \cdot 10^{-11}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y a)))))
   (if (<= a -1.15e+147)
     (+ x y)
     (if (<= a -1.42e-10)
       t_1
       (if (<= a 2.6e-85)
         (+ x (* y (/ z t)))
         (if (<= a 2.35e+79) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / a));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = x + y;
	} else if (a <= -1.42e-10) {
		tmp = t_1;
	} else if (a <= 2.6e-85) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.35e+79) {
		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 - (z * (y / a))
    if (a <= (-1.15d+147)) then
        tmp = x + y
    else if (a <= (-1.42d-10)) then
        tmp = t_1
    else if (a <= 2.6d-85) then
        tmp = x + (y * (z / t))
    else if (a <= 2.35d+79) 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 - (z * (y / a));
	double tmp;
	if (a <= -1.15e+147) {
		tmp = x + y;
	} else if (a <= -1.42e-10) {
		tmp = t_1;
	} else if (a <= 2.6e-85) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.35e+79) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (y / a))
	tmp = 0
	if a <= -1.15e+147:
		tmp = x + y
	elif a <= -1.42e-10:
		tmp = t_1
	elif a <= 2.6e-85:
		tmp = x + (y * (z / t))
	elif a <= 2.35e+79:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.15e+147)
		tmp = Float64(x + y);
	elseif (a <= -1.42e-10)
		tmp = t_1;
	elseif (a <= 2.6e-85)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= 2.35e+79)
		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 - (z * (y / a));
	tmp = 0.0;
	if (a <= -1.15e+147)
		tmp = x + y;
	elseif (a <= -1.42e-10)
		tmp = t_1;
	elseif (a <= 2.6e-85)
		tmp = x + (y * (z / t));
	elseif (a <= 2.35e+79)
		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[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+147], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.42e-10], t$95$1, If[LessEqual[a, 2.6e-85], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+79], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e147 or 2.35000000000000011e79 < a

   1. Initial program 77.0%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 95.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 95.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 84.4%

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

   if -1.15e147 < a < -1.42000000000000001e-10 or 2.60000000000000011e-85 < a < 2.35000000000000011e79

   1. Initial program 87.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 88.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 88.9%

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

      1. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{y \cdot z}{\color{blue}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{z \cdot y}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 87.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 87.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, a\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 79.8%

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

   if -1.42000000000000001e-10 < a < 2.60000000000000011e-85

   1. Initial program 75.5%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 90.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 90.0%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 84.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 84.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z a)))))
   (if (<= a -1.5e+147)
     (+ x y)
     (if (<= a -3.9e-7)
       t_1
       (if (<= a 2.6e-85)
         (+ x (* y (/ z t)))
         (if (<= a 2.6e+79) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / a));
	double tmp;
	if (a <= -1.5e+147) {
		tmp = x + y;
	} else if (a <= -3.9e-7) {
		tmp = t_1;
	} else if (a <= 2.6e-85) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.6e+79) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (z / a))
    if (a <= (-1.5d+147)) then
        tmp = x + y
    else if (a <= (-3.9d-7)) then
        tmp = t_1
    else if (a <= 2.6d-85) then
        tmp = x + (y * (z / t))
    else if (a <= 2.6d+79) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / a));
	double tmp;
	if (a <= -1.5e+147) {
		tmp = x + y;
	} else if (a <= -3.9e-7) {
		tmp = t_1;
	} else if (a <= 2.6e-85) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.6e+79) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / a))
	tmp = 0
	if a <= -1.5e+147:
		tmp = x + y
	elif a <= -3.9e-7:
		tmp = t_1
	elif a <= 2.6e-85:
		tmp = x + (y * (z / t))
	elif a <= 2.6e+79:
		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 / a)))
	tmp = 0.0
	if (a <= -1.5e+147)
		tmp = Float64(x + y);
	elseif (a <= -3.9e-7)
		tmp = t_1;
	elseif (a <= 2.6e-85)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= 2.6e+79)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / a));
	tmp = 0.0;
	if (a <= -1.5e+147)
		tmp = x + y;
	elseif (a <= -3.9e-7)
		tmp = t_1;
	elseif (a <= 2.6e-85)
		tmp = x + (y * (z / t));
	elseif (a <= 2.6e+79)
		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 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+147], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.9e-7], t$95$1, If[LessEqual[a, 2.6e-85], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+79], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999997e147 or 2.60000000000000015e79 < a

   1. Initial program 77.0%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 95.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 95.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 84.4%

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

   if -1.49999999999999997e147 < a < -3.90000000000000025e-7 or 2.60000000000000011e-85 < a < 2.60000000000000015e79

   1. Initial program 86.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 88.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 88.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 80.2%

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

   if -3.90000000000000025e-7 < a < 2.60000000000000011e-85

   1. Initial program 75.9%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 90.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 90.2%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 84.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 84.2%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+147}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+79}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z \cdot \left(\frac{-1}{a - t} - \frac{\frac{t}{t - a} + -1}{z}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (* z (- (/ -1.0 (- a t)) (/ (+ (/ t (- t a)) -1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (z * ((-1.0 / (a - t)) - (((t / (t - a)) + -1.0) / z))));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * (z * (((-1.0d0) / (a - t)) - (((t / (t - a)) + (-1.0d0)) / z))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (z * ((-1.0 / (a - t)) - (((t / (t - a)) + -1.0) / z))));
}

Python

def code(x, y, z, t, a):
	return x + (y * (z * ((-1.0 / (a - t)) - (((t / (t - a)) + -1.0) / z))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(z * Float64(Float64(-1.0 / Float64(a - t)) - Float64(Float64(Float64(t / Float64(t - a)) + -1.0) / z)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (z * ((-1.0 / (a - t)) - (((t / (t - a)) + -1.0) / z))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(z * N[(N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.0%

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

   1. associate--l+ N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

   4. cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

   5. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   9. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

   10. distribute-frac-neg2 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

   12. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   13. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   15. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   16. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   17. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   19. metadata-eval 93.7%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

3. Simplified 93.7%

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

5. Taylor expanded in z around -inf

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)\right)\right)}\right)\right) \]
6. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(-1 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)}\right)\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)}\right)\right)\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(0 - z\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{t - a}\right)\right)}\right)\right)\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{+.f64}\left(\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{t - a}\right)\right)}\right)\right)\right)\right) \]

7. Simplified 96.2%

   \[\leadsto x + y \cdot \color{blue}{\left(\left(0 - z\right) \cdot \left(\frac{1 - \frac{t}{t - a}}{0 - z} + \frac{-1}{t - a}\right)\right)} \]

8. Final simplification 96.2%

   \[\leadsto x + y \cdot \left(z \cdot \left(\frac{-1}{a - t} - \frac{\frac{t}{t - a} + -1}{z}\right)\right) \]
9. Add Preprocessing

Alternative 6: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-13}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e-13)
   (- (+ x y) (* z (/ y a)))
   (if (<= a 2.8e-92) (+ x (* y (/ (- z a) t))) (- (+ x y) (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-13) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 2.8e-92) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.4d-13)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= 2.8d-92) then
        tmp = x + (y * ((z - a) / t))
    else
        tmp = (x + y) - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-13) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 2.8e-92) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.4e-13:
		tmp = (x + y) - (z * (y / a))
	elif a <= 2.8e-92:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = (x + y) - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e-13)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= 2.8e-92)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.4e-13)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= 2.8e-92)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = (x + y) - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e-13], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-92], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.39999999999999999e-13

   1. Initial program 81.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 92.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 92.7%

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

      1. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{y \cdot z}{\color{blue}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{z \cdot y}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 93.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -6.39999999999999999e-13 < a < 2.8e-92

   1. Initial program 75.2%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z + -1 \cdot a\right)}{t}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z + -1 \cdot a}{t}}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z + \left(\mathsf{neg}\left(a\right)\right)}{t}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z - a}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - a\right), \color{blue}{t}\right)\right)\right) \]

      7. --lowering--.f64 87.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, a\right), t\right)\right)\right) \]

   7. Simplified 87.7%

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

   if 2.8e-92 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 88.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 88.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{y}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 88.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 88.9%

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

Alternative 7: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{-10}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.26e-10)
   (- (+ x y) (* z (/ y a)))
   (if (<= a 1.05e-85) (+ x (* y (/ (- z a) t))) (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.26e-10) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 1.05e-85) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) - (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 (a <= (-1.26d-10)) then
        tmp = (x + y) - (z * (y / a))
    else if (a <= 1.05d-85) then
        tmp = x + (y * ((z - a) / t))
    else
        tmp = (x + y) - (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 (a <= -1.26e-10) {
		tmp = (x + y) - (z * (y / a));
	} else if (a <= 1.05e-85) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.26e-10:
		tmp = (x + y) - (z * (y / a))
	elif a <= 1.05e-85:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.26e-10)
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	elseif (a <= 1.05e-85)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.26e-10)
		tmp = (x + y) - (z * (y / a));
	elseif (a <= 1.05e-85)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.26e-10], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-85], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.26000000000000004e-10

   1. Initial program 81.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 92.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 92.7%

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

      1. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{y \cdot z}{\color{blue}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{z \cdot y}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 93.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 93.0%

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

   if -1.26000000000000004e-10 < a < 1.05e-85

   1. Initial program 75.2%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z + -1 \cdot a\right)}{t}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z + -1 \cdot a}{t}}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z + \left(\mathsf{neg}\left(a\right)\right)}{t}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z - a}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - a\right), \color{blue}{t}\right)\right)\right) \]

      7. --lowering--.f64 87.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, a\right), t\right)\right)\right) \]

   7. Simplified 87.7%

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

   if 1.05e-85 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 88.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 88.9%

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

Alternative 8: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;x + y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* y (/ z a)))))
   (if (<= a -1.65e-11)
     t_1
     (if (<= a 7.5e-86) (+ x (* y (/ (- z a) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -1.65e-11) {
		tmp = t_1;
	} else if (a <= 7.5e-86) {
		tmp = x + (y * ((z - 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) - (y * (z / a))
    if (a <= (-1.65d-11)) then
        tmp = t_1
    else if (a <= 7.5d-86) then
        tmp = x + (y * ((z - 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) - (y * (z / a));
	double tmp;
	if (a <= -1.65e-11) {
		tmp = t_1;
	} else if (a <= 7.5e-86) {
		tmp = x + (y * ((z - a) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -1.65e-11:
		tmp = t_1
	elif a <= 7.5e-86:
		tmp = x + (y * ((z - a) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -1.65e-11)
		tmp = t_1;
	elseif (a <= 7.5e-86)
		tmp = Float64(x + Float64(y * Float64(Float64(z - a) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -1.65e-11)
		tmp = t_1;
	elseif (a <= 7.5e-86)
		tmp = x + (y * ((z - a) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-11], t$95$1, If[LessEqual[a, 7.5e-86], N[(x + N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6500000000000001e-11 or 7.50000000000000055e-86 < a

   1. Initial program 81.7%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 90.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 90.6%

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

   if -1.6500000000000001e-11 < a < 7.50000000000000055e-86

   1. Initial program 75.2%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.9%

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

   5. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot \left(z + -1 \cdot a\right)}{t}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z + -1 \cdot a}{t}}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z + \left(\mathsf{neg}\left(a\right)\right)}{t}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{z - a}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - a}{t}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - a\right), \color{blue}{t}\right)\right)\right) \]

      7. --lowering--.f64 87.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, a\right), t\right)\right)\right) \]

   7. Simplified 87.7%

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

Alternative 9: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-212}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-212)
   (+ x y)
   (if (<= a 8.5e-259) (/ (* y z) t) (if (<= a 1.2e-95) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-212) {
		tmp = x + y;
	} else if (a <= 8.5e-259) {
		tmp = (y * z) / t;
	} else if (a <= 1.2e-95) {
		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 <= (-1.2d-212)) then
        tmp = x + y
    else if (a <= 8.5d-259) then
        tmp = (y * z) / t
    else if (a <= 1.2d-95) 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 <= -1.2e-212) {
		tmp = x + y;
	} else if (a <= 8.5e-259) {
		tmp = (y * z) / t;
	} else if (a <= 1.2e-95) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-212:
		tmp = x + y
	elif a <= 8.5e-259:
		tmp = (y * z) / t
	elif a <= 1.2e-95:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-212)
		tmp = Float64(x + y);
	elseif (a <= 8.5e-259)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 1.2e-95)
		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 <= -1.2e-212)
		tmp = x + y;
	elseif (a <= 8.5e-259)
		tmp = (y * z) / t;
	elseif (a <= 1.2e-95)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-212], N[(x + y), $MachinePrecision], If[LessEqual[a, 8.5e-259], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.2e-95], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.19999999999999995e-212 or 1.2e-95 < a

   1. Initial program 82.0%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 94.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 67.3%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 67.3%

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

   if -1.19999999999999995e-212 < a < 8.4999999999999994e-259

   1. Initial program 76.7%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.2%

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

   5. Taylor expanded in a around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{t}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 90.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   7. Simplified 90.1%

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

   8. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 60.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right) \]

   10. Simplified 60.4%

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

   if 8.4999999999999994e-259 < a < 1.2e-95

   1. Initial program 64.6%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 90.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 59.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-212}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -57:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -57.0) (+ x y) (if (<= a 2.4e-50) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -57.0) {
		tmp = x + y;
	} else if (a <= 2.4e-50) {
		tmp = x + (y * (z / t));
	} 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 <= (-57.0d0)) then
        tmp = x + y
    else if (a <= 2.4d-50) then
        tmp = x + (y * (z / t))
    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 <= -57.0) {
		tmp = x + y;
	} else if (a <= 2.4e-50) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -57.0:
		tmp = x + y
	elif a <= 2.4e-50:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -57.0)
		tmp = Float64(x + y);
	elseif (a <= 2.4e-50)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -57.0)
		tmp = x + y;
	elseif (a <= 2.4e-50)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -57.0], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.4e-50], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -57 or 2.40000000000000002e-50 < a

   1. Initial program 81.0%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 96.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 96.7%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 76.1%

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

   if -57 < a < 2.40000000000000002e-50

   1. Initial program 76.9%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 90.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 90.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 81.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   7. Simplified 81.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -57:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+220}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -8.5e+149) t_1 (if (<= z 2.7e+220) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -8.5e+149) {
		tmp = t_1;
	} else if (z <= 2.7e+220) {
		tmp = x + y;
	} 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 = y * (z / (t - a))
    if (z <= (-8.5d+149)) then
        tmp = t_1
    else if (z <= 2.7d+220) then
        tmp = x + y
    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 * (z / (t - a));
	double tmp;
	if (z <= -8.5e+149) {
		tmp = t_1;
	} else if (z <= 2.7e+220) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -8.5e+149:
		tmp = t_1
	elif z <= 2.7e+220:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -8.5e+149)
		tmp = t_1;
	elseif (z <= 2.7e+220)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (z <= -8.5e+149)
		tmp = t_1;
	elseif (z <= 2.7e+220)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+149], t$95$1, If[LessEqual[z, 2.7e+220], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999956e149 or 2.6999999999999998e220 < z

   1. Initial program 76.8%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(z \cdot \left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(-1 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(-1 \cdot z\right), \color{blue}{\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} - \frac{1}{t - a}\right)}\right)\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(0 - z\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(\color{blue}{-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}} - \frac{1}{t - a}\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{t - a}\right)\right)}\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(0, z\right), \mathsf{+.f64}\left(\left(-1 \cdot \frac{1 + -1 \cdot \frac{t}{t - a}}{z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{t - a}\right)\right)}\right)\right)\right)\right) \]

   7. Simplified 96.1%

      \[\leadsto x + y \cdot \color{blue}{\left(\left(0 - z\right) \cdot \left(\frac{1 - \frac{t}{t - a}}{0 - z} + \frac{-1}{t - a}\right)\right)} \]

   8. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{t - a}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\left(t - a\right)}\right)\right) \]

      4. --lowering--.f64 63.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 63.9%

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

   if -8.49999999999999956e149 < z < 2.6999999999999998e220

   1. Initial program 79.6%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 66.5%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 66.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+220}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(0 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+239}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (- 0.0 (/ y a)))))
   (if (<= z -2e+214) t_1 (if (<= z 1.75e+239) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (0.0 - (y / a));
	double tmp;
	if (z <= -2e+214) {
		tmp = t_1;
	} else if (z <= 1.75e+239) {
		tmp = x + y;
	} 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 = z * (0.0d0 - (y / a))
    if (z <= (-2d+214)) then
        tmp = t_1
    else if (z <= 1.75d+239) then
        tmp = x + y
    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 = z * (0.0 - (y / a));
	double tmp;
	if (z <= -2e+214) {
		tmp = t_1;
	} else if (z <= 1.75e+239) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (0.0 - (y / a))
	tmp = 0
	if z <= -2e+214:
		tmp = t_1
	elif z <= 1.75e+239:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(0.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2e+214)
		tmp = t_1;
	elseif (z <= 1.75e+239)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (0.0 - (y / a));
	tmp = 0.0;
	if (z <= -2e+214)
		tmp = t_1;
	elseif (z <= 1.75e+239)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(0.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+214], t$95$1, If[LessEqual[z, 1.75e+239], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e214 or 1.7500000000000001e239 < z

   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 t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]
   4. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      3. /-lowering-/.f64 75.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 75.5%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. neg-mul-1 N/A

         \[\leadsto \frac{\mathsf{neg}\left(y \cdot z\right)}{a} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot z\right)\right), \color{blue}{a}\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - y \cdot z\right), a\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(y \cdot z\right)\right), a\right) \]

      6. *-lowering-*.f64 48.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, z\right)\right), a\right) \]

   8. Simplified 48.3%

      \[\leadsto \color{blue}{\frac{0 - y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(y \cdot z\right)}{a} \]

      2. distribute-frac-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot z}{a}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{a} \cdot z\right) \]

      4. distribute-lft-neg-in N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{y}{a}\right)\right), \color{blue}{z}\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(\frac{y}{a}\right)\right), z\right) \]

      7. /-lowering-/.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{/.f64}\left(y, a\right)\right), z\right) \]

   10. Applied egg-rr 63.2%

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

   if -1.9999999999999999e214 < z < 1.7500000000000001e239

   1. Initial program 79.4%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 93.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 64.1%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 64.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+214}:\\ \;\;\;\;z \cdot \left(0 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+239}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(0 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+135) x (if (<= t 9.8e+89) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+135) {
		tmp = x;
	} else if (t <= 9.8e+89) {
		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 (t <= (-2.7d+135)) then
        tmp = x
    else if (t <= 9.8d+89) 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 (t <= -2.7e+135) {
		tmp = x;
	} else if (t <= 9.8e+89) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+135:
		tmp = x
	elif t <= 9.8e+89:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+135)
		tmp = x;
	elseif (t <= 9.8e+89)
		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 (t <= -2.7e+135)
		tmp = x;
	elseif (t <= 9.8e+89)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+135], x, If[LessEqual[t, 9.8e+89], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999985e135 or 9.79999999999999992e89 < t

   1. Initial program 54.5%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 73.2%

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

   if -2.69999999999999985e135 < t < 9.79999999999999992e89

   1. Initial program 89.2%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 95.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 95.4%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 59.9%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 59.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+90}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.2e+90) y (if (<= y 1.2e+67) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+90) {
		tmp = y;
	} else if (y <= 1.2e+67) {
		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 <= (-6.2d+90)) then
        tmp = y
    else if (y <= 1.2d+67) 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 <= -6.2e+90) {
		tmp = y;
	} else if (y <= 1.2e+67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.2e+90:
		tmp = y
	elif y <= 1.2e+67:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.2e+90)
		tmp = y;
	elseif (y <= 1.2e+67)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.2e+90)
		tmp = y;
	elseif (y <= 1.2e+67)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.2e+90], y, If[LessEqual[y, 1.2e+67], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999977e90 or 1.20000000000000001e67 < y

   1. Initial program 60.9%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 89.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 42.8%

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 42.8%

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

   8. Taylor expanded in y around inf

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

   10. Simplified 32.4%

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

   if -6.19999999999999977e90 < y < 1.20000000000000001e67

   1. Initial program 90.5%

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

      5. distribute-rgt1-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

      10. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      16. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      17. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

      19. metadata-eval 96.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 66.1%

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

Alternative 15: 51.3% 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 79.0%

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

   1. associate--l+ N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y - \frac{\left(z - t\right) \cdot y}{a - t}\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y - \frac{z - t}{a - t} \cdot \color{blue}{y}\right)\right) \]

   4. cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) \cdot y}\right)\right) \]

   5. distribute-rgt1-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right) \cdot \color{blue}{y}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + 1\right)}\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   9. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{z - t}{a - t}\right)\right), \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right)\right) \]

   10. distribute-frac-neg2 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{z - t}{\mathsf{neg}\left(\left(a - t\right)\right)}\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right)\right) \]

   12. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a - t\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   13. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   15. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   16. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   17. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(t - a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), \left(\mathsf{neg}\left(-1\right)\right)\right)\right)\right) \]

   19. metadata-eval 93.7%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{\_.f64}\left(t, a\right)\right), 1\right)\right)\right) \]

3. Simplified 93.7%

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

5. Taylor expanded in x around inf

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

7. Simplified 47.9%

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

Developer Target 1: 88.1% 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 2024158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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