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

Percentage Accurate: 77.4% → 89.3%

Time: 10.7s

Alternatives: 14

Speedup: 0.7×

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: 77.4% 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: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-168} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (or (<= t_1 -4e-168) (not (<= t_1 0.0)))
     (fma (- z t) (/ y (- t a)) (+ x y))
     (+ x (/ (* y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-168) || !(t_1 <= 0.0)) {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -4e-168) || !(t_1 <= 0.0))
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-168], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.0000000000000002e-168 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 79.2%

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

      1. sub-neg 79.2%

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

      2. +-commutative 79.2%

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

      3. distribute-frac-neg 79.2%

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

      4. distribute-rgt-neg-out 79.2%

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

      5. associate-/l* 90.7%

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

      6. fma-define 90.7%

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

      7. distribute-frac-neg 90.7%

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

      8. distribute-neg-frac2 90.7%

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

      9. sub-neg 90.7%

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

      10. distribute-neg-in 90.7%

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

      11. remove-double-neg 90.7%

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

      12. +-commutative 90.7%

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

      13. sub-neg 90.7%

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

   3. Simplified 90.7%

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

   if -4.0000000000000002e-168 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 23.4%

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

   3. Taylor expanded in t around inf 92.4%

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

      1. associate--l+ 92.4%

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

      2. distribute-lft-out-- 92.4%

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

      3. div-sub 92.4%

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

      4. mul-1-neg 92.4%

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

      5. unsub-neg 92.4%

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

      6. *-commutative 92.4%

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

      7. distribute-lft-out-- 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-168} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-168} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{z - t}{\frac{t - a}{y}} + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (or (<= t_1 -4e-168) (not (<= t_1 0.0)))
     (+ (/ (- z t) (/ (- t a) y)) (+ x y))
     (+ x (/ (* y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-168) || !(t_1 <= 0.0)) {
		tmp = ((z - t) / ((t - a) / y)) + (x + y);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) + ((y * (z - t)) / (t - a))
    if ((t_1 <= (-4d-168)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = ((z - t) / ((t - a) / y)) + (x + y)
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if ((t_1 <= -4e-168) || !(t_1 <= 0.0)) {
		tmp = ((z - t) / ((t - a) / y)) + (x + y);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (z - t)) / (t - a))
	tmp = 0
	if (t_1 <= -4e-168) or not (t_1 <= 0.0):
		tmp = ((z - t) / ((t - a) / y)) + (x + y)
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -4e-168) || !(t_1 <= 0.0))
		tmp = Float64(Float64(Float64(z - t) / Float64(Float64(t - a) / y)) + Float64(x + y));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (z - t)) / (t - a));
	tmp = 0.0;
	if ((t_1 <= -4e-168) || ~((t_1 <= 0.0)))
		tmp = ((z - t) / ((t - a) / y)) + (x + y);
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-168], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -4.0000000000000002e-168 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 79.2%

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

      1. sub-neg 79.2%

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

      2. +-commutative 79.2%

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

      3. distribute-frac-neg 79.2%

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

      4. distribute-rgt-neg-out 79.2%

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

      5. associate-/l* 90.7%

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

      6. fma-define 90.7%

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

      7. distribute-frac-neg 90.7%

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

      8. distribute-neg-frac2 90.7%

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

      9. sub-neg 90.7%

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

      10. distribute-neg-in 90.7%

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

      11. remove-double-neg 90.7%

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

      12. +-commutative 90.7%

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

      13. sub-neg 90.7%

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

   3. Simplified 90.7%

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

      1. fma-undefine 90.7%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.3%

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

      4. +-commutative 90.3%

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

   6. Applied egg-rr 90.3%

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

   if -4.0000000000000002e-168 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 23.4%

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

   3. Taylor expanded in t around inf 92.4%

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

      1. associate--l+ 92.4%

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

      2. distribute-lft-out-- 92.4%

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

      3. div-sub 92.4%

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

      4. mul-1-neg 92.4%

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

      5. unsub-neg 92.4%

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

      6. *-commutative 92.4%

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

      7. distribute-lft-out-- 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -4 \cdot 10^{-168} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0\right):\\ \;\;\;\;\frac{z - t}{\frac{t - a}{y}} + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;a \leq -740000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+175}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (* t (/ y (- a t))))) (t_2 (- (+ x y) (/ (* y z) a))))
   (if (<= a -9e+204)
     t_1
     (if (<= a -2.1e+172)
       (* y (+ 1.0 (/ (- z t) (- t a))))
       (if (<= a -740000000.0)
         t_2
         (if (<= a 8.8e-91)
           (+ x (/ (* y (- z a)) t))
           (if (<= a 2.45e+175) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + (t * (y / (a - t)));
	double t_2 = (x + y) - ((y * z) / a);
	double tmp;
	if (a <= -9e+204) {
		tmp = t_1;
	} else if (a <= -2.1e+172) {
		tmp = y * (1.0 + ((z - t) / (t - a)));
	} else if (a <= -740000000.0) {
		tmp = t_2;
	} else if (a <= 8.8e-91) {
		tmp = x + ((y * (z - a)) / t);
	} else if (a <= 2.45e+175) {
		tmp = t_2;
	} 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) + (t * (y / (a - t)))
    t_2 = (x + y) - ((y * z) / a)
    if (a <= (-9d+204)) then
        tmp = t_1
    else if (a <= (-2.1d+172)) then
        tmp = y * (1.0d0 + ((z - t) / (t - a)))
    else if (a <= (-740000000.0d0)) then
        tmp = t_2
    else if (a <= 8.8d-91) then
        tmp = x + ((y * (z - a)) / t)
    else if (a <= 2.45d+175) then
        tmp = t_2
    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) + (t * (y / (a - t)));
	double t_2 = (x + y) - ((y * z) / a);
	double tmp;
	if (a <= -9e+204) {
		tmp = t_1;
	} else if (a <= -2.1e+172) {
		tmp = y * (1.0 + ((z - t) / (t - a)));
	} else if (a <= -740000000.0) {
		tmp = t_2;
	} else if (a <= 8.8e-91) {
		tmp = x + ((y * (z - a)) / t);
	} else if (a <= 2.45e+175) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + (t * (y / (a - t)))
	t_2 = (x + y) - ((y * z) / a)
	tmp = 0
	if a <= -9e+204:
		tmp = t_1
	elif a <= -2.1e+172:
		tmp = y * (1.0 + ((z - t) / (t - a)))
	elif a <= -740000000.0:
		tmp = t_2
	elif a <= 8.8e-91:
		tmp = x + ((y * (z - a)) / t)
	elif a <= 2.45e+175:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(t * Float64(y / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(y * z) / a))
	tmp = 0.0
	if (a <= -9e+204)
		tmp = t_1;
	elseif (a <= -2.1e+172)
		tmp = Float64(y * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	elseif (a <= -740000000.0)
		tmp = t_2;
	elseif (a <= 8.8e-91)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	elseif (a <= 2.45e+175)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + (t * (y / (a - t)));
	t_2 = (x + y) - ((y * z) / a);
	tmp = 0.0;
	if (a <= -9e+204)
		tmp = t_1;
	elseif (a <= -2.1e+172)
		tmp = y * (1.0 + ((z - t) / (t - a)));
	elseif (a <= -740000000.0)
		tmp = t_2;
	elseif (a <= 8.8e-91)
		tmp = x + ((y * (z - a)) / t);
	elseif (a <= 2.45e+175)
		tmp = t_2;
	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[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+204], t$95$1, If[LessEqual[a, -2.1e+172], N[(y * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -740000000.0], t$95$2, If[LessEqual[a, 8.8e-91], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+175], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.00000000000000004e204 or 2.45e175 < a

   1. Initial program 71.9%

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

      1. sub-neg 71.9%

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

      2. +-commutative 71.9%

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

      3. distribute-frac-neg 71.9%

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

      4. distribute-rgt-neg-out 71.9%

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

      5. associate-/l* 98.7%

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

      6. fma-define 98.6%

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

      7. distribute-frac-neg 98.6%

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

      8. distribute-neg-frac2 98.6%

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

      9. sub-neg 98.6%

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

      10. distribute-neg-in 98.6%

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

      11. remove-double-neg 98.6%

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

      12. +-commutative 98.6%

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

      13. sub-neg 98.6%

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

   3. Simplified 98.6%

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

      1. fma-undefine 98.7%

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

      2. clear-num 98.7%

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

      3. un-div-inv 98.5%

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

      4. +-commutative 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around 0 79.4%

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

      1. associate-+r+ 79.4%

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

      2. +-commutative 79.4%

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

      3. mul-1-neg 79.4%

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

      4. unsub-neg 79.4%

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

      5. associate-/l* 94.3%

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

   9. Simplified 94.3%

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

   if -9.00000000000000004e204 < a < -2.1000000000000001e172

   1. Initial program 36.4%

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

      1. sub-neg 36.4%

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

      2. +-commutative 36.4%

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

      3. distribute-frac-neg 36.4%

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

      4. distribute-rgt-neg-out 36.4%

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

      5. associate-/l* 81.0%

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

      6. fma-define 80.7%

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

      7. distribute-frac-neg 80.7%

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

      8. distribute-neg-frac2 80.7%

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

      9. sub-neg 80.7%

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

      10. distribute-neg-in 80.7%

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

      11. remove-double-neg 80.7%

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

      12. +-commutative 80.7%

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

      13. sub-neg 80.7%

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

   3. Simplified 80.7%

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

      1. fma-undefine 81.0%

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

      2. clear-num 74.3%

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

      3. un-div-inv 74.3%

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

      4. +-commutative 74.3%

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

   6. Applied egg-rr 74.3%

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

   7. Taylor expanded in y around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. div-sub 83.1%

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

   9. Simplified 83.1%

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

   if -2.1000000000000001e172 < a < -7.4e8 or 8.8000000000000003e-91 < a < 2.45e175

   1. Initial program 73.4%

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

   3. Taylor expanded in t around 0 68.9%

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

      1. +-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -7.4e8 < a < 8.8000000000000003e-91

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate--l+ 85.4%

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

      2. distribute-lft-out-- 85.4%

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

      3. div-sub 85.4%

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

      4. mul-1-neg 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. distribute-lft-out-- 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;\left(x + y\right) + t \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;a \leq -740000000:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+175}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-112}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+204)
   (+ x y)
   (if (<= a -2.1e+172)
     (* y (/ z (- t a)))
     (if (<= a -9.5e-10)
       (+ x y)
       (if (<= a -7.2e-214)
         x
         (if (<= a 5e-112) (/ (* y z) (- t a)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if (a <= -9.5e-10) {
		tmp = x + y;
	} else if (a <= -7.2e-214) {
		tmp = x;
	} else if (a <= 5e-112) {
		tmp = (y * z) / (t - a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+204)) then
        tmp = x + y
    else if (a <= (-2.1d+172)) then
        tmp = y * (z / (t - a))
    else if (a <= (-9.5d-10)) then
        tmp = x + y
    else if (a <= (-7.2d-214)) then
        tmp = x
    else if (a <= 5d-112) then
        tmp = (y * z) / (t - a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if (a <= -9.5e-10) {
		tmp = x + y;
	} else if (a <= -7.2e-214) {
		tmp = x;
	} else if (a <= 5e-112) {
		tmp = (y * z) / (t - a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+204:
		tmp = x + y
	elif a <= -2.1e+172:
		tmp = y * (z / (t - a))
	elif a <= -9.5e-10:
		tmp = x + y
	elif a <= -7.2e-214:
		tmp = x
	elif a <= 5e-112:
		tmp = (y * z) / (t - a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+204)
		tmp = Float64(x + y);
	elseif (a <= -2.1e+172)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= -9.5e-10)
		tmp = Float64(x + y);
	elseif (a <= -7.2e-214)
		tmp = x;
	elseif (a <= 5e-112)
		tmp = Float64(Float64(y * z) / Float64(t - a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+204)
		tmp = x + y;
	elseif (a <= -2.1e+172)
		tmp = y * (z / (t - a));
	elseif (a <= -9.5e-10)
		tmp = x + y;
	elseif (a <= -7.2e-214)
		tmp = x;
	elseif (a <= 5e-112)
		tmp = (y * z) / (t - a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+204], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e+172], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-10], N[(x + y), $MachinePrecision], If[LessEqual[a, -7.2e-214], x, If[LessEqual[a, 5e-112], N[(N[(y * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.00000000000000004e204 or -2.1000000000000001e172 < a < -9.50000000000000028e-10 or 5.00000000000000044e-112 < a

   1. Initial program 73.2%

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

   3. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -9.00000000000000004e204 < a < -2.1000000000000001e172

   1. Initial program 36.4%

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

   3. Taylor expanded in z around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 81.2%

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

      3. distribute-rgt-neg-in 81.2%

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

      4. distribute-neg-frac2 81.2%

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

      5. sub0-neg 81.2%

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

      6. associate--r- 81.2%

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

      7. neg-sub0 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in z around 0 81.2%

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

   if -9.50000000000000028e-10 < a < -7.2e-214

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.0%

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

   if -7.2e-214 < a < 5.00000000000000044e-112

   1. Initial program 75.8%

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

      1. sub-neg 75.8%

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

      2. +-commutative 75.8%

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

      3. distribute-frac-neg 75.8%

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

      4. distribute-rgt-neg-out 75.8%

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

      5. associate-/l* 79.4%

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

      6. fma-define 79.4%

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

      7. distribute-frac-neg 79.4%

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

      8. distribute-neg-frac2 79.4%

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

      9. sub-neg 79.4%

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

      10. distribute-neg-in 79.4%

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

      11. remove-double-neg 79.4%

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

      12. +-commutative 79.4%

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

      13. sub-neg 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 65.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-112}:\\ \;\;\;\;\frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;a \leq -12200000000 \lor \neg \left(a \leq 7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+204)
   (+ x y)
   (if (<= a -2.1e+172)
     (* y (+ 1.0 (/ (- z t) (- t a))))
     (if (or (<= a -12200000000.0) (not (<= a 7e-92)))
       (- (+ x y) (/ (* y z) a))
       (+ x (/ (* y (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (1.0 + ((z - t) / (t - a)));
	} else if ((a <= -12200000000.0) || !(a <= 7e-92)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+204)) then
        tmp = x + y
    else if (a <= (-2.1d+172)) then
        tmp = y * (1.0d0 + ((z - t) / (t - a)))
    else if ((a <= (-12200000000.0d0)) .or. (.not. (a <= 7d-92))) then
        tmp = (x + y) - ((y * z) / a)
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (1.0 + ((z - t) / (t - a)));
	} else if ((a <= -12200000000.0) || !(a <= 7e-92)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+204:
		tmp = x + y
	elif a <= -2.1e+172:
		tmp = y * (1.0 + ((z - t) / (t - a)))
	elif (a <= -12200000000.0) or not (a <= 7e-92):
		tmp = (x + y) - ((y * z) / a)
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+204)
		tmp = Float64(x + y);
	elseif (a <= -2.1e+172)
		tmp = Float64(y * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	elseif ((a <= -12200000000.0) || !(a <= 7e-92))
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+204)
		tmp = x + y;
	elseif (a <= -2.1e+172)
		tmp = y * (1.0 + ((z - t) / (t - a)));
	elseif ((a <= -12200000000.0) || ~((a <= 7e-92)))
		tmp = (x + y) - ((y * z) / a);
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+204], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e+172], N[(y * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -12200000000.0], N[Not[LessEqual[a, 7e-92]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.00000000000000004e204

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 96.5%

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

      1. +-commutative 96.5%

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

   5. Simplified 96.5%

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

   if -9.00000000000000004e204 < a < -2.1000000000000001e172

   1. Initial program 36.4%

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

      1. sub-neg 36.4%

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

      2. +-commutative 36.4%

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

      3. distribute-frac-neg 36.4%

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

      4. distribute-rgt-neg-out 36.4%

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

      5. associate-/l* 81.0%

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

      6. fma-define 80.7%

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

      7. distribute-frac-neg 80.7%

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

      8. distribute-neg-frac2 80.7%

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

      9. sub-neg 80.7%

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

      10. distribute-neg-in 80.7%

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

      11. remove-double-neg 80.7%

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

      12. +-commutative 80.7%

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

      13. sub-neg 80.7%

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

   3. Simplified 80.7%

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

      1. fma-undefine 81.0%

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

      2. clear-num 74.3%

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

      3. un-div-inv 74.3%

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

      4. +-commutative 74.3%

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

   6. Applied egg-rr 74.3%

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

   7. Taylor expanded in y around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. div-sub 83.1%

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

   9. Simplified 83.1%

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

   if -2.1000000000000001e172 < a < -1.22e10 or 7e-92 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -1.22e10 < a < 7e-92

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate--l+ 85.4%

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

      2. distribute-lft-out-- 85.4%

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

      3. div-sub 85.4%

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

      4. mul-1-neg 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. distribute-lft-out-- 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{elif}\;a \leq -12200000000 \lor \neg \left(a \leq 7 \cdot 10^{-92}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -88000000 \lor \neg \left(a \leq 1.75 \cdot 10^{-87}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+204)
   (+ x y)
   (if (<= a -2.1e+172)
     (* y (/ z (- t a)))
     (if (or (<= a -88000000.0) (not (<= a 1.75e-87)))
       (- (+ x y) (/ (* y z) a))
       (+ x (/ (* y (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if ((a <= -88000000.0) || !(a <= 1.75e-87)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+204)) then
        tmp = x + y
    else if (a <= (-2.1d+172)) then
        tmp = y * (z / (t - a))
    else if ((a <= (-88000000.0d0)) .or. (.not. (a <= 1.75d-87))) then
        tmp = (x + y) - ((y * z) / a)
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if ((a <= -88000000.0) || !(a <= 1.75e-87)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+204:
		tmp = x + y
	elif a <= -2.1e+172:
		tmp = y * (z / (t - a))
	elif (a <= -88000000.0) or not (a <= 1.75e-87):
		tmp = (x + y) - ((y * z) / a)
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+204)
		tmp = Float64(x + y);
	elseif (a <= -2.1e+172)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif ((a <= -88000000.0) || !(a <= 1.75e-87))
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+204)
		tmp = x + y;
	elseif (a <= -2.1e+172)
		tmp = y * (z / (t - a));
	elseif ((a <= -88000000.0) || ~((a <= 1.75e-87)))
		tmp = (x + y) - ((y * z) / a);
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+204], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e+172], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -88000000.0], N[Not[LessEqual[a, 1.75e-87]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.00000000000000004e204

   1. Initial program 77.9%

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

   3. Taylor expanded in a around inf 96.5%

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

      1. +-commutative 96.5%

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

   5. Simplified 96.5%

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

   if -9.00000000000000004e204 < a < -2.1000000000000001e172

   1. Initial program 36.4%

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

   3. Taylor expanded in z around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 81.2%

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

      3. distribute-rgt-neg-in 81.2%

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

      4. distribute-neg-frac2 81.2%

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

      5. sub0-neg 81.2%

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

      6. associate--r- 81.2%

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

      7. neg-sub0 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in z around 0 81.2%

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

   if -2.1000000000000001e172 < a < -8.8e7 or 1.75000000000000006e-87 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -8.8e7 < a < 1.75000000000000006e-87

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate--l+ 85.4%

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

      2. distribute-lft-out-- 85.4%

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

      3. div-sub 85.4%

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

      4. mul-1-neg 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. distribute-lft-out-- 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -88000000 \lor \neg \left(a \leq 1.75 \cdot 10^{-87}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -4500000000 \lor \neg \left(a \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+204)
   (+ x y)
   (if (<= a -2.1e+172)
     (* y (/ z (- t a)))
     (if (or (<= a -4500000000.0) (not (<= a 1.8e-110)))
       (+ x y)
       (+ x (/ (* y (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if ((a <= -4500000000.0) || !(a <= 1.8e-110)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+204)) then
        tmp = x + y
    else if (a <= (-2.1d+172)) then
        tmp = y * (z / (t - a))
    else if ((a <= (-4500000000.0d0)) .or. (.not. (a <= 1.8d-110))) then
        tmp = x + y
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+204) {
		tmp = x + y;
	} else if (a <= -2.1e+172) {
		tmp = y * (z / (t - a));
	} else if ((a <= -4500000000.0) || !(a <= 1.8e-110)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+204:
		tmp = x + y
	elif a <= -2.1e+172:
		tmp = y * (z / (t - a))
	elif (a <= -4500000000.0) or not (a <= 1.8e-110):
		tmp = x + y
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+204)
		tmp = Float64(x + y);
	elseif (a <= -2.1e+172)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif ((a <= -4500000000.0) || !(a <= 1.8e-110))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+204)
		tmp = x + y;
	elseif (a <= -2.1e+172)
		tmp = y * (z / (t - a));
	elseif ((a <= -4500000000.0) || ~((a <= 1.8e-110)))
		tmp = x + y;
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+204], N[(x + y), $MachinePrecision], If[LessEqual[a, -2.1e+172], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -4500000000.0], N[Not[LessEqual[a, 1.8e-110]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.00000000000000004e204 or -2.1000000000000001e172 < a < -4.5e9 or 1.79999999999999997e-110 < a

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -9.00000000000000004e204 < a < -2.1000000000000001e172

   1. Initial program 36.4%

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

   3. Taylor expanded in z around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 81.2%

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

      3. distribute-rgt-neg-in 81.2%

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

      4. distribute-neg-frac2 81.2%

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

      5. sub0-neg 81.2%

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

      6. associate--r- 81.2%

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

      7. neg-sub0 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in z around 0 81.2%

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

   if -4.5e9 < a < 1.79999999999999997e-110

   1. Initial program 76.5%

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

   3. Taylor expanded in t around inf 84.8%

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

      1. associate--l+ 84.8%

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

      2. distribute-lft-out-- 84.8%

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

      3. div-sub 84.8%

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

      4. mul-1-neg 84.8%

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

      5. unsub-neg 84.8%

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

      6. *-commutative 84.8%

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

      7. distribute-lft-out-- 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+204}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -4500000000 \lor \neg \left(a \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+51} \lor \neg \left(z \leq 9.5 \cdot 10^{+109}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -3e+148)
     t_1
     (if (<= z -1.86e+109)
       x
       (if (or (<= z -1.9e+51) (not (<= z 9.5e+109))) t_1 (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -3e+148) {
		tmp = t_1;
	} else if (z <= -1.86e+109) {
		tmp = x;
	} else if ((z <= -1.9e+51) || !(z <= 9.5e+109)) {
		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 = y * (z / (t - a))
    if (z <= (-3d+148)) then
        tmp = t_1
    else if (z <= (-1.86d+109)) then
        tmp = x
    else if ((z <= (-1.9d+51)) .or. (.not. (z <= 9.5d+109))) 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 = y * (z / (t - a));
	double tmp;
	if (z <= -3e+148) {
		tmp = t_1;
	} else if (z <= -1.86e+109) {
		tmp = x;
	} else if ((z <= -1.9e+51) || !(z <= 9.5e+109)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -3e+148:
		tmp = t_1
	elif z <= -1.86e+109:
		tmp = x
	elif (z <= -1.9e+51) or not (z <= 9.5e+109):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -3e+148)
		tmp = t_1;
	elseif (z <= -1.86e+109)
		tmp = x;
	elseif ((z <= -1.9e+51) || !(z <= 9.5e+109))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	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 <= -3e+148)
		tmp = t_1;
	elseif (z <= -1.86e+109)
		tmp = x;
	elseif ((z <= -1.9e+51) || ~((z <= 9.5e+109)))
		tmp = t_1;
	else
		tmp = x + y;
	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, -3e+148], t$95$1, If[LessEqual[z, -1.86e+109], x, If[Or[LessEqual[z, -1.9e+51], N[Not[LessEqual[z, 9.5e+109]], $MachinePrecision]], t$95$1, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000015e148 or -1.86000000000000008e109 < z < -1.8999999999999999e51 or 9.49999999999999972e109 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. associate-/l* 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

      4. distribute-neg-frac2 58.9%

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

      5. sub0-neg 58.9%

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

      6. associate--r- 58.9%

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

      7. neg-sub0 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around 0 58.9%

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

   if -3.00000000000000015e148 < z < -1.86000000000000008e109

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf 87.7%

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

   if -1.8999999999999999e51 < z < 9.49999999999999972e109

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 71.4%

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

      1. +-commutative 71.4%

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

   5. Simplified 71.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+51} \lor \neg \left(z \leq 9.5 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e-11)
   (+ x y)
   (if (<= a -1.7e-216) x (if (<= a 3.1e-112) (* z (/ y t)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e-11) {
		tmp = x + y;
	} else if (a <= -1.7e-216) {
		tmp = x;
	} else if (a <= 3.1e-112) {
		tmp = z * (y / 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 <= (-5.2d-11)) then
        tmp = x + y
    else if (a <= (-1.7d-216)) then
        tmp = x
    else if (a <= 3.1d-112) then
        tmp = z * (y / 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 <= -5.2e-11) {
		tmp = x + y;
	} else if (a <= -1.7e-216) {
		tmp = x;
	} else if (a <= 3.1e-112) {
		tmp = z * (y / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e-11:
		tmp = x + y
	elif a <= -1.7e-216:
		tmp = x
	elif a <= 3.1e-112:
		tmp = z * (y / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e-11)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-216)
		tmp = x;
	elseif (a <= 3.1e-112)
		tmp = Float64(z * Float64(y / 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 <= -5.2e-11)
		tmp = x + y;
	elseif (a <= -1.7e-216)
		tmp = x;
	elseif (a <= 3.1e-112)
		tmp = z * (y / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e-11], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-216], x, If[LessEqual[a, 3.1e-112], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2000000000000001e-11 or 3.0999999999999998e-112 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in a around inf 70.4%

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

      1. +-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -5.2000000000000001e-11 < a < -1.6999999999999999e-216

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.0%

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

   if -1.6999999999999999e-216 < a < 3.0999999999999998e-112

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. associate-/l* 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. distribute-neg-frac2 61.9%

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

      5. sub0-neg 61.9%

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

      6. associate--r- 61.9%

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

      7. neg-sub0 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 61.3%

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

   8. Applied egg-rr 61.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-112}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -56000000 \lor \neg \left(a \leq 7.5 \cdot 10^{-88}\right):\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -56000000.0) (not (<= a 7.5e-88)))
   (- (+ x y) (* z (/ y a)))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -56000000.0) || !(a <= 7.5e-88)) {
		tmp = (x + y) - (z * (y / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-56000000.0d0)) .or. (.not. (a <= 7.5d-88))) then
        tmp = (x + y) - (z * (y / a))
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -56000000.0) || !(a <= 7.5e-88)) {
		tmp = (x + y) - (z * (y / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -56000000.0) or not (a <= 7.5e-88):
		tmp = (x + y) - (z * (y / a))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -56000000.0) || !(a <= 7.5e-88))
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -56000000.0) || ~((a <= 7.5e-88)))
		tmp = (x + y) - (z * (y / a));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -56000000.0], N[Not[LessEqual[a, 7.5e-88]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6e7 or 7.50000000000000041e-88 < a

   1. Initial program 71.3%

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

   3. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

   5. Simplified 73.1%

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

      1. *-commutative 73.1%

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

      2. *-un-lft-identity 73.1%

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

      3. times-frac 81.5%

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

   7. Applied egg-rr 81.5%

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

   if -5.6e7 < a < 7.50000000000000041e-88

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate--l+ 85.4%

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

      2. distribute-lft-out-- 85.4%

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

      3. div-sub 85.4%

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

      4. mul-1-neg 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. distribute-lft-out-- 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -56000000 \lor \neg \left(a \leq 7.5 \cdot 10^{-88}\right):\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-166} \lor \neg \left(a \leq 4.8 \cdot 10^{-112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-166) (not (<= a 4.8e-112))) (+ x y) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-166) || !(a <= 4.8e-112)) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d-166)) .or. (.not. (a <= 4.8d-112))) then
        tmp = x + y
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-166) || !(a <= 4.8e-112)) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-166) or not (a <= 4.8e-112):
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-166) || !(a <= 4.8e-112))
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-166) || ~((a <= 4.8e-112)))
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-166], N[Not[LessEqual[a, 4.8e-112]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5e-166 or 4.8000000000000001e-112 < a

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf 68.8%

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

      1. +-commutative 68.8%

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

   5. Simplified 68.8%

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

   if -8.5e-166 < a < 4.8000000000000001e-112

   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 z around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/l* 59.2%

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

      3. distribute-rgt-neg-in 59.2%

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

      4. distribute-neg-frac2 59.2%

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

      5. sub0-neg 59.2%

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

      6. associate--r- 59.2%

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

      7. neg-sub0 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in a around 0 53.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-166} \lor \neg \left(a \leq 4.8 \cdot 10^{-112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.4 \cdot 10^{+168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 7.4e+168) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 7.4e+168) {
		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 <= 7.4d+168) 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 <= 7.4e+168) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 7.4e+168:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 7.4e+168)
		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 <= 7.4e+168)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 7.4e+168], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 7.40000000000000018e168

   1. Initial program 77.1%

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

   3. Taylor expanded in a around inf 59.3%

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

      1. +-commutative 59.3%

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

   5. Simplified 59.3%

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

   if 7.40000000000000018e168 < t

   1. Initial program 44.6%

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

   3. Taylor expanded in x around inf 78.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.4 \cdot 10^{+168}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 1.6e+77) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.6e+77) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.6d+77) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.6e+77) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.6e+77:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.6e+77)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.6e+77)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.6e+77], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.6000000000000001e77

   1. Initial program 77.9%

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

   3. Taylor expanded in x around inf 57.6%

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

   if 1.6000000000000001e77 < y

   1. Initial program 55.2%

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

   3. Taylor expanded in t around 0 56.6%

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

      1. +-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around 0 47.0%

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

   7. Taylor expanded in z around 0 33.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.1% 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 73.8%

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

3. Taylor expanded in x around inf 50.2%

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

Developer target: 88.2% 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 2024097 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

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

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