Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.6% → 89.1%

Time: 15.5s

Alternatives: 25

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-279}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e+303)
     t_1
     (if (<= t_2 -1e-279)
       t_2
       (if (<= t_2 0.0) (+ t (/ (* (- t x) (- a y)) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e+303) {
		tmp = t_1;
	} else if (t_2 <= -1e-279) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} 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 - z) * ((t - x) / (a - z)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-5d+303)) then
        tmp = t_1
    else if (t_2 <= (-1d-279)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e+303) {
		tmp = t_1;
	} else if (t_2 <= -1e-279) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -5e+303:
		tmp = t_1
	elif t_2 <= -1e-279:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e+303)
		tmp = t_1;
	elseif (t_2 <= -1e-279)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e+303)
		tmp = t_1;
	elseif (t_2 <= -1e-279)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+303], t$95$1, If[LessEqual[t$95$2, -1e-279], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.9999999999999997e303 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 63.3%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   if -4.9999999999999997e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000006e-279

   1. Initial program 97.7%

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

   if -1.00000000000000006e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{+303}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-279}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \left(a - y\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-279} \lor \neg \left(t\_2 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(\mathsf{fma}\left({a}^{2}, \frac{t\_1}{{z}^{3}}, y \cdot \frac{x - t}{z}\right) + \mathsf{fma}\left(a, \frac{t - x}{z}, a \cdot \frac{t\_1}{{z}^{2}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (- a y))) (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_2 -1e-279) (not (<= t_2 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+
      t
      (+
       (fma (pow a 2.0) (/ t_1 (pow z 3.0)) (* y (/ (- x t) z)))
       (fma a (/ (- t x) z) (* a (/ t_1 (pow z 2.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (a - y);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_2 <= -1e-279) || !(t_2 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (fma(pow(a, 2.0), (t_1 / pow(z, 3.0)), (y * ((x - t) / z))) + fma(a, ((t - x) / z), (a * (t_1 / pow(z, 2.0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(a - y))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_2 <= -1e-279) || !(t_2 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(fma((a ^ 2.0), Float64(t_1 / (z ^ 3.0)), Float64(y * Float64(Float64(x - t) / z))) + fma(a, Float64(Float64(t - x) / z), Float64(a * Float64(t_1 / (z ^ 2.0))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e-279], N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[Power[a, 2.0], $MachinePrecision] * N[(t$95$1 / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] + N[(a * N[(t$95$1 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000006e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.3%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 88.1%

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

      4. clear-num 88.1%

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

      5. un-div-inv 88.3%

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

   6. Applied egg-rr 88.3%

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

   if -1.00000000000000006e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

      \[\leadsto \color{blue}{\left(t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \frac{{a}^{2} \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{3}}\right)\right) - \left(-1 \cdot \frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{a \cdot \left(-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)\right)}{{z}^{2}}\right)} \]

   7. Simplified 99.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(\mathsf{fma}\left({a}^{2}, \frac{\left(t - x\right) \cdot \left(a - y\right)}{{z}^{3}}, y \cdot \frac{x - t}{z}\right) + \mathsf{fma}\left(a, \frac{t - x}{z}, a \cdot \frac{\left(t - x\right) \cdot \left(a - y\right)}{{z}^{2}}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \left(\frac{x}{z} \cdot \frac{y - a}{t} + \frac{a - y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-279) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (* t (+ (* (/ x z) (/ (- y a) t)) (/ (- a y) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (t * (((x / z) * ((y - a) / t)) + ((a - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    else
        tmp = t + (t * (((x / z) * ((y - a) / t)) + ((a - y) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (t * (((x / z) * ((y - a) / t)) + ((a - y) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-279) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + (t * (((x / z) * ((y - a) / t)) + ((a - y) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(t * Float64(Float64(Float64(x / z) * Float64(Float64(y - a) / t)) + Float64(Float64(a - y) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + (t * (((x / z) * ((y - a) / t)) + ((a - y) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(t * N[(N[(N[(x / z), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000006e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.3%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 88.1%

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

      4. clear-num 88.1%

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

      5. un-div-inv 88.3%

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

   6. Applied egg-rr 88.3%

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

   if -1.00000000000000006e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-rgt-neg-in 99.5%

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

      3. +-commutative 99.5%

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

      4. neg-mul-1 99.5%

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

      5. unsub-neg 99.5%

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

      6. *-commutative 99.5%

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

      7. times-frac 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + t \cdot \left(\frac{x}{z} \cdot \frac{y - a}{t} + \frac{a - y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-279} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-279) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-279)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-279) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-279) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-279) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000006e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.3%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 88.1%

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

      4. clear-num 88.1%

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

      5. un-div-inv 88.3%

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

   6. Applied egg-rr 88.3%

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

   if -1.00000000000000006e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+106}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+143} \lor \neg \left(x \leq 5.2 \cdot 10^{+189}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.2e+193)
     t_1
     (if (<= x -4e+165)
       (* y (/ (- x t) z))
       (if (<= x -8e+106)
         (- x (/ (* x y) a))
         (if (<= x 9e-26)
           (* t (/ (- z y) (- z a)))
           (if (or (<= x 1.95e+143) (not (<= x 5.2e+189)))
             t_1
             (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+193) {
		tmp = t_1;
	} else if (x <= -4e+165) {
		tmp = y * ((x - t) / z);
	} else if (x <= -8e+106) {
		tmp = x - ((x * y) / a);
	} else if (x <= 9e-26) {
		tmp = t * ((z - y) / (z - a));
	} else if ((x <= 1.95e+143) || !(x <= 5.2e+189)) {
		tmp = t_1;
	} else {
		tmp = x * ((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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-4.2d+193)) then
        tmp = t_1
    else if (x <= (-4d+165)) then
        tmp = y * ((x - t) / z)
    else if (x <= (-8d+106)) then
        tmp = x - ((x * y) / a)
    else if (x <= 9d-26) then
        tmp = t * ((z - y) / (z - a))
    else if ((x <= 1.95d+143) .or. (.not. (x <= 5.2d+189))) then
        tmp = t_1
    else
        tmp = x * ((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 t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+193) {
		tmp = t_1;
	} else if (x <= -4e+165) {
		tmp = y * ((x - t) / z);
	} else if (x <= -8e+106) {
		tmp = x - ((x * y) / a);
	} else if (x <= 9e-26) {
		tmp = t * ((z - y) / (z - a));
	} else if ((x <= 1.95e+143) || !(x <= 5.2e+189)) {
		tmp = t_1;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.2e+193:
		tmp = t_1
	elif x <= -4e+165:
		tmp = y * ((x - t) / z)
	elif x <= -8e+106:
		tmp = x - ((x * y) / a)
	elif x <= 9e-26:
		tmp = t * ((z - y) / (z - a))
	elif (x <= 1.95e+143) or not (x <= 5.2e+189):
		tmp = t_1
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.2e+193)
		tmp = t_1;
	elseif (x <= -4e+165)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (x <= -8e+106)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (x <= 9e-26)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif ((x <= 1.95e+143) || !(x <= 5.2e+189))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -4.2e+193)
		tmp = t_1;
	elseif (x <= -4e+165)
		tmp = y * ((x - t) / z);
	elseif (x <= -8e+106)
		tmp = x - ((x * y) / a);
	elseif (x <= 9e-26)
		tmp = t * ((z - y) / (z - a));
	elseif ((x <= 1.95e+143) || ~((x <= 5.2e+189)))
		tmp = t_1;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+193], t$95$1, If[LessEqual[x, -4e+165], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e+106], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-26], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.95e+143], N[Not[LessEqual[x, 5.2e+189]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.2e193 or 8.9999999999999998e-26 < x < 1.9499999999999999e143 or 5.19999999999999963e189 < x

   1. Initial program 62.9%

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

      1. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around 0 57.8%

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

      1. associate-/l* 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in x around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   10. Simplified 64.4%

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

   if -4.2e193 < x < -3.9999999999999996e165

   1. Initial program 47.3%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 68.5%

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

      1. associate--l+ 68.5%

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

      2. associate-*r/ 68.5%

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

      3. associate-*r/ 68.5%

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

      4. mul-1-neg 68.5%

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

      5. div-sub 68.5%

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

      6. mul-1-neg 68.5%

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

      7. distribute-lft-out-- 68.5%

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

      8. associate-*r/ 68.5%

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

      9. mul-1-neg 68.5%

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

      10. unsub-neg 68.5%

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

      11. distribute-rgt-out-- 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   10. Simplified 100.0%

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

   if -3.9999999999999996e165 < x < -8.00000000000000073e106

   1. Initial program 86.3%

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

      1. associate-/l* 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in z around 0 71.4%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 65.2%

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

      1. associate-*r/ 65.2%

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

      2. mul-1-neg 65.2%

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

      3. *-commutative 65.2%

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

   10. Simplified 65.2%

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

   if -8.00000000000000073e106 < x < 8.9999999999999998e-26

   1. Initial program 74.9%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around 0 56.6%

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

      1. associate-/l* 70.6%

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

   7. Simplified 70.6%

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

   if 1.9499999999999999e143 < x < 5.19999999999999963e189

   1. Initial program 44.1%

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

      1. associate-/l* 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. associate--l+ 61.1%

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

      2. associate-*r/ 61.1%

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

      3. associate-*r/ 61.1%

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

      4. mul-1-neg 61.1%

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

      5. div-sub 61.1%

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

      6. mul-1-neg 61.1%

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

      7. distribute-lft-out-- 61.1%

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

      8. associate-*r/ 61.1%

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

      9. mul-1-neg 61.1%

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

      10. unsub-neg 61.1%

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

      11. distribute-rgt-out-- 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in t around 0 49.1%

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

      1. associate-/l* 54.7%

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

   10. Simplified 54.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+106}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+143} \lor \neg \left(x \leq 5.2 \cdot 10^{+189}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{x - t}{\frac{a}{z - y}}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- x t) (/ a (- z y))))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= a -5e-49)
     t_1
     (if (<= a 1.1e-257)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 1.05e-68)
         t_2
         (if (<= a 2e-41)
           (+ t (/ (* (- t x) a) z))
           (if (<= a 6.5e+107) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) / (a / (z - y)));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -5e-49) {
		tmp = t_1;
	} else if (a <= 1.1e-257) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.05e-68) {
		tmp = t_2;
	} else if (a <= 2e-41) {
		tmp = t + (((t - x) * a) / z);
	} else if (a <= 6.5e+107) {
		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 + ((x - t) / (a / (z - y)))
    t_2 = y * ((t - x) / (a - z))
    if (a <= (-5d-49)) then
        tmp = t_1
    else if (a <= 1.1d-257) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.05d-68) then
        tmp = t_2
    else if (a <= 2d-41) then
        tmp = t + (((t - x) * a) / z)
    else if (a <= 6.5d+107) 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 + ((x - t) / (a / (z - y)));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -5e-49) {
		tmp = t_1;
	} else if (a <= 1.1e-257) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.05e-68) {
		tmp = t_2;
	} else if (a <= 2e-41) {
		tmp = t + (((t - x) * a) / z);
	} else if (a <= 6.5e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) / (a / (z - y)))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if a <= -5e-49:
		tmp = t_1
	elif a <= 1.1e-257:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.05e-68:
		tmp = t_2
	elif a <= 2e-41:
		tmp = t + (((t - x) * a) / z)
	elif a <= 6.5e+107:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) / Float64(a / Float64(z - y))))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -5e-49)
		tmp = t_1;
	elseif (a <= 1.1e-257)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.05e-68)
		tmp = t_2;
	elseif (a <= 2e-41)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (a <= 6.5e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) / (a / (z - y)));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (a <= -5e-49)
		tmp = t_1;
	elseif (a <= 1.1e-257)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.05e-68)
		tmp = t_2;
	elseif (a <= 2e-41)
		tmp = t + (((t - x) * a) / z);
	elseif (a <= 6.5e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] / N[(a / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-49], t$95$1, If[LessEqual[a, 1.1e-257], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-68], t$95$2, If[LessEqual[a, 2e-41], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+107], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.9999999999999999e-49 or 6.5000000000000006e107 < a

   1. Initial program 72.3%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 95.4%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in a around inf 78.0%

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

   if -4.9999999999999999e-49 < a < 1.09999999999999994e-257

   1. Initial program 67.6%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*r/ 79.5%

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

      4. mul-1-neg 79.5%

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

      5. div-sub 79.5%

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

      6. mul-1-neg 79.5%

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

      7. distribute-lft-out-- 79.5%

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

      8. associate-*r/ 79.5%

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

      9. mul-1-neg 79.5%

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

      10. unsub-neg 79.5%

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

      11. distribute-rgt-out-- 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in y around inf 79.3%

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

   if 1.09999999999999994e-257 < a < 1.05000000000000004e-68 or 2.00000000000000001e-41 < a < 6.5000000000000006e107

   1. Initial program 65.8%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. div-sub 69.4%

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

   7. Simplified 69.4%

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

   if 1.05000000000000004e-68 < a < 2.00000000000000001e-41

   1. Initial program 36.1%

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

      1. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in z around inf 84.3%

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

      1. associate--l+ 84.3%

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

      2. associate-*r/ 84.3%

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

      3. associate-*r/ 84.3%

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

      4. mul-1-neg 84.3%

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

      5. div-sub 84.3%

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

      6. mul-1-neg 84.3%

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

      7. distribute-lft-out-- 84.3%

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

      8. associate-*r/ 84.3%

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

      9. mul-1-neg 84.3%

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

      10. unsub-neg 84.3%

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

      11. distribute-rgt-out-- 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in y around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. mul-1-neg 84.3%

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

      3. distribute-lft-neg-out 84.3%

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

      4. *-commutative 84.3%

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

   10. Simplified 84.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z - y}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-258}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= a -2.2e-48)
     t_1
     (if (<= a 3.4e-258)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 1.1e-68)
         t_2
         (if (<= a 1.35e-41)
           (+ t (/ (* (- t x) a) z))
           (if (<= a 6.5e+107) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.2e-48) {
		tmp = t_1;
	} else if (a <= 3.4e-258) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.1e-68) {
		tmp = t_2;
	} else if (a <= 1.35e-41) {
		tmp = t + (((t - x) * a) / z);
	} else if (a <= 6.5e+107) {
		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 + ((t - x) / (a / y))
    t_2 = y * ((t - x) / (a - z))
    if (a <= (-2.2d-48)) then
        tmp = t_1
    else if (a <= 3.4d-258) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.1d-68) then
        tmp = t_2
    else if (a <= 1.35d-41) then
        tmp = t + (((t - x) * a) / z)
    else if (a <= 6.5d+107) 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 + ((t - x) / (a / y));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -2.2e-48) {
		tmp = t_1;
	} else if (a <= 3.4e-258) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.1e-68) {
		tmp = t_2;
	} else if (a <= 1.35e-41) {
		tmp = t + (((t - x) * a) / z);
	} else if (a <= 6.5e+107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if a <= -2.2e-48:
		tmp = t_1
	elif a <= 3.4e-258:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.1e-68:
		tmp = t_2
	elif a <= 1.35e-41:
		tmp = t + (((t - x) * a) / z)
	elif a <= 6.5e+107:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.2e-48)
		tmp = t_1;
	elseif (a <= 3.4e-258)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.1e-68)
		tmp = t_2;
	elseif (a <= 1.35e-41)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * a) / z));
	elseif (a <= 6.5e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (a <= -2.2e-48)
		tmp = t_1;
	elseif (a <= 3.4e-258)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.1e-68)
		tmp = t_2;
	elseif (a <= 1.35e-41)
		tmp = t + (((t - x) * a) / z);
	elseif (a <= 6.5e+107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-48], t$95$1, If[LessEqual[a, 3.4e-258], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-68], t$95$2, If[LessEqual[a, 1.35e-41], N[(t + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+107], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.20000000000000013e-48 or 6.5000000000000006e107 < a

   1. Initial program 72.3%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 95.4%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in z around 0 72.7%

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

   if -2.20000000000000013e-48 < a < 3.3999999999999998e-258

   1. Initial program 67.6%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*r/ 79.5%

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

      4. mul-1-neg 79.5%

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

      5. div-sub 79.5%

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

      6. mul-1-neg 79.5%

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

      7. distribute-lft-out-- 79.5%

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

      8. associate-*r/ 79.5%

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

      9. mul-1-neg 79.5%

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

      10. unsub-neg 79.5%

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

      11. distribute-rgt-out-- 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in y around inf 79.3%

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

   if 3.3999999999999998e-258 < a < 1.10000000000000001e-68 or 1.35e-41 < a < 6.5000000000000006e107

   1. Initial program 65.8%

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

      1. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. div-sub 69.4%

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

   7. Simplified 69.4%

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

   if 1.10000000000000001e-68 < a < 1.35e-41

   1. Initial program 36.1%

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

      1. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in z around inf 84.3%

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

      1. associate--l+ 84.3%

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

      2. associate-*r/ 84.3%

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

      3. associate-*r/ 84.3%

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

      4. mul-1-neg 84.3%

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

      5. div-sub 84.3%

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

      6. mul-1-neg 84.3%

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

      7. distribute-lft-out-- 84.3%

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

      8. associate-*r/ 84.3%

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

      9. mul-1-neg 84.3%

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

      10. unsub-neg 84.3%

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

      11. distribute-rgt-out-- 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in y around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. mul-1-neg 84.3%

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

      3. distribute-lft-neg-out 84.3%

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

      4. *-commutative 84.3%

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

   10. Simplified 84.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-258}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-184}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-286}:\\ \;\;\;\;t + \frac{t \cdot a}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-30)
   (+ x (/ t (/ a y)))
   (if (<= a -3e-184)
     (/ (* t (- z y)) z)
     (if (<= a -5e-246)
       (* x (/ (- y a) z))
       (if (<= a 1.4e-286)
         (+ t (/ (* t a) z))
         (if (<= a 1.02e+76) (* y (/ (- x t) z)) (+ x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-30) {
		tmp = x + (t / (a / y));
	} else if (a <= -3e-184) {
		tmp = (t * (z - y)) / z;
	} else if (a <= -5e-246) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.4e-286) {
		tmp = t + ((t * a) / z);
	} else if (a <= 1.02e+76) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d-30)) then
        tmp = x + (t / (a / y))
    else if (a <= (-3d-184)) then
        tmp = (t * (z - y)) / z
    else if (a <= (-5d-246)) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.4d-286) then
        tmp = t + ((t * a) / z)
    else if (a <= 1.02d+76) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-30) {
		tmp = x + (t / (a / y));
	} else if (a <= -3e-184) {
		tmp = (t * (z - y)) / z;
	} else if (a <= -5e-246) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.4e-286) {
		tmp = t + ((t * a) / z);
	} else if (a <= 1.02e+76) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-30:
		tmp = x + (t / (a / y))
	elif a <= -3e-184:
		tmp = (t * (z - y)) / z
	elif a <= -5e-246:
		tmp = x * ((y - a) / z)
	elif a <= 1.4e-286:
		tmp = t + ((t * a) / z)
	elif a <= 1.02e+76:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-30)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= -3e-184)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (a <= -5e-246)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.4e-286)
		tmp = Float64(t + Float64(Float64(t * a) / z));
	elseif (a <= 1.02e+76)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-30)
		tmp = x + (t / (a / y));
	elseif (a <= -3e-184)
		tmp = (t * (z - y)) / z;
	elseif (a <= -5e-246)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.4e-286)
		tmp = t + ((t * a) / z);
	elseif (a <= 1.02e+76)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-30], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-184], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, -5e-246], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-286], N[(t + N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+76], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.49999999999999967e-30

   1. Initial program 71.0%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 61.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in t around inf 56.3%

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

      1. associate-/l* 62.7%

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

   10. Simplified 62.7%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -4.49999999999999967e-30 < a < -2.99999999999999991e-184

   1. Initial program 73.4%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around 0 58.0%

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

   6. Taylor expanded in a around 0 54.1%

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

      1. associate-*r/ 54.1%

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

      2. mul-1-neg 54.1%

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

      3. distribute-rgt-neg-out 54.1%

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

   8. Simplified 54.1%

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

   if -2.99999999999999991e-184 < a < -4.9999999999999997e-246

   1. Initial program 67.7%

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

      1. associate-/l* 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. associate-*r/ 78.0%

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

      3. associate-*r/ 78.0%

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

      4. mul-1-neg 78.0%

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

      5. div-sub 78.0%

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

      6. mul-1-neg 78.0%

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

      7. distribute-lft-out-- 78.0%

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

      8. associate-*r/ 78.0%

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

      9. mul-1-neg 78.0%

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

      10. unsub-neg 78.0%

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

      11. distribute-rgt-out-- 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in t around 0 67.5%

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

      1. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -4.9999999999999997e-246 < a < 1.4e-286

   1. Initial program 61.0%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in x around 0 56.7%

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

   6. Taylor expanded in y around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. associate-/l* 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in z around inf 60.4%

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

   if 1.4e-286 < a < 1.02000000000000007e76

   1. Initial program 65.9%

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

      1. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-*r/ 63.2%

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

      4. mul-1-neg 63.2%

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

      5. div-sub 63.3%

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

      6. mul-1-neg 63.3%

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

      7. distribute-lft-out-- 63.3%

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

      8. associate-*r/ 63.3%

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

      9. mul-1-neg 63.3%

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

      10. unsub-neg 63.3%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around inf 46.7%

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

      1. div-sub 46.7%

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

   10. Simplified 46.7%

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

   if 1.02000000000000007e76 < a

   1. Initial program 68.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in t around inf 56.2%

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

      1. associate-/l* 63.9%

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

   10. Simplified 63.9%

       \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-184}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-286}:\\ \;\;\;\;t + \frac{t \cdot a}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e-30)
   (+ x (/ t (/ a y)))
   (if (<= a -6.9e-184)
     (/ (* t (- z y)) z)
     (if (<= a -1.4e-293)
       (/ (* y (- x t)) z)
       (if (<= a 1.65e-286)
         t
         (if (<= a 1.02e+76) (* y (/ (- x t) z)) (+ x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e-30) {
		tmp = x + (t / (a / y));
	} else if (a <= -6.9e-184) {
		tmp = (t * (z - y)) / z;
	} else if (a <= -1.4e-293) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.65e-286) {
		tmp = t;
	} else if (a <= 1.02e+76) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d-30)) then
        tmp = x + (t / (a / y))
    else if (a <= (-6.9d-184)) then
        tmp = (t * (z - y)) / z
    else if (a <= (-1.4d-293)) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.65d-286) then
        tmp = t
    else if (a <= 1.02d+76) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e-30) {
		tmp = x + (t / (a / y));
	} else if (a <= -6.9e-184) {
		tmp = (t * (z - y)) / z;
	} else if (a <= -1.4e-293) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.65e-286) {
		tmp = t;
	} else if (a <= 1.02e+76) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e-30:
		tmp = x + (t / (a / y))
	elif a <= -6.9e-184:
		tmp = (t * (z - y)) / z
	elif a <= -1.4e-293:
		tmp = (y * (x - t)) / z
	elif a <= 1.65e-286:
		tmp = t
	elif a <= 1.02e+76:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e-30)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= -6.9e-184)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (a <= -1.4e-293)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.65e-286)
		tmp = t;
	elseif (a <= 1.02e+76)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e-30)
		tmp = x + (t / (a / y));
	elseif (a <= -6.9e-184)
		tmp = (t * (z - y)) / z;
	elseif (a <= -1.4e-293)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.65e-286)
		tmp = t;
	elseif (a <= 1.02e+76)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e-30], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.9e-184], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, -1.4e-293], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.65e-286], t, If[LessEqual[a, 1.02e+76], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.0500000000000002e-30

   1. Initial program 71.0%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 61.2%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in t around inf 56.3%

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

      1. associate-/l* 62.7%

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

   10. Simplified 62.7%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -2.0500000000000002e-30 < a < -6.89999999999999985e-184

   1. Initial program 73.4%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around 0 58.0%

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

   6. Taylor expanded in a around 0 54.1%

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

      1. associate-*r/ 54.1%

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

      2. mul-1-neg 54.1%

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

      3. distribute-rgt-neg-out 54.1%

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

   8. Simplified 54.1%

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

   if -6.89999999999999985e-184 < a < -1.40000000000000013e-293

   1. Initial program 66.2%

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

      1. associate-/l* 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in z around inf 85.1%

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

      1. associate--l+ 85.1%

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

      2. associate-*r/ 85.1%

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

      3. associate-*r/ 85.1%

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

      4. mul-1-neg 85.1%

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

      5. div-sub 85.1%

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

      6. mul-1-neg 85.1%

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

      7. distribute-lft-out-- 85.1%

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

      8. associate-*r/ 85.1%

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

      9. mul-1-neg 85.1%

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

      10. unsub-neg 85.1%

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

      11. distribute-rgt-out-- 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in y around -inf 61.1%

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

      1. associate-*r/ 61.1%

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

      2. associate-*r* 61.1%

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

      3. mul-1-neg 61.1%

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

   10. Simplified 61.1%

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

   if -1.40000000000000013e-293 < a < 1.6499999999999999e-286

   1. Initial program 57.0%

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

      1. associate-/l* 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in z around inf 82.3%

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

   if 1.6499999999999999e-286 < a < 1.02000000000000007e76

   1. Initial program 65.9%

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

      1. associate-/l* 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-*r/ 63.2%

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

      4. mul-1-neg 63.2%

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

      5. div-sub 63.3%

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

      6. mul-1-neg 63.3%

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

      7. distribute-lft-out-- 63.3%

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

      8. associate-*r/ 63.3%

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

      9. mul-1-neg 63.3%

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

      10. unsub-neg 63.3%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around inf 46.7%

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

      1. div-sub 46.7%

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

   10. Simplified 46.7%

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

   if 1.02000000000000007e76 < a

   1. Initial program 68.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in t around inf 56.2%

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

      1. associate-/l* 63.9%

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

   10. Simplified 63.9%

       \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-13)
   x
   (if (<= a -6.2e-129)
     (* x (/ y (- a)))
     (if (<= a -2.2e-238)
       (* x (/ y z))
       (if (<= a 1.65e-286) t (if (<= a 6.8e+107) (/ x (/ z y)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-13) {
		tmp = x;
	} else if (a <= -6.2e-129) {
		tmp = x * (y / -a);
	} else if (a <= -2.2e-238) {
		tmp = x * (y / z);
	} else if (a <= 1.65e-286) {
		tmp = t;
	} else if (a <= 6.8e+107) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d-13)) then
        tmp = x
    else if (a <= (-6.2d-129)) then
        tmp = x * (y / -a)
    else if (a <= (-2.2d-238)) then
        tmp = x * (y / z)
    else if (a <= 1.65d-286) then
        tmp = t
    else if (a <= 6.8d+107) then
        tmp = x / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-13) {
		tmp = x;
	} else if (a <= -6.2e-129) {
		tmp = x * (y / -a);
	} else if (a <= -2.2e-238) {
		tmp = x * (y / z);
	} else if (a <= 1.65e-286) {
		tmp = t;
	} else if (a <= 6.8e+107) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-13:
		tmp = x
	elif a <= -6.2e-129:
		tmp = x * (y / -a)
	elif a <= -2.2e-238:
		tmp = x * (y / z)
	elif a <= 1.65e-286:
		tmp = t
	elif a <= 6.8e+107:
		tmp = x / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e-13)
		tmp = x;
	elseif (a <= -6.2e-129)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif (a <= -2.2e-238)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.65e-286)
		tmp = t;
	elseif (a <= 6.8e+107)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e-13)
		tmp = x;
	elseif (a <= -6.2e-129)
		tmp = x * (y / -a);
	elseif (a <= -2.2e-238)
		tmp = x * (y / z);
	elseif (a <= 1.65e-286)
		tmp = t;
	elseif (a <= 6.8e+107)
		tmp = x / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e-13], x, If[LessEqual[a, -6.2e-129], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.2e-238], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-286], t, If[LessEqual[a, 6.8e+107], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.90000000000000004e-13 or 6.7999999999999994e107 < a

   1. Initial program 70.7%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around inf 54.5%

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

   if -3.90000000000000004e-13 < a < -6.2000000000000001e-129

   1. Initial program 75.9%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around 0 56.9%

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

      1. associate-/l* 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in x around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. unsub-neg 44.3%

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

   10. Simplified 44.3%

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

   11. Taylor expanded in y around inf 31.3%

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

       1. mul-1-neg 31.3%

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

       2. associate-*r/ 34.6%

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

       3. *-commutative 34.6%

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

       4. distribute-rgt-neg-in 34.6%

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

   13. Simplified 34.6%

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

   if -6.2000000000000001e-129 < a < -2.19999999999999991e-238

   1. Initial program 68.2%

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

      1. associate-/l* 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. mul-1-neg 67.6%

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

      5. div-sub 67.6%

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

      6. mul-1-neg 67.6%

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

      7. distribute-lft-out-- 67.6%

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

      8. associate-*r/ 67.6%

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

      9. mul-1-neg 67.6%

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

      10. unsub-neg 67.6%

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

      11. distribute-rgt-out-- 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in y around -inf 40.0%

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

      1. associate-*r/ 40.0%

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

      2. associate-*r* 40.0%

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

      3. mul-1-neg 40.0%

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

   10. Simplified 40.0%

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

   11. Taylor expanded in t around 0 30.7%

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

       1. associate-/l* 48.8%

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

   13. Simplified 48.8%

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

   if -2.19999999999999991e-238 < a < 1.6499999999999999e-286

   1. Initial program 61.0%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in z around inf 60.4%

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

   if 1.6499999999999999e-286 < a < 6.7999999999999994e107

   1. Initial program 65.1%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. associate-*r/ 60.1%

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

      3. associate-*r/ 60.1%

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

      4. mul-1-neg 60.1%

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

      5. div-sub 60.2%

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

      6. mul-1-neg 60.2%

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

      7. distribute-lft-out-- 60.2%

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

      8. associate-*r/ 60.2%

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

      9. mul-1-neg 60.2%

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

      10. unsub-neg 60.2%

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

      11. distribute-rgt-out-- 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in y around -inf 36.1%

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

      1. associate-*r/ 36.1%

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

      2. associate-*r* 36.1%

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

      3. mul-1-neg 36.1%

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

   10. Simplified 36.1%

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

   11. Taylor expanded in t around 0 26.1%

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

       1. associate-/l* 34.6%

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

   13. Simplified 34.6%

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

       1. clear-num 34.6%

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

       2. un-div-inv 34.7%

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

   15. Applied egg-rr 34.7%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-238}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.45e-182)
     t_2
     (if (<= a -1e-241)
       t_1
       (if (<= a 1.5e-286) t (if (<= a 7.8e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.45e-182) {
		tmp = t_2;
	} else if (a <= -1e-241) {
		tmp = t_1;
	} else if (a <= 1.5e-286) {
		tmp = t;
	} else if (a <= 7.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.45d-182)) then
        tmp = t_2
    else if (a <= (-1d-241)) then
        tmp = t_1
    else if (a <= 1.5d-286) then
        tmp = t
    else if (a <= 7.8d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.45e-182) {
		tmp = t_2;
	} else if (a <= -1e-241) {
		tmp = t_1;
	} else if (a <= 1.5e-286) {
		tmp = t;
	} else if (a <= 7.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.45e-182:
		tmp = t_2
	elif a <= -1e-241:
		tmp = t_1
	elif a <= 1.5e-286:
		tmp = t
	elif a <= 7.8e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.45e-182)
		tmp = t_2;
	elseif (a <= -1e-241)
		tmp = t_1;
	elseif (a <= 1.5e-286)
		tmp = t;
	elseif (a <= 7.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.45e-182)
		tmp = t_2;
	elseif (a <= -1e-241)
		tmp = t_1;
	elseif (a <= 1.5e-286)
		tmp = t;
	elseif (a <= 7.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-182], t$95$2, If[LessEqual[a, -1e-241], t$95$1, If[LessEqual[a, 1.5e-286], t, If[LessEqual[a, 7.8e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.44999999999999993e-182 or 7.7999999999999996e65 < a

   1. Initial program 71.4%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in x around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   10. Simplified 54.6%

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

   if -1.44999999999999993e-182 < a < -9.9999999999999997e-242 or 1.5e-286 < a < 7.7999999999999996e65

   1. Initial program 64.9%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. associate--l+ 65.7%

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

      2. associate-*r/ 65.7%

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

      3. associate-*r/ 65.7%

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

      4. mul-1-neg 65.7%

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

      5. div-sub 65.8%

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

      6. mul-1-neg 65.8%

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

      7. distribute-lft-out-- 65.8%

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

      8. associate-*r/ 65.8%

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

      9. mul-1-neg 65.8%

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

      10. unsub-neg 65.8%

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

      11. distribute-rgt-out-- 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in t around 0 40.6%

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

      1. associate-/l* 49.3%

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

   10. Simplified 49.3%

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

   if -9.9999999999999997e-242 < a < 1.5e-286

   1. Initial program 61.0%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in z around inf 60.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.68 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.68e-124)
     t_2
     (if (<= a -5.8e-274)
       t_1
       (if (<= a 1.4e-286) t (if (<= a 6.5e+107) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.68e-124) {
		tmp = t_2;
	} else if (a <= -5.8e-274) {
		tmp = t_1;
	} else if (a <= 1.4e-286) {
		tmp = t;
	} else if (a <= 6.5e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.68d-124)) then
        tmp = t_2
    else if (a <= (-5.8d-274)) then
        tmp = t_1
    else if (a <= 1.4d-286) then
        tmp = t
    else if (a <= 6.5d+107) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.68e-124) {
		tmp = t_2;
	} else if (a <= -5.8e-274) {
		tmp = t_1;
	} else if (a <= 1.4e-286) {
		tmp = t;
	} else if (a <= 6.5e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.68e-124:
		tmp = t_2
	elif a <= -5.8e-274:
		tmp = t_1
	elif a <= 1.4e-286:
		tmp = t
	elif a <= 6.5e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.68e-124)
		tmp = t_2;
	elseif (a <= -5.8e-274)
		tmp = t_1;
	elseif (a <= 1.4e-286)
		tmp = t;
	elseif (a <= 6.5e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.68e-124)
		tmp = t_2;
	elseif (a <= -5.8e-274)
		tmp = t_1;
	elseif (a <= 1.4e-286)
		tmp = t;
	elseif (a <= 6.5e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.68e-124], t$95$2, If[LessEqual[a, -5.8e-274], t$95$1, If[LessEqual[a, 1.4e-286], t, If[LessEqual[a, 6.5e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.68e-124 or 6.5000000000000006e107 < a

   1. Initial program 71.6%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in z around 0 59.7%

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

      1. associate-/l* 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in x around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

   10. Simplified 59.7%

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

   if -1.68e-124 < a < -5.79999999999999952e-274 or 1.4e-286 < a < 6.5000000000000006e107

   1. Initial program 65.8%

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

      1. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-*r/ 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

      5. div-sub 63.7%

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

      6. mul-1-neg 63.7%

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

      7. distribute-lft-out-- 63.7%

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

      8. associate-*r/ 63.7%

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

      9. mul-1-neg 63.7%

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

      10. unsub-neg 63.7%

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

      11. distribute-rgt-out-- 63.8%

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

   7. Simplified 63.8%

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

   8. Taylor expanded in y around inf 46.5%

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

      1. div-sub 47.4%

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

   10. Simplified 47.4%

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

   if -5.79999999999999952e-274 < a < 1.4e-286

   1. Initial program 59.6%

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

      1. associate-/l* 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in z around inf 72.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.68 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -5.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))))
   (if (<= a -5.9e-125)
     (* x (- 1.0 (/ y a)))
     (if (<= a -4.7e-273)
       t_1
       (if (<= a 1.9e-286) t (if (<= a 1.55e+76) t_1 (+ x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (a <= -5.9e-125) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -4.7e-273) {
		tmp = t_1;
	} else if (a <= 1.9e-286) {
		tmp = t;
	} else if (a <= 1.55e+76) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    if (a <= (-5.9d-125)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-4.7d-273)) then
        tmp = t_1
    else if (a <= 1.9d-286) then
        tmp = t
    else if (a <= 1.55d+76) then
        tmp = t_1
    else
        tmp = x + (t * (y / a))
    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 - t) / z);
	double tmp;
	if (a <= -5.9e-125) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -4.7e-273) {
		tmp = t_1;
	} else if (a <= 1.9e-286) {
		tmp = t;
	} else if (a <= 1.55e+76) {
		tmp = t_1;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	tmp = 0
	if a <= -5.9e-125:
		tmp = x * (1.0 - (y / a))
	elif a <= -4.7e-273:
		tmp = t_1
	elif a <= 1.9e-286:
		tmp = t
	elif a <= 1.55e+76:
		tmp = t_1
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -5.9e-125)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -4.7e-273)
		tmp = t_1;
	elseif (a <= 1.9e-286)
		tmp = t;
	elseif (a <= 1.55e+76)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -5.9e-125)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -4.7e-273)
		tmp = t_1;
	elseif (a <= 1.9e-286)
		tmp = t;
	elseif (a <= 1.55e+76)
		tmp = t_1;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.9e-125], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.7e-273], t$95$1, If[LessEqual[a, 1.9e-286], t, If[LessEqual[a, 1.55e+76], t$95$1, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.89999999999999959e-125

   1. Initial program 72.1%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in z around 0 60.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in x around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. unsub-neg 58.0%

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

   10. Simplified 58.0%

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

   if -5.89999999999999959e-125 < a < -4.69999999999999962e-273 or 1.9000000000000001e-286 < a < 1.55000000000000006e76

   1. Initial program 66.5%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 66.1%

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

      1. associate--l+ 66.1%

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

      2. associate-*r/ 66.1%

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

      3. associate-*r/ 66.1%

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

      4. mul-1-neg 66.1%

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

      5. div-sub 66.1%

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

      6. mul-1-neg 66.1%

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

      7. distribute-lft-out-- 66.1%

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

      8. associate-*r/ 66.1%

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

      9. mul-1-neg 66.1%

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

      10. unsub-neg 66.1%

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

      11. distribute-rgt-out-- 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in y around inf 47.1%

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

      1. div-sub 48.0%

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

   10. Simplified 48.0%

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

   if -4.69999999999999962e-273 < a < 1.9000000000000001e-286

   1. Initial program 59.6%

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

      1. associate-/l* 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in z around inf 72.3%

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

   if 1.55000000000000006e76 < a

   1. Initial program 68.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-/l* 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in t around inf 56.2%

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

      1. associate-/l* 63.9%

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

   10. Simplified 63.9%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;a \leq -2.75 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))))
   (if (<= a -2.75e-87)
     t_1
     (if (<= a 2.1e-286)
       (* t (/ (- z y) (- z a)))
       (if (<= a 6.5e+107) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double tmp;
	if (a <= -2.75e-87) {
		tmp = t_1;
	} else if (a <= 2.1e-286) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} 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 * ((x - t) / a))
    if (a <= (-2.75d-87)) then
        tmp = t_1
    else if (a <= 2.1d-286) then
        tmp = t * ((z - y) / (z - a))
    else if (a <= 6.5d+107) then
        tmp = y * ((t - x) / (a - z))
    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 * ((x - t) / a));
	double tmp;
	if (a <= -2.75e-87) {
		tmp = t_1;
	} else if (a <= 2.1e-286) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	tmp = 0
	if a <= -2.75e-87:
		tmp = t_1
	elif a <= 2.1e-286:
		tmp = t * ((z - y) / (z - a))
	elif a <= 6.5e+107:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (a <= -2.75e-87)
		tmp = t_1;
	elseif (a <= 2.1e-286)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (a <= 6.5e+107)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (a <= -2.75e-87)
		tmp = t_1;
	elseif (a <= 2.1e-286)
		tmp = t * ((z - y) / (z - a));
	elseif (a <= 6.5e+107)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.75e-87], t$95$1, If[LessEqual[a, 2.1e-286], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+107], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7500000000000002e-87 or 6.5000000000000006e107 < a

   1. Initial program 72.5%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around 0 60.5%

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

      1. associate-/l* 70.4%

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

   7. Simplified 70.4%

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

   if -2.7500000000000002e-87 < a < 2.09999999999999988e-286

   1. Initial program 64.6%

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

      1. associate-/l* 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

   if 2.09999999999999988e-286 < a < 6.5000000000000006e107

   1. Initial program 65.1%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. div-sub 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-87}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -2.65e-85)
     t_1
     (if (<= a 1.75e-286)
       (* t (/ (- z y) (- z a)))
       (if (<= a 6.5e+107) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -2.65e-85) {
		tmp = t_1;
	} else if (a <= 1.75e-286) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} 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 + ((t - x) / (a / y))
    if (a <= (-2.65d-85)) then
        tmp = t_1
    else if (a <= 1.75d-286) then
        tmp = t * ((z - y) / (z - a))
    else if (a <= 6.5d+107) then
        tmp = y * ((t - x) / (a - z))
    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 + ((t - x) / (a / y));
	double tmp;
	if (a <= -2.65e-85) {
		tmp = t_1;
	} else if (a <= 1.75e-286) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	tmp = 0
	if a <= -2.65e-85:
		tmp = t_1
	elif a <= 1.75e-286:
		tmp = t * ((z - y) / (z - a))
	elif a <= 6.5e+107:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -2.65e-85)
		tmp = t_1;
	elseif (a <= 1.75e-286)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (a <= 6.5e+107)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	tmp = 0.0;
	if (a <= -2.65e-85)
		tmp = t_1;
	elseif (a <= 1.75e-286)
		tmp = t * ((z - y) / (z - a));
	elseif (a <= 6.5e+107)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.65e-85], t$95$1, If[LessEqual[a, 1.75e-286], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+107], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.64999999999999984e-85 or 6.5000000000000006e107 < a

   1. Initial program 72.5%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 72.5%

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

      3. associate-*r/ 94.0%

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

      4. clear-num 94.0%

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

      5. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in z around 0 71.2%

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

   if -2.64999999999999984e-85 < a < 1.74999999999999994e-286

   1. Initial program 64.6%

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

      1. associate-/l* 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

   if 1.74999999999999994e-286 < a < 6.5000000000000006e107

   1. Initial program 65.1%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. div-sub 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-254}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -1.15e-48)
     t_1
     (if (<= a 5.4e-254)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 6.5e+107) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -1.15e-48) {
		tmp = t_1;
	} else if (a <= 5.4e-254) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} 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 + ((t - x) / (a / y))
    if (a <= (-1.15d-48)) then
        tmp = t_1
    else if (a <= 5.4d-254) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 6.5d+107) then
        tmp = y * ((t - x) / (a - z))
    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 + ((t - x) / (a / y));
	double tmp;
	if (a <= -1.15e-48) {
		tmp = t_1;
	} else if (a <= 5.4e-254) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 6.5e+107) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	tmp = 0
	if a <= -1.15e-48:
		tmp = t_1
	elif a <= 5.4e-254:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 6.5e+107:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.15e-48)
		tmp = t_1;
	elseif (a <= 5.4e-254)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 6.5e+107)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	tmp = 0.0;
	if (a <= -1.15e-48)
		tmp = t_1;
	elseif (a <= 5.4e-254)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 6.5e+107)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-48], t$95$1, If[LessEqual[a, 5.4e-254], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+107], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e-48 or 6.5000000000000006e107 < a

   1. Initial program 72.3%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 95.4%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in z around 0 72.7%

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

   if -1.15e-48 < a < 5.40000000000000013e-254

   1. Initial program 67.6%

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

      1. associate-/l* 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in z around inf 79.5%

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

      1. associate--l+ 79.5%

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

      2. associate-*r/ 79.5%

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

      3. associate-*r/ 79.5%

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

      4. mul-1-neg 79.5%

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

      5. div-sub 79.5%

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

      6. mul-1-neg 79.5%

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

      7. distribute-lft-out-- 79.5%

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

      8. associate-*r/ 79.5%

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

      9. mul-1-neg 79.5%

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

      10. unsub-neg 79.5%

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

      11. distribute-rgt-out-- 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in y around inf 79.3%

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

   if 5.40000000000000013e-254 < a < 6.5000000000000006e107

   1. Initial program 63.5%

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

      1. associate-/l* 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in y around inf 63.1%

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

      1. div-sub 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-254}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+262}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+154)
   (* t (/ (- z y) (- z a)))
   (if (<= z 1.95e+262)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (+ t (/ (* y (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+154) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.95e+262) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.15d+154)) then
        tmp = t * ((z - y) / (z - a))
    else if (z <= 1.95d+262) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+154) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.95e+262) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+154:
		tmp = t * ((z - y) / (z - a))
	elif z <= 1.95e+262:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+154)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (z <= 1.95e+262)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+154)
		tmp = t * ((z - y) / (z - a));
	elseif (z <= 1.95e+262)
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+154], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+262], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1499999999999999e154

   1. Initial program 34.1%

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

      1. associate-/l* 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in x around 0 47.3%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   if -2.1499999999999999e154 < z < 1.94999999999999993e262

   1. Initial program 77.0%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   if 1.94999999999999993e262 < z

   1. Initial program 15.8%

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

      1. associate-/l* 51.1%

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

   3. Simplified 51.1%

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

   5. Taylor expanded in z around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. associate-*r/ 76.1%

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

      3. associate-*r/ 76.1%

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

      4. mul-1-neg 76.1%

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

      5. div-sub 76.1%

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

      6. mul-1-neg 76.1%

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

      7. distribute-lft-out-- 76.1%

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

      8. associate-*r/ 76.1%

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

      9. mul-1-neg 76.1%

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

      10. unsub-neg 76.1%

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

      11. distribute-rgt-out-- 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in y around inf 76.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+262}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+92}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+107)
   (* t (/ (- z y) (- z a)))
   (if (<= z 1.3e+92)
     (+ x (/ (- t x) (/ (- a z) y)))
     (+ t (/ (* y (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+107) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.3e+92) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.2d+107)) then
        tmp = t * ((z - y) / (z - a))
    else if (z <= 1.3d+92) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+107) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.3e+92) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+107:
		tmp = t * ((z - y) / (z - a))
	elif z <= 1.3e+92:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+107)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (z <= 1.3e+92)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+107)
		tmp = t * ((z - y) / (z - a));
	elseif (z <= 1.3e+92)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+107], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+92], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000029e107

   1. Initial program 47.0%

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

      1. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in x around 0 51.9%

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

      1. associate-/l* 74.2%

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

   7. Simplified 74.2%

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

   if -3.20000000000000029e107 < z < 1.2999999999999999e92

   1. Initial program 85.0%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*l/ 85.0%

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

      3. associate-*r/ 91.8%

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

      4. clear-num 91.7%

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

      5. un-div-inv 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in y around inf 81.2%

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

   if 1.2999999999999999e92 < z

   1. Initial program 31.7%

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

      1. associate-/l* 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. associate-*r/ 65.1%

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

      3. associate-*r/ 65.1%

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

      4. mul-1-neg 65.1%

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

      5. div-sub 65.1%

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

      6. mul-1-neg 65.1%

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

      7. distribute-lft-out-- 65.1%

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

      8. associate-*r/ 65.1%

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

      9. mul-1-neg 65.1%

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

      10. unsub-neg 65.1%

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

      11. distribute-rgt-out-- 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in y around inf 61.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+92}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+107)
   (* t (/ (- z y) (- z a)))
   (if (<= z 1.6e+39)
     (+ x (/ (- t x) (/ (- a z) y)))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+107) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.6e+39) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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 (z <= (-8.6d+107)) then
        tmp = t * ((z - y) / (z - a))
    else if (z <= 1.6d+39) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t + (((t - x) * (a - y)) / 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 (z <= -8.6e+107) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.6e+39) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+107:
		tmp = t * ((z - y) / (z - a))
	elif z <= 1.6e+39:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+107)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (z <= 1.6e+39)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e+107)
		tmp = t * ((z - y) / (z - a));
	elseif (z <= 1.6e+39)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+107], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+39], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999999e107

   1. Initial program 47.0%

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

      1. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in x around 0 51.9%

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

      1. associate-/l* 74.2%

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

   7. Simplified 74.2%

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

   if -8.5999999999999999e107 < z < 1.59999999999999996e39

   1. Initial program 86.1%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 86.1%

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

      3. associate-*r/ 92.6%

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

      4. clear-num 92.5%

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

      5. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in y around inf 83.0%

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

   if 1.59999999999999996e39 < z

   1. Initial program 35.8%

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

      1. associate-/l* 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. mul-1-neg 64.9%

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

      5. div-sub 64.9%

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

      6. mul-1-neg 64.9%

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

      7. distribute-lft-out-- 64.9%

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

      8. associate-*r/ 64.9%

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

      9. mul-1-neg 64.9%

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

      10. unsub-neg 64.9%

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

      11. distribute-rgt-out-- 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-16)
   x
   (if (<= a 2.9e-286) t (if (<= a 1.32e+108) (* x (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-16) {
		tmp = x;
	} else if (a <= 2.9e-286) {
		tmp = t;
	} else if (a <= 1.32e+108) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d-16)) then
        tmp = x
    else if (a <= 2.9d-286) then
        tmp = t
    else if (a <= 1.32d+108) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-16) {
		tmp = x;
	} else if (a <= 2.9e-286) {
		tmp = t;
	} else if (a <= 1.32e+108) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-16:
		tmp = x
	elif a <= 2.9e-286:
		tmp = t
	elif a <= 1.32e+108:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-16)
		tmp = x;
	elseif (a <= 2.9e-286)
		tmp = t;
	elseif (a <= 1.32e+108)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-16)
		tmp = x;
	elseif (a <= 2.9e-286)
		tmp = t;
	elseif (a <= 1.32e+108)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-16], x, If[LessEqual[a, 2.9e-286], t, If[LessEqual[a, 1.32e+108], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000002e-16 or 1.32000000000000013e108 < a

   1. Initial program 70.7%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around inf 54.5%

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

   if -1.20000000000000002e-16 < a < 2.8999999999999998e-286

   1. Initial program 69.0%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 37.4%

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

   if 2.8999999999999998e-286 < a < 1.32000000000000013e108

   1. Initial program 65.1%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. associate-*r/ 60.1%

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

      3. associate-*r/ 60.1%

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

      4. mul-1-neg 60.1%

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

      5. div-sub 60.2%

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

      6. mul-1-neg 60.2%

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

      7. distribute-lft-out-- 60.2%

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

      8. associate-*r/ 60.2%

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

      9. mul-1-neg 60.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 60.2%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 60.3%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 60.3%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in y around -inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 36.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} \]

      2. associate-*r* 36.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z} \]

      3. mul-1-neg 36.1%

         \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z} \]

   10. Simplified 36.1%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(t - x\right)}{z}} \]

   11. Taylor expanded in t around 0 26.1%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-/l* 34.6%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   13. Simplified 34.6%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-12)
   x
   (if (<= a 1.7e-286) t (if (<= a 6.5e+107) (/ x (/ z y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-12) {
		tmp = x;
	} else if (a <= 1.7e-286) {
		tmp = t;
	} else if (a <= 6.5e+107) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d-12)) then
        tmp = x
    else if (a <= 1.7d-286) then
        tmp = t
    else if (a <= 6.5d+107) then
        tmp = x / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-12) {
		tmp = x;
	} else if (a <= 1.7e-286) {
		tmp = t;
	} else if (a <= 6.5e+107) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-12:
		tmp = x
	elif a <= 1.7e-286:
		tmp = t
	elif a <= 6.5e+107:
		tmp = x / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-12)
		tmp = x;
	elseif (a <= 1.7e-286)
		tmp = t;
	elseif (a <= 6.5e+107)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e-12)
		tmp = x;
	elseif (a <= 1.7e-286)
		tmp = t;
	elseif (a <= 6.5e+107)
		tmp = x / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-12], x, If[LessEqual[a, 1.7e-286], t, If[LessEqual[a, 6.5e+107], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.39999999999999987e-12 or 6.5000000000000006e107 < a

   1. Initial program 70.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 54.5%

      \[\leadsto \color{blue}{x} \]

   if -2.39999999999999987e-12 < a < 1.7000000000000001e-286

   1. Initial program 69.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 70.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 37.4%

      \[\leadsto \color{blue}{t} \]

   if 1.7000000000000001e-286 < a < 6.5000000000000006e107

   1. Initial program 65.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 75.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 60.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 60.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 60.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 60.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 60.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 60.2%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 60.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 60.2%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 60.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 60.2%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 60.3%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 60.3%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in y around -inf 36.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 36.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} \]

      2. associate-*r* 36.1%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z} \]

      3. mul-1-neg 36.1%

         \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z} \]

   10. Simplified 36.1%

       \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(t - x\right)}{z}} \]

   11. Taylor expanded in t around 0 26.1%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-/l* 34.6%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   13. Simplified 34.6%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   14. Step-by-step derivation

       1. clear-num 34.6%

          \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y}}} \]

       2. un-div-inv 34.7%

          \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   15. Applied egg-rr 34.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-286}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+102} \lor \neg \left(x \leq 1.52 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.8e+102) (not (<= x 1.52e-34)))
   (* x (+ (/ y (- z a)) 1.0))
   (* t (/ (- z y) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.8e+102) || !(x <= 1.52e-34)) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t * ((z - 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 ((x <= (-6.8d+102)) .or. (.not. (x <= 1.52d-34))) then
        tmp = x * ((y / (z - a)) + 1.0d0)
    else
        tmp = t * ((z - 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 ((x <= -6.8e+102) || !(x <= 1.52e-34)) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t * ((z - y) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.8e+102) or not (x <= 1.52e-34):
		tmp = x * ((y / (z - a)) + 1.0)
	else:
		tmp = t * ((z - y) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.8e+102) || !(x <= 1.52e-34))
		tmp = Float64(x * Float64(Float64(y / Float64(z - a)) + 1.0));
	else
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.8e+102) || ~((x <= 1.52e-34)))
		tmp = x * ((y / (z - a)) + 1.0);
	else
		tmp = t * ((z - y) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.8e+102], N[Not[LessEqual[x, 1.52e-34]], $MachinePrecision]], N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8000000000000001e102 or 1.52e-34 < x

   1. Initial program 62.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 76.3%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 62.4%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 79.0%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 79.0%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 79.0%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   6. Applied egg-rr 79.0%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   7. Taylor expanded in y around inf 70.9%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a - z}{y}}} \]

   8. Taylor expanded in x around inf 66.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a - z}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 66.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a - z}\right)}\right) \]

      2. unsub-neg 66.0%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a - z}\right)} \]

   10. Simplified 66.0%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a - z}\right)} \]

   if -6.8000000000000001e102 < x < 1.52e-34

   1. Initial program 75.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 85.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 57.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.5%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+102} \lor \neg \left(x \leq 1.52 \cdot 10^{-34}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+104) t (if (<= z 9.2e+148) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+104) {
		tmp = t;
	} else if (z <= 9.2e+148) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = 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 (z <= (-2.4d+104)) then
        tmp = t
    else if (z <= 9.2d+148) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = 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 (z <= -2.4e+104) {
		tmp = t;
	} else if (z <= 9.2e+148) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+104:
		tmp = t
	elif z <= 9.2e+148:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+104)
		tmp = t;
	elseif (z <= 9.2e+148)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+104)
		tmp = t;
	elseif (z <= 9.2e+148)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+104], t, If[LessEqual[z, 9.2e+148], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e104 or 9.2000000000000002e148 < z

   1. Initial program 37.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 62.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 48.8%

      \[\leadsto \color{blue}{t} \]

   if -2.4e104 < z < 9.2000000000000002e148

   1. Initial program 83.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 61.1%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 66.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 66.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in x around inf 53.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 53.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

      2. unsub-neg 53.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+104}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e-13) x (if (<= a 1.5e+128) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-13) {
		tmp = x;
	} else if (a <= 1.5e+128) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d-13)) then
        tmp = x
    else if (a <= 1.5d+128) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-13) {
		tmp = x;
	} else if (a <= 1.5e+128) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e-13:
		tmp = x
	elif a <= 1.5e+128:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e-13)
		tmp = x;
	elseif (a <= 1.5e+128)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e-13)
		tmp = x;
	elseif (a <= 1.5e+128)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e-13], x, If[LessEqual[a, 1.5e+128], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.0000000000000001e-13 or 1.4999999999999999e128 < a

   1. Initial program 72.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{x} \]

   if -2.0000000000000001e-13 < a < 1.4999999999999999e128

   1. Initial program 65.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 73.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 27.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return 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 = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 68.3%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 80.7%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 80.7%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 23.5%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 23.5%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024072 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))