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

Percentage Accurate: 68.3% → 88.6%

Time: 15.8s

Alternatives: 24

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \left(t - z\right)\\ t_2 := x + \frac{t\_1}{t - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{t\_1}}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y x) (- t z))) (t_2 (+ x (/ t_1 (- t a)))))
   (if (<= t_2 (- INFINITY))
     (- x (* (- z t) (* (- y x) (/ -1.0 (- a t)))))
     (if (<= t_2 -1e-216)
       (+ x (/ -1.0 (/ (- a t) t_1)))
       (if (<= t_2 0.0)
         (- y (/ (* (- a z) (- x y)) t))
         (if (<= t_2 1e+305) t_2 (+ y (* (/ (- x y) t) (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - x) * (t - z);
	double t_2 = x + (t_1 / (t - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	} else if (t_2 <= -1e-216) {
		tmp = x + (-1.0 / ((a - t) / t_1));
	} else if (t_2 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

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 + (t_1 / (t - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	} else if (t_2 <= -1e-216) {
		tmp = x + (-1.0 / ((a - t) / t_1));
	} else if (t_2 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - x) * (t - z)
	t_2 = x + (t_1 / (t - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))))
	elif t_2 <= -1e-216:
		tmp = x + (-1.0 / ((a - t) / t_1))
	elif t_2 <= 0.0:
		tmp = y - (((a - z) * (x - y)) / t)
	elif t_2 <= 1e+305:
		tmp = t_2
	else:
		tmp = y + (((x - y) / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - x) * Float64(t - z))
	t_2 = Float64(x + Float64(t_1 / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(a - t)))));
	elseif (t_2 <= -1e-216)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / t_1)));
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(Float64(Float64(x - y) / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - x) * (t - z);
	t_2 = x + (t_1 / (t - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	elseif (t_2 <= -1e-216)
		tmp = x + (-1.0 / ((a - t) / t_1));
	elseif (t_2 <= 0.0)
		tmp = y - (((a - z) * (x - y)) / t);
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	else
		tmp = y + (((x - y) / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-216], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], t$95$2, N[(y + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 43.2%

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

      1. div-inv 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 85.5%

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

   4. Applied egg-rr 85.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-216

   1. Initial program 97.1%

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

      1. clear-num 97.1%

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

      2. inv-pow 97.1%

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

      3. *-commutative 97.1%

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

      4. associate-/r* 97.1%

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

   4. Applied egg-rr 97.1%

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

      1. unpow-1 97.1%

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

      2. associate-/l/ 97.1%

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

      3. *-commutative 97.1%

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

   6. Simplified 97.1%

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

   if -1e-216 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

      1. div-inv 9.7%

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

      2. *-commutative 9.7%

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

      3. associate-*l* 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

   7. Simplified 100.0%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 99.4%

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

   if 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 22.1%

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

   3. Taylor expanded in t around inf 49.0%

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

      1. associate--l+ 49.0%

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

      2. distribute-lft-out-- 49.0%

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

      3. div-sub 49.1%

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

      4. mul-1-neg 49.1%

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

      5. unsub-neg 49.1%

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

      6. div-sub 49.0%

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

      7. associate-/l* 61.2%

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

      8. associate-/l* 68.5%

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

      9. distribute-rgt-out-- 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -1 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-216} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- t z)) (- t a)))))
   (if (or (<= t_1 -1e-216) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (- y (/ (* (- a z) (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if ((t_1 <= -1e-216) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - (((a - z) * (x - y)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -1e-216) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-216], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-216 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 90.0%

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

      3. fma-define 90.0%

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

   3. Simplified 90.0%

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

   if -1e-216 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

      1. div-inv 9.7%

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

      2. *-commutative 9.7%

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

      3. associate-*l* 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -1 \cdot 10^{-216} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- t z)) (- t a)))))
   (if (<= t_1 (- INFINITY))
     (- x (* (- z t) (* (- y x) (/ -1.0 (- a t)))))
     (if (<= t_1 -1e-216)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- a z) (- x y)) t))
         (if (<= t_1 1e+305) t_1 (+ y (* (/ (- x y) t) (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	} else if (t_1 <= -1e-216) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	} else if (t_1 <= -1e-216) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (t - z)) / (t - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))))
	elif t_1 <= -1e-216:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((a - z) * (x - y)) / t)
	elif t_1 <= 1e+305:
		tmp = t_1
	else:
		tmp = y + (((x - y) / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(a - t)))));
	elseif (t_1 <= -1e-216)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(x - y) / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (t - z)) / (t - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((z - t) * ((y - x) * (-1.0 / (a - t))));
	elseif (t_1 <= -1e-216)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((a - z) * (x - y)) / t);
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = y + (((x - y) / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-216], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], t$95$1, N[(y + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 43.2%

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

      1. div-inv 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 85.5%

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

   4. Applied egg-rr 85.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-216 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 98.3%

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

   if -1e-216 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

      1. div-inv 9.7%

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

      2. *-commutative 9.7%

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

      3. associate-*l* 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

   7. Simplified 100.0%

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

   if 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 22.1%

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

   3. Taylor expanded in t around inf 49.0%

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

      1. associate--l+ 49.0%

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

      2. distribute-lft-out-- 49.0%

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

      3. div-sub 49.1%

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

      4. mul-1-neg 49.1%

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

      5. unsub-neg 49.1%

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

      6. div-sub 49.0%

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

      7. associate-/l* 61.2%

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

      8. associate-/l* 68.5%

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

      9. distribute-rgt-out-- 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -\infty:\\ \;\;\;\;x - \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -1 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- t z)) (- t a)))))
   (if (<= t_1 (- INFINITY))
     (/ z (/ (- a t) (- y x)))
     (if (<= t_1 -1e-216)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- a z) (- x y)) t))
         (if (<= t_1 1e+305) t_1 (+ y (* (/ (- x y) t) (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z / ((a - t) / (y - x));
	} else if (t_1 <= -1e-216) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z / ((a - t) / (y - x));
	} else if (t_1 <= -1e-216) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((a - z) * (x - y)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = y + (((x - y) / t) * (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (t - z)) / (t - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z / ((a - t) / (y - x))
	elif t_1 <= -1e-216:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((a - z) * (x - y)) / t)
	elif t_1 <= 1e+305:
		tmp = t_1
	else:
		tmp = y + (((x - y) / t) * (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (t_1 <= -1e-216)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(a - z) * Float64(x - y)) / t));
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(Float64(x - y) / t) * Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (t - z)) / (t - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z / ((a - t) / (y - x));
	elseif (t_1 <= -1e-216)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((a - z) * (x - y)) / t);
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = y + (((x - y) / t) * (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-216], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(a - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], t$95$1, N[(y + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 43.2%

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

      1. div-inv 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 85.5%

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

   4. Applied egg-rr 85.5%

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

   5. Taylor expanded in z around inf 62.5%

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

      1. div-sub 64.4%

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

   7. Simplified 64.4%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.5%

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

   9. Applied egg-rr 64.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-216 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 98.3%

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

   if -1e-216 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.2%

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

      1. div-inv 9.7%

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

      2. *-commutative 9.7%

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

      3. associate-*l* 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

   7. Simplified 100.0%

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

   if 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 22.1%

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

   3. Taylor expanded in t around inf 49.0%

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

      1. associate--l+ 49.0%

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

      2. distribute-lft-out-- 49.0%

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

      3. div-sub 49.1%

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

      4. mul-1-neg 49.1%

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

      5. unsub-neg 49.1%

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

      6. div-sub 49.0%

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

      7. associate-/l* 61.2%

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

      8. associate-/l* 68.5%

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

      9. distribute-rgt-out-- 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -\infty:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq -1 \cdot 10^{-216}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 0:\\ \;\;\;\;y - \frac{\left(a - z\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -42000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 43000000000:\\ \;\;\;\;x + \frac{-1}{\frac{-1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= a -42000000000.0)
     (+ x (/ y (/ a z)))
     (if (<= a -5.2e-169)
       (* x (/ (- z a) t))
       (if (<= a -9.5e-190)
         y
         (if (<= a -9.2e-302)
           t_1
           (if (<= a 2.7e-252)
             y
             (if (<= a 3.2e-129)
               t_1
               (if (<= a 43000000000.0)
                 (+ x (/ -1.0 (/ -1.0 y)))
                 (+ x (* y (/ z a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -42000000000.0) {
		tmp = x + (y / (a / z));
	} else if (a <= -5.2e-169) {
		tmp = x * ((z - a) / t);
	} else if (a <= -9.5e-190) {
		tmp = y;
	} else if (a <= -9.2e-302) {
		tmp = t_1;
	} else if (a <= 2.7e-252) {
		tmp = y;
	} else if (a <= 3.2e-129) {
		tmp = t_1;
	} else if (a <= 43000000000.0) {
		tmp = x + (-1.0 / (-1.0 / y));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (a <= (-42000000000.0d0)) then
        tmp = x + (y / (a / z))
    else if (a <= (-5.2d-169)) then
        tmp = x * ((z - a) / t)
    else if (a <= (-9.5d-190)) then
        tmp = y
    else if (a <= (-9.2d-302)) then
        tmp = t_1
    else if (a <= 2.7d-252) then
        tmp = y
    else if (a <= 3.2d-129) then
        tmp = t_1
    else if (a <= 43000000000.0d0) then
        tmp = x + ((-1.0d0) / ((-1.0d0) / y))
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (a <= -42000000000.0) {
		tmp = x + (y / (a / z));
	} else if (a <= -5.2e-169) {
		tmp = x * ((z - a) / t);
	} else if (a <= -9.5e-190) {
		tmp = y;
	} else if (a <= -9.2e-302) {
		tmp = t_1;
	} else if (a <= 2.7e-252) {
		tmp = y;
	} else if (a <= 3.2e-129) {
		tmp = t_1;
	} else if (a <= 43000000000.0) {
		tmp = x + (-1.0 / (-1.0 / y));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if a <= -42000000000.0:
		tmp = x + (y / (a / z))
	elif a <= -5.2e-169:
		tmp = x * ((z - a) / t)
	elif a <= -9.5e-190:
		tmp = y
	elif a <= -9.2e-302:
		tmp = t_1
	elif a <= 2.7e-252:
		tmp = y
	elif a <= 3.2e-129:
		tmp = t_1
	elif a <= 43000000000.0:
		tmp = x + (-1.0 / (-1.0 / y))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -42000000000.0)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= -5.2e-169)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= -9.5e-190)
		tmp = y;
	elseif (a <= -9.2e-302)
		tmp = t_1;
	elseif (a <= 2.7e-252)
		tmp = y;
	elseif (a <= 3.2e-129)
		tmp = t_1;
	elseif (a <= 43000000000.0)
		tmp = Float64(x + Float64(-1.0 / Float64(-1.0 / y)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (a <= -42000000000.0)
		tmp = x + (y / (a / z));
	elseif (a <= -5.2e-169)
		tmp = x * ((z - a) / t);
	elseif (a <= -9.5e-190)
		tmp = y;
	elseif (a <= -9.2e-302)
		tmp = t_1;
	elseif (a <= 2.7e-252)
		tmp = y;
	elseif (a <= 3.2e-129)
		tmp = t_1;
	elseif (a <= 43000000000.0)
		tmp = x + (-1.0 / (-1.0 / y));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -42000000000.0], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e-169], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-190], y, If[LessEqual[a, -9.2e-302], t$95$1, If[LessEqual[a, 2.7e-252], y, If[LessEqual[a, 3.2e-129], t$95$1, If[LessEqual[a, 43000000000.0], N[(x + N[(-1.0 / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.2e10

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 72.6%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*r/ 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-/r/ 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in t around 0 69.0%

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

   if -4.2e10 < a < -5.20000000000000028e-169

   1. Initial program 54.3%

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

      1. div-inv 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*l* 60.2%

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

   4. Applied egg-rr 60.2%

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

   5. Taylor expanded in t around inf 59.2%

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

      1. associate--l+ 59.2%

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

      2. associate-*r/ 59.2%

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

      3. associate-*r/ 59.2%

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

      4. mul-1-neg 59.2%

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

      5. div-sub 59.2%

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

      6. mul-1-neg 59.2%

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

      7. distribute-lft-out-- 59.2%

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

      8. associate-*r/ 59.2%

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

      9. mul-1-neg 59.2%

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

      10. unsub-neg 59.2%

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

      11. distribute-rgt-out-- 59.2%

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

   7. Simplified 59.2%

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

   8. Taylor expanded in y around 0 29.1%

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

      1. associate-/l* 36.9%

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

   10. Simplified 36.9%

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

   if -5.20000000000000028e-169 < a < -9.50000000000000055e-190 or -9.20000000000000007e-302 < a < 2.69999999999999981e-252

   1. Initial program 48.0%

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

   3. Taylor expanded in t around inf 78.7%

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

   if -9.50000000000000055e-190 < a < -9.20000000000000007e-302 or 2.69999999999999981e-252 < a < 3.2000000000000003e-129

   1. Initial program 70.0%

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

      1. div-inv 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*l* 68.3%

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

   4. Applied egg-rr 68.3%

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

   5. Taylor expanded in t around inf 77.0%

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

      1. associate--l+ 77.0%

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

      2. associate-*r/ 77.0%

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

      3. associate-*r/ 77.0%

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

      4. mul-1-neg 77.0%

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

      5. div-sub 77.0%

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

      6. mul-1-neg 77.0%

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

      7. distribute-lft-out-- 77.0%

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

      8. associate-*r/ 77.0%

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

      9. mul-1-neg 77.0%

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

      10. unsub-neg 77.0%

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

      11. distribute-rgt-out-- 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in z around -inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 64.7%

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

      3. *-commutative 64.7%

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

      4. distribute-rgt-neg-in 64.7%

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

   10. Simplified 64.7%

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

   if 3.2000000000000003e-129 < a < 4.3e10

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 54.6%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

      1. associate-*r/ 54.6%

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

      2. clear-num 54.4%

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

   7. Applied egg-rr 54.4%

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

   8. Taylor expanded in t around inf 53.0%

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

   if 4.3e10 < a

   1. Initial program 64.6%

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

   3. Taylor expanded in t around 0 58.6%

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

   4. Taylor expanded in y around inf 58.2%

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

      1. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -42000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-190}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 43000000000:\\ \;\;\;\;x + \frac{-1}{\frac{-1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -180000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{-1}{\frac{-1}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= a -180000000000.0)
     (+ x (/ y (/ a z)))
     (if (<= a -9.2e-302)
       t_1
       (if (<= a 3.4e-252)
         y
         (if (<= a 2.1e-82)
           t_1
           (if (<= a 4e-18)
             (+ x (/ -1.0 (/ -1.0 y)))
             (if (<= a 1.2e+52) t_1 (+ x (* y (/ z a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -180000000000.0) {
		tmp = x + (y / (a / z));
	} else if (a <= -9.2e-302) {
		tmp = t_1;
	} else if (a <= 3.4e-252) {
		tmp = y;
	} else if (a <= 2.1e-82) {
		tmp = t_1;
	} else if (a <= 4e-18) {
		tmp = x + (-1.0 / (-1.0 / y));
	} else if (a <= 1.2e+52) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (a <= (-180000000000.0d0)) then
        tmp = x + (y / (a / z))
    else if (a <= (-9.2d-302)) then
        tmp = t_1
    else if (a <= 3.4d-252) then
        tmp = y
    else if (a <= 2.1d-82) then
        tmp = t_1
    else if (a <= 4d-18) then
        tmp = x + ((-1.0d0) / ((-1.0d0) / y))
    else if (a <= 1.2d+52) then
        tmp = t_1
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -180000000000.0) {
		tmp = x + (y / (a / z));
	} else if (a <= -9.2e-302) {
		tmp = t_1;
	} else if (a <= 3.4e-252) {
		tmp = y;
	} else if (a <= 2.1e-82) {
		tmp = t_1;
	} else if (a <= 4e-18) {
		tmp = x + (-1.0 / (-1.0 / y));
	} else if (a <= 1.2e+52) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -180000000000.0:
		tmp = x + (y / (a / z))
	elif a <= -9.2e-302:
		tmp = t_1
	elif a <= 3.4e-252:
		tmp = y
	elif a <= 2.1e-82:
		tmp = t_1
	elif a <= 4e-18:
		tmp = x + (-1.0 / (-1.0 / y))
	elif a <= 1.2e+52:
		tmp = t_1
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -180000000000.0)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= -9.2e-302)
		tmp = t_1;
	elseif (a <= 3.4e-252)
		tmp = y;
	elseif (a <= 2.1e-82)
		tmp = t_1;
	elseif (a <= 4e-18)
		tmp = Float64(x + Float64(-1.0 / Float64(-1.0 / y)));
	elseif (a <= 1.2e+52)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -180000000000.0)
		tmp = x + (y / (a / z));
	elseif (a <= -9.2e-302)
		tmp = t_1;
	elseif (a <= 3.4e-252)
		tmp = y;
	elseif (a <= 2.1e-82)
		tmp = t_1;
	elseif (a <= 4e-18)
		tmp = x + (-1.0 / (-1.0 / y));
	elseif (a <= 1.2e+52)
		tmp = t_1;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -180000000000.0], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e-302], t$95$1, If[LessEqual[a, 3.4e-252], y, If[LessEqual[a, 2.1e-82], t$95$1, If[LessEqual[a, 4e-18], N[(x + N[(-1.0 / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+52], t$95$1, N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.8e11

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 72.6%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*r/ 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-/r/ 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in t around 0 69.0%

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

   if -1.8e11 < a < -9.20000000000000007e-302 or 3.4e-252 < a < 2.1e-82 or 4.0000000000000003e-18 < a < 1.2e52

   1. Initial program 63.9%

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

      1. div-inv 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*l* 67.2%

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

   4. Applied egg-rr 67.2%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. div-sub 58.1%

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

   7. Simplified 58.1%

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

   if -9.20000000000000007e-302 < a < 3.4e-252

   1. Initial program 55.2%

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

   3. Taylor expanded in t around inf 78.3%

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

   if 2.1e-82 < a < 4.0000000000000003e-18

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

      1. associate-*r/ 64.1%

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

      2. clear-num 63.6%

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

   7. Applied egg-rr 63.6%

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

   8. Taylor expanded in t around inf 68.8%

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

   if 1.2e52 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in t around 0 58.8%

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

   4. Taylor expanded in y around inf 61.8%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -180000000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-252}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{-1}{\frac{-1}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+124}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -45000000000:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-177}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -3.6e+124)
     y
     (if (<= t -5.5e+54)
       t_1
       (if (<= t -45000000000.0)
         (/ (* y z) (- a t))
         (if (<= t -4.4e-278)
           t_1
           (if (<= t 2.7e-177)
             (- x (/ x (/ a z)))
             (if (<= t 1.46e+125) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -3.6e+124) {
		tmp = y;
	} else if (t <= -5.5e+54) {
		tmp = t_1;
	} else if (t <= -45000000000.0) {
		tmp = (y * z) / (a - t);
	} else if (t <= -4.4e-278) {
		tmp = t_1;
	} else if (t <= 2.7e-177) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.46e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-3.6d+124)) then
        tmp = y
    else if (t <= (-5.5d+54)) then
        tmp = t_1
    else if (t <= (-45000000000.0d0)) then
        tmp = (y * z) / (a - t)
    else if (t <= (-4.4d-278)) then
        tmp = t_1
    else if (t <= 2.7d-177) then
        tmp = x - (x / (a / z))
    else if (t <= 1.46d+125) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -3.6e+124) {
		tmp = y;
	} else if (t <= -5.5e+54) {
		tmp = t_1;
	} else if (t <= -45000000000.0) {
		tmp = (y * z) / (a - t);
	} else if (t <= -4.4e-278) {
		tmp = t_1;
	} else if (t <= 2.7e-177) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.46e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -3.6e+124:
		tmp = y
	elif t <= -5.5e+54:
		tmp = t_1
	elif t <= -45000000000.0:
		tmp = (y * z) / (a - t)
	elif t <= -4.4e-278:
		tmp = t_1
	elif t <= 2.7e-177:
		tmp = x - (x / (a / z))
	elif t <= 1.46e+125:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -3.6e+124)
		tmp = y;
	elseif (t <= -5.5e+54)
		tmp = t_1;
	elseif (t <= -45000000000.0)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= -4.4e-278)
		tmp = t_1;
	elseif (t <= 2.7e-177)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 1.46e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -3.6e+124)
		tmp = y;
	elseif (t <= -5.5e+54)
		tmp = t_1;
	elseif (t <= -45000000000.0)
		tmp = (y * z) / (a - t);
	elseif (t <= -4.4e-278)
		tmp = t_1;
	elseif (t <= 2.7e-177)
		tmp = x - (x / (a / z));
	elseif (t <= 1.46e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+124], y, If[LessEqual[t, -5.5e+54], t$95$1, If[LessEqual[t, -45000000000.0], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-278], t$95$1, If[LessEqual[t, 2.7e-177], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.46e+125], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.59999999999999986e124 or 1.45999999999999999e125 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 52.3%

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

   if -3.59999999999999986e124 < t < -5.50000000000000026e54 or -4.5e10 < t < -4.4000000000000002e-278 or 2.7000000000000002e-177 < t < 1.45999999999999999e125

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 55.6%

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

   4. Taylor expanded in y around inf 53.7%

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

      1. associate-/l* 59.6%

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

   6. Simplified 59.6%

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

   if -5.50000000000000026e54 < t < -4.5e10

   1. Initial program 89.7%

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

      1. div-inv 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around 0 89.3%

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

   6. Taylor expanded in z around inf 68.0%

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

   if -4.4000000000000002e-278 < t < 2.7000000000000002e-177

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 84.0%

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

   4. Taylor expanded in y around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. unsub-neg 84.0%

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

      3. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.8%

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

   8. Applied egg-rr 87.8%

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

Alternative 8: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+122}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -45000000000:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-175}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -8.5e+122)
     y
     (if (<= t -8.5e+52)
       t_1
       (if (<= t -45000000000.0)
         (* z (/ y (- a t)))
         (if (<= t -2e-277)
           t_1
           (if (<= t 1e-175)
             (- x (/ x (/ a z)))
             (if (<= t 1.56e+125) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -8.5e+122) {
		tmp = y;
	} else if (t <= -8.5e+52) {
		tmp = t_1;
	} else if (t <= -45000000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= -2e-277) {
		tmp = t_1;
	} else if (t <= 1e-175) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.56e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-8.5d+122)) then
        tmp = y
    else if (t <= (-8.5d+52)) then
        tmp = t_1
    else if (t <= (-45000000000.0d0)) then
        tmp = z * (y / (a - t))
    else if (t <= (-2d-277)) then
        tmp = t_1
    else if (t <= 1d-175) then
        tmp = x - (x / (a / z))
    else if (t <= 1.56d+125) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -8.5e+122) {
		tmp = y;
	} else if (t <= -8.5e+52) {
		tmp = t_1;
	} else if (t <= -45000000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= -2e-277) {
		tmp = t_1;
	} else if (t <= 1e-175) {
		tmp = x - (x / (a / z));
	} else if (t <= 1.56e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -8.5e+122:
		tmp = y
	elif t <= -8.5e+52:
		tmp = t_1
	elif t <= -45000000000.0:
		tmp = z * (y / (a - t))
	elif t <= -2e-277:
		tmp = t_1
	elif t <= 1e-175:
		tmp = x - (x / (a / z))
	elif t <= 1.56e+125:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -8.5e+122)
		tmp = y;
	elseif (t <= -8.5e+52)
		tmp = t_1;
	elseif (t <= -45000000000.0)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= -2e-277)
		tmp = t_1;
	elseif (t <= 1e-175)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 1.56e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -8.5e+122)
		tmp = y;
	elseif (t <= -8.5e+52)
		tmp = t_1;
	elseif (t <= -45000000000.0)
		tmp = z * (y / (a - t));
	elseif (t <= -2e-277)
		tmp = t_1;
	elseif (t <= 1e-175)
		tmp = x - (x / (a / z));
	elseif (t <= 1.56e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+122], y, If[LessEqual[t, -8.5e+52], t$95$1, If[LessEqual[t, -45000000000.0], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-277], t$95$1, If[LessEqual[t, 1e-175], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e+125], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000003e122 or 1.56e125 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 52.3%

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

   if -8.50000000000000003e122 < t < -8.49999999999999994e52 or -4.5e10 < t < -1.99999999999999994e-277 or 1e-175 < t < 1.56e125

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 55.6%

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

   4. Taylor expanded in y around inf 53.7%

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

      1. associate-/l* 59.6%

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

   6. Simplified 59.6%

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

   if -8.49999999999999994e52 < t < -4.5e10

   1. Initial program 89.7%

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

      1. div-inv 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around inf 78.6%

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

      1. div-sub 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 67.8%

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

   if -1.99999999999999994e-277 < t < 1e-175

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 84.0%

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

   4. Taylor expanded in y around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. unsub-neg 84.0%

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

      3. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

      1. clear-num 87.7%

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

      2. un-div-inv 87.8%

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

   8. Applied egg-rr 87.8%

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

Alternative 9: 51.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -10500000000:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-175}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -1.85e+121)
     y
     (if (<= t -1.3e+51)
       t_1
       (if (<= t -10500000000.0)
         (* z (/ y (- a t)))
         (if (<= t -1.65e-277)
           t_1
           (if (<= t 8.2e-175)
             (- x (* x (/ z a)))
             (if (<= t 1.85e+125) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.85e+121) {
		tmp = y;
	} else if (t <= -1.3e+51) {
		tmp = t_1;
	} else if (t <= -10500000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= -1.65e-277) {
		tmp = t_1;
	} else if (t <= 8.2e-175) {
		tmp = x - (x * (z / a));
	} else if (t <= 1.85e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-1.85d+121)) then
        tmp = y
    else if (t <= (-1.3d+51)) then
        tmp = t_1
    else if (t <= (-10500000000.0d0)) then
        tmp = z * (y / (a - t))
    else if (t <= (-1.65d-277)) then
        tmp = t_1
    else if (t <= 8.2d-175) then
        tmp = x - (x * (z / a))
    else if (t <= 1.85d+125) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -1.85e+121) {
		tmp = y;
	} else if (t <= -1.3e+51) {
		tmp = t_1;
	} else if (t <= -10500000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= -1.65e-277) {
		tmp = t_1;
	} else if (t <= 8.2e-175) {
		tmp = x - (x * (z / a));
	} else if (t <= 1.85e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -1.85e+121:
		tmp = y
	elif t <= -1.3e+51:
		tmp = t_1
	elif t <= -10500000000.0:
		tmp = z * (y / (a - t))
	elif t <= -1.65e-277:
		tmp = t_1
	elif t <= 8.2e-175:
		tmp = x - (x * (z / a))
	elif t <= 1.85e+125:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.85e+121)
		tmp = y;
	elseif (t <= -1.3e+51)
		tmp = t_1;
	elseif (t <= -10500000000.0)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= -1.65e-277)
		tmp = t_1;
	elseif (t <= 8.2e-175)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 1.85e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.85e+121)
		tmp = y;
	elseif (t <= -1.3e+51)
		tmp = t_1;
	elseif (t <= -10500000000.0)
		tmp = z * (y / (a - t));
	elseif (t <= -1.65e-277)
		tmp = t_1;
	elseif (t <= 8.2e-175)
		tmp = x - (x * (z / a));
	elseif (t <= 1.85e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+121], y, If[LessEqual[t, -1.3e+51], t$95$1, If[LessEqual[t, -10500000000.0], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e-277], t$95$1, If[LessEqual[t, 8.2e-175], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+125], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.85000000000000006e121 or 1.8499999999999999e125 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 52.3%

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

   if -1.85000000000000006e121 < t < -1.3000000000000001e51 or -1.05e10 < t < -1.64999999999999991e-277 or 8.19999999999999997e-175 < t < 1.8499999999999999e125

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 55.6%

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

   4. Taylor expanded in y around inf 53.7%

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

      1. associate-/l* 59.6%

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

   6. Simplified 59.6%

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

   if -1.3000000000000001e51 < t < -1.05e10

   1. Initial program 89.7%

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

      1. div-inv 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around inf 78.6%

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

      1. div-sub 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 67.8%

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

   if -1.64999999999999991e-277 < t < 8.19999999999999997e-175

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 84.0%

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

   4. Taylor expanded in y around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. unsub-neg 84.0%

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

      3. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

Alternative 10: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -135000000:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -9.8e+123)
     y
     (if (<= t -9e+52)
       t_1
       (if (<= t -135000000.0)
         (* z (/ y (- a t)))
         (if (<= t 2.3e+63)
           t_1
           (if (<= t 8e+90)
             (* a (/ (- y x) t))
             (if (<= t 1.22e+125) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -9.8e+123) {
		tmp = y;
	} else if (t <= -9e+52) {
		tmp = t_1;
	} else if (t <= -135000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.3e+63) {
		tmp = t_1;
	} else if (t <= 8e+90) {
		tmp = a * ((y - x) / t);
	} else if (t <= 1.22e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-9.8d+123)) then
        tmp = y
    else if (t <= (-9d+52)) then
        tmp = t_1
    else if (t <= (-135000000.0d0)) then
        tmp = z * (y / (a - t))
    else if (t <= 2.3d+63) then
        tmp = t_1
    else if (t <= 8d+90) then
        tmp = a * ((y - x) / t)
    else if (t <= 1.22d+125) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -9.8e+123) {
		tmp = y;
	} else if (t <= -9e+52) {
		tmp = t_1;
	} else if (t <= -135000000.0) {
		tmp = z * (y / (a - t));
	} else if (t <= 2.3e+63) {
		tmp = t_1;
	} else if (t <= 8e+90) {
		tmp = a * ((y - x) / t);
	} else if (t <= 1.22e+125) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -9.8e+123:
		tmp = y
	elif t <= -9e+52:
		tmp = t_1
	elif t <= -135000000.0:
		tmp = z * (y / (a - t))
	elif t <= 2.3e+63:
		tmp = t_1
	elif t <= 8e+90:
		tmp = a * ((y - x) / t)
	elif t <= 1.22e+125:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -9.8e+123)
		tmp = y;
	elseif (t <= -9e+52)
		tmp = t_1;
	elseif (t <= -135000000.0)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= 2.3e+63)
		tmp = t_1;
	elseif (t <= 8e+90)
		tmp = Float64(a * Float64(Float64(y - x) / t));
	elseif (t <= 1.22e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -9.8e+123)
		tmp = y;
	elseif (t <= -9e+52)
		tmp = t_1;
	elseif (t <= -135000000.0)
		tmp = z * (y / (a - t));
	elseif (t <= 2.3e+63)
		tmp = t_1;
	elseif (t <= 8e+90)
		tmp = a * ((y - x) / t);
	elseif (t <= 1.22e+125)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.8e+123], y, If[LessEqual[t, -9e+52], t$95$1, If[LessEqual[t, -135000000.0], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+63], t$95$1, If[LessEqual[t, 8e+90], N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+125], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.79999999999999952e123 or 1.22e125 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 52.3%

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

   if -9.79999999999999952e123 < t < -8.9999999999999999e52 or -1.35e8 < t < 2.29999999999999993e63 or 7.99999999999999973e90 < t < 1.22e125

   1. Initial program 81.1%

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

   3. Taylor expanded in t around 0 61.5%

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

   4. Taylor expanded in y around inf 57.0%

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

      1. associate-/l* 62.3%

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

   6. Simplified 62.3%

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

   if -8.9999999999999999e52 < t < -1.35e8

   1. Initial program 89.7%

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

      1. div-inv 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around inf 78.6%

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

      1. div-sub 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around inf 67.8%

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

   if 2.29999999999999993e63 < t < 7.99999999999999973e90

   1. Initial program 44.7%

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

      1. div-inv 46.2%

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

      2. *-commutative 46.2%

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

      3. associate-*l* 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in t around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r/ 71.3%

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

      4. mul-1-neg 71.3%

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

      5. div-sub 71.5%

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

      6. mul-1-neg 71.5%

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

      7. distribute-lft-out-- 71.5%

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

      8. associate-*r/ 71.5%

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

      9. mul-1-neg 71.5%

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

      10. unsub-neg 71.5%

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

      11. distribute-rgt-out-- 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in a around inf 65.7%

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

      1. associate-/l* 65.5%

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

   10. Simplified 65.5%

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

Alternative 11: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 3.85:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-51)
   (+ x (/ y (/ a (- z t))))
   (if (<= a 7.5e-252)
     (* y (/ (- z t) (- a t)))
     (if (<= a 6.4e-92)
       (/ z (/ (- a t) (- y x)))
       (if (<= a 3.85) (+ x (* y (/ (- t z) t))) (+ x (* y (/ (- z t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-51) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 7.5e-252) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 6.4e-92) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 3.85) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d-51)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 7.5d-252) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 6.4d-92) then
        tmp = z / ((a - t) / (y - x))
    else if (a <= 3.85d0) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-51) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 7.5e-252) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 6.4e-92) {
		tmp = z / ((a - t) / (y - x));
	} else if (a <= 3.85) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-51:
		tmp = x + (y / (a / (z - t)))
	elif a <= 7.5e-252:
		tmp = y * ((z - t) / (a - t))
	elif a <= 6.4e-92:
		tmp = z / ((a - t) / (y - x))
	elif a <= 3.85:
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-51)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 7.5e-252)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 6.4e-92)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (a <= 3.85)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-51)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 7.5e-252)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 6.4e-92)
		tmp = z / ((a - t) / (y - x));
	elseif (a <= 3.85)
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-51], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-252], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-92], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.85], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e-51

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/r/ 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in a around inf 71.6%

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

   if -1.2e-51 < a < 7.4999999999999996e-252

   1. Initial program 61.9%

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

      1. div-inv 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*l* 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in x around 0 54.2%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

   7. Applied egg-rr 74.7%

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

   if 7.4999999999999996e-252 < a < 6.3999999999999994e-92

   1. Initial program 57.9%

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

      1. div-inv 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 61.6%

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

   4. Applied egg-rr 61.6%

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

   5. Taylor expanded in z around inf 73.6%

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

      1. div-sub 73.6%

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

   7. Simplified 73.6%

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

      1. clear-num 73.6%

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

      2. un-div-inv 73.6%

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

   9. Applied egg-rr 73.6%

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

   if 6.3999999999999994e-92 < a < 3.85000000000000009

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 78.5%

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

   8. Simplified 78.5%

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

   if 3.85000000000000009 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf 72.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;a \leq 3.85:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 58:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-51)
   (+ x (/ y (/ a (- z t))))
   (if (<= a 4.3e-251)
     (* y (/ (- z t) (- a t)))
     (if (<= a 2.1e-82)
       (* z (/ (- y x) (- a t)))
       (if (<= a 58.0) (+ x (* y (/ (- t z) t))) (+ x (* y (/ (- z t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-51) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 4.3e-251) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2.1e-82) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 58.0) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d-51)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 4.3d-251) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 2.1d-82) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 58.0d0) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-51) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 4.3e-251) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 2.1e-82) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 58.0) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-51:
		tmp = x + (y / (a / (z - t)))
	elif a <= 4.3e-251:
		tmp = y * ((z - t) / (a - t))
	elif a <= 2.1e-82:
		tmp = z * ((y - x) / (a - t))
	elif a <= 58.0:
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-51)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 4.3e-251)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 2.1e-82)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 58.0)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-51)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 4.3e-251)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 2.1e-82)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 58.0)
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-51], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-251], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-82], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 58.0], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e-51

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/r/ 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in a around inf 71.6%

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

   if -1.2e-51 < a < 4.3000000000000002e-251

   1. Initial program 61.9%

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

      1. div-inv 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*l* 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in x around 0 54.2%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

   7. Applied egg-rr 74.7%

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

   if 4.3000000000000002e-251 < a < 2.1e-82

   1. Initial program 57.9%

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

      1. div-inv 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 61.6%

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

   4. Applied egg-rr 61.6%

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

   5. Taylor expanded in z around inf 73.6%

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

      1. div-sub 73.6%

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

   7. Simplified 73.6%

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

   if 2.1e-82 < a < 58

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

      3. associate-/l* 78.5%

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

   8. Simplified 78.5%

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

   if 58 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf 72.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 58:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -1.85e-53)
     (+ x (/ y (/ a (- z t))))
     (if (<= a 1.14e-250)
       t_1
       (if (<= a 3.1e-80)
         (* z (/ (- y x) (- a t)))
         (if (<= a 9.5e+30) t_1 (+ x (* y (/ (- z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.85e-53) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 1.14e-250) {
		tmp = t_1;
	} else if (a <= 3.1e-80) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.5e+30) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-1.85d-53)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 1.14d-250) then
        tmp = t_1
    else if (a <= 3.1d-80) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 9.5d+30) then
        tmp = t_1
    else
        tmp = x + (y * ((z - t) / 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 * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.85e-53) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 1.14e-250) {
		tmp = t_1;
	} else if (a <= 3.1e-80) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 9.5e+30) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -1.85e-53:
		tmp = x + (y / (a / (z - t)))
	elif a <= 1.14e-250:
		tmp = t_1
	elif a <= 3.1e-80:
		tmp = z * ((y - x) / (a - t))
	elif a <= 9.5e+30:
		tmp = t_1
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.85e-53)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 1.14e-250)
		tmp = t_1;
	elseif (a <= 3.1e-80)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 9.5e+30)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -1.85e-53)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 1.14e-250)
		tmp = t_1;
	elseif (a <= 3.1e-80)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 9.5e+30)
		tmp = t_1;
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-53], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.14e-250], t$95$1, If[LessEqual[a, 3.1e-80], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+30], t$95$1, N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.84999999999999991e-53

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/r/ 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in a around inf 71.6%

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

   if -1.84999999999999991e-53 < a < 1.14000000000000007e-250 or 3.10000000000000016e-80 < a < 9.5000000000000003e30

   1. Initial program 65.7%

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

      1. div-inv 65.5%

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

      2. *-commutative 65.5%

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

      3. associate-*l* 72.8%

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

   4. Applied egg-rr 72.8%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. associate-*r/ 73.5%

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

      2. *-commutative 73.5%

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

   7. Applied egg-rr 73.5%

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

   if 1.14000000000000007e-250 < a < 3.10000000000000016e-80

   1. Initial program 59.5%

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

      1. div-inv 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-*l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in z around inf 71.1%

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

      1. div-sub 71.1%

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

   7. Simplified 71.1%

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

   if 9.5000000000000003e30 < a

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 64.6%

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

      1. associate-/l* 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in a around inf 74.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-250}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ (- z t) a)))))
   (if (<= a -1.2e-51)
     t_2
     (if (<= a 3.15e-248)
       t_1
       (if (<= a 2.05e-78)
         (* z (/ (- y x) (- a t)))
         (if (<= a 4e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -1.2e-51) {
		tmp = t_2;
	} else if (a <= 3.15e-248) {
		tmp = t_1;
	} else if (a <= 2.05e-78) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4e+28) {
		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 * ((z - t) / (a - t))
    t_2 = x + (y * ((z - t) / a))
    if (a <= (-1.2d-51)) then
        tmp = t_2
    else if (a <= 3.15d-248) then
        tmp = t_1
    else if (a <= 2.05d-78) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 4d+28) 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 * ((z - t) / (a - t));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -1.2e-51) {
		tmp = t_2;
	} else if (a <= 3.15e-248) {
		tmp = t_1;
	} else if (a <= 2.05e-78) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * ((z - t) / a))
	tmp = 0
	if a <= -1.2e-51:
		tmp = t_2
	elif a <= 3.15e-248:
		tmp = t_1
	elif a <= 2.05e-78:
		tmp = z * ((y - x) / (a - t))
	elif a <= 4e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -1.2e-51)
		tmp = t_2;
	elseif (a <= 3.15e-248)
		tmp = t_1;
	elseif (a <= 2.05e-78)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 4e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -1.2e-51)
		tmp = t_2;
	elseif (a <= 3.15e-248)
		tmp = t_1;
	elseif (a <= 2.05e-78)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 4e+28)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-51], t$95$2, If[LessEqual[a, 3.15e-248], t$95$1, If[LessEqual[a, 2.05e-78], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e-51 or 3.99999999999999983e28 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in y around inf 66.9%

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

      1. associate-/l* 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in a around inf 72.9%

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

   if -1.2e-51 < a < 3.14999999999999997e-248 or 2.0499999999999999e-78 < a < 3.99999999999999983e28

   1. Initial program 65.7%

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

      1. div-inv 65.5%

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

      2. *-commutative 65.5%

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

      3. associate-*l* 72.8%

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

   4. Applied egg-rr 72.8%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. associate-*r/ 73.5%

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

      2. *-commutative 73.5%

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

   7. Applied egg-rr 73.5%

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

   if 3.14999999999999997e-248 < a < 2.0499999999999999e-78

   1. Initial program 59.5%

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

      1. div-inv 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-*l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in z around inf 71.1%

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

      1. div-sub 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -1.8e+67)
     t_2
     (if (<= a 1.6e-249)
       t_1
       (if (<= a 2.15e-78)
         (* z (/ (- y x) (- a t)))
         (if (<= a 4.3e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -1.8e+67) {
		tmp = t_2;
	} else if (a <= 1.6e-249) {
		tmp = t_1;
	} else if (a <= 2.15e-78) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.3e+61) {
		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 * ((z - t) / (a - t))
    t_2 = x + (y * (z / a))
    if (a <= (-1.8d+67)) then
        tmp = t_2
    else if (a <= 1.6d-249) then
        tmp = t_1
    else if (a <= 2.15d-78) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 4.3d+61) 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 * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -1.8e+67) {
		tmp = t_2;
	} else if (a <= 1.6e-249) {
		tmp = t_1;
	} else if (a <= 2.15e-78) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.3e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -1.8e+67:
		tmp = t_2
	elif a <= 1.6e-249:
		tmp = t_1
	elif a <= 2.15e-78:
		tmp = z * ((y - x) / (a - t))
	elif a <= 4.3e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -1.8e+67)
		tmp = t_2;
	elseif (a <= 1.6e-249)
		tmp = t_1;
	elseif (a <= 2.15e-78)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 4.3e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -1.8e+67)
		tmp = t_2;
	elseif (a <= 1.6e-249)
		tmp = t_1;
	elseif (a <= 2.15e-78)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 4.3e+61)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+67], t$95$2, If[LessEqual[a, 1.6e-249], t$95$1, If[LessEqual[a, 2.15e-78], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7999999999999999e67 or 4.3000000000000001e61 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in t around 0 64.3%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. associate-/l* 70.9%

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

   6. Simplified 70.9%

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

   if -1.7999999999999999e67 < a < 1.6000000000000001e-249 or 2.14999999999999997e-78 < a < 4.3000000000000001e61

   1. Initial program 65.0%

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

      1. div-inv 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*l* 72.1%

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

   4. Applied egg-rr 72.1%

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

   5. Taylor expanded in x around 0 49.0%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

   7. Applied egg-rr 64.9%

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

   if 1.6000000000000001e-249 < a < 2.14999999999999997e-78

   1. Initial program 59.5%

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

      1. div-inv 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-*l* 59.5%

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

   4. Applied egg-rr 59.5%

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

   5. Taylor expanded in z around inf 71.1%

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

      1. div-sub 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+67}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-240}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) a))))
   (if (<= z -5.9e+65)
     t_1
     (if (<= z -1.85e-69) x (if (<= z -6e-240) y (if (<= z 3e+37) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -5.9e+65) {
		tmp = t_1;
	} else if (z <= -1.85e-69) {
		tmp = x;
	} else if (z <= -6e-240) {
		tmp = y;
	} else if (z <= 3e+37) {
		tmp = 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 = z * ((y - x) / a)
    if (z <= (-5.9d+65)) then
        tmp = t_1
    else if (z <= (-1.85d-69)) then
        tmp = x
    else if (z <= (-6d-240)) then
        tmp = y
    else if (z <= 3d+37) then
        tmp = 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 = z * ((y - x) / a);
	double tmp;
	if (z <= -5.9e+65) {
		tmp = t_1;
	} else if (z <= -1.85e-69) {
		tmp = x;
	} else if (z <= -6e-240) {
		tmp = y;
	} else if (z <= 3e+37) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / a)
	tmp = 0
	if z <= -5.9e+65:
		tmp = t_1
	elif z <= -1.85e-69:
		tmp = x
	elif z <= -6e-240:
		tmp = y
	elif z <= 3e+37:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (z <= -5.9e+65)
		tmp = t_1;
	elseif (z <= -1.85e-69)
		tmp = x;
	elseif (z <= -6e-240)
		tmp = y;
	elseif (z <= 3e+37)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / a);
	tmp = 0.0;
	if (z <= -5.9e+65)
		tmp = t_1;
	elseif (z <= -1.85e-69)
		tmp = x;
	elseif (z <= -6e-240)
		tmp = y;
	elseif (z <= 3e+37)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.9e+65], t$95$1, If[LessEqual[z, -1.85e-69], x, If[LessEqual[z, -6e-240], y, If[LessEqual[z, 3e+37], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9000000000000003e65 or 3.00000000000000022e37 < z

   1. Initial program 68.0%

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

      1. div-inv 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*l* 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in z around inf 69.9%

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

      1. div-sub 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in a around inf 37.6%

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

      1. associate-/l* 44.8%

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

   10. Simplified 44.8%

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

   if -5.9000000000000003e65 < z < -1.8500000000000001e-69 or -5.99999999999999982e-240 < z < 3.00000000000000022e37

   1. Initial program 65.7%

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

   3. Taylor expanded in a around inf 46.1%

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

   if -1.8500000000000001e-69 < z < -5.99999999999999982e-240

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf 43.2%

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

Alternative 17: 38.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+110}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 0.85:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e+110)
   y
   (if (<= t -7e-96)
     (* z (/ y (- a t)))
     (if (<= t 0.85) x (if (<= t 7.4e+124) (* x (/ (- z a) t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+110) {
		tmp = y;
	} else if (t <= -7e-96) {
		tmp = z * (y / (a - t));
	} else if (t <= 0.85) {
		tmp = x;
	} else if (t <= 7.4e+124) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.8d+110)) then
        tmp = y
    else if (t <= (-7d-96)) then
        tmp = z * (y / (a - t))
    else if (t <= 0.85d0) then
        tmp = x
    else if (t <= 7.4d+124) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+110) {
		tmp = y;
	} else if (t <= -7e-96) {
		tmp = z * (y / (a - t));
	} else if (t <= 0.85) {
		tmp = x;
	} else if (t <= 7.4e+124) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e+110:
		tmp = y
	elif t <= -7e-96:
		tmp = z * (y / (a - t))
	elif t <= 0.85:
		tmp = x
	elif t <= 7.4e+124:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e+110)
		tmp = y;
	elseif (t <= -7e-96)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t <= 0.85)
		tmp = x;
	elseif (t <= 7.4e+124)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e+110)
		tmp = y;
	elseif (t <= -7e-96)
		tmp = z * (y / (a - t));
	elseif (t <= 0.85)
		tmp = x;
	elseif (t <= 7.4e+124)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e+110], y, If[LessEqual[t, -7e-96], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.85], x, If[LessEqual[t, 7.4e+124], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.7999999999999999e110 or 7.40000000000000016e124 < t

   1. Initial program 32.8%

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

   3. Taylor expanded in t around inf 51.0%

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

   if -5.7999999999999999e110 < t < -6.9999999999999998e-96

   1. Initial program 77.9%

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

      1. div-inv 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l* 90.1%

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

   4. Applied egg-rr 90.1%

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

   5. Taylor expanded in z around inf 56.4%

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

      1. div-sub 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in y around inf 40.2%

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

   if -6.9999999999999998e-96 < t < 0.849999999999999978

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 47.2%

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

   if 0.849999999999999978 < t < 7.40000000000000016e124

   1. Initial program 53.8%

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

      1. div-inv 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*l* 69.2%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in t around inf 47.0%

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

      1. associate--l+ 47.0%

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

      2. associate-*r/ 47.0%

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

      3. associate-*r/ 47.0%

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

      4. mul-1-neg 47.0%

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

      5. div-sub 47.1%

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

      6. mul-1-neg 47.1%

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

      7. distribute-lft-out-- 47.1%

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

      8. associate-*r/ 47.1%

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

      9. mul-1-neg 47.1%

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

      10. unsub-neg 47.1%

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

      11. distribute-rgt-out-- 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in y around 0 33.6%

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

      1. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

Alternative 18: 38.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.9e+100)
   y
   (if (<= t 4.2) x (if (<= t 3.6e+124) (* x (/ (- z a) t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.9e+100) {
		tmp = y;
	} else if (t <= 4.2) {
		tmp = x;
	} else if (t <= 3.6e+124) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.9d+100)) then
        tmp = y
    else if (t <= 4.2d0) then
        tmp = x
    else if (t <= 3.6d+124) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.9e+100) {
		tmp = y;
	} else if (t <= 4.2) {
		tmp = x;
	} else if (t <= 3.6e+124) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.9e+100:
		tmp = y
	elif t <= 4.2:
		tmp = x
	elif t <= 3.6e+124:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.9e+100)
		tmp = y;
	elseif (t <= 4.2)
		tmp = x;
	elseif (t <= 3.6e+124)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.9e+100)
		tmp = y;
	elseif (t <= 4.2)
		tmp = x;
	elseif (t <= 3.6e+124)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.9e+100], y, If[LessEqual[t, 4.2], x, If[LessEqual[t, 3.6e+124], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.90000000000000027e100 or 3.59999999999999986e124 < t

   1. Initial program 31.8%

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

   3. Taylor expanded in t around inf 49.1%

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

   if -5.90000000000000027e100 < t < 4.20000000000000018

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 40.4%

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

   if 4.20000000000000018 < t < 3.59999999999999986e124

   1. Initial program 53.8%

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

      1. div-inv 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*l* 69.2%

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

   4. Applied egg-rr 69.2%

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

   5. Taylor expanded in t around inf 47.0%

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

      1. associate--l+ 47.0%

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

      2. associate-*r/ 47.0%

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

      3. associate-*r/ 47.0%

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

      4. mul-1-neg 47.0%

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

      5. div-sub 47.1%

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

      6. mul-1-neg 47.1%

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

      7. distribute-lft-out-- 47.1%

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

      8. associate-*r/ 47.1%

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

      9. mul-1-neg 47.1%

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

      10. unsub-neg 47.1%

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

      11. distribute-rgt-out-- 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in y around 0 33.6%

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

      1. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

Alternative 19: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+98}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+98)
   y
   (if (<= t 7.4e+56)
     x
     (if (<= t 8e+90) (* a (/ (- y x) t)) (if (<= t 8.5e+124) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+98) {
		tmp = y;
	} else if (t <= 7.4e+56) {
		tmp = x;
	} else if (t <= 8e+90) {
		tmp = a * ((y - x) / t);
	} else if (t <= 8.5e+124) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.8d+98)) then
        tmp = y
    else if (t <= 7.4d+56) then
        tmp = x
    else if (t <= 8d+90) then
        tmp = a * ((y - x) / t)
    else if (t <= 8.5d+124) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+98) {
		tmp = y;
	} else if (t <= 7.4e+56) {
		tmp = x;
	} else if (t <= 8e+90) {
		tmp = a * ((y - x) / t);
	} else if (t <= 8.5e+124) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+98:
		tmp = y
	elif t <= 7.4e+56:
		tmp = x
	elif t <= 8e+90:
		tmp = a * ((y - x) / t)
	elif t <= 8.5e+124:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+98)
		tmp = y;
	elseif (t <= 7.4e+56)
		tmp = x;
	elseif (t <= 8e+90)
		tmp = Float64(a * Float64(Float64(y - x) / t));
	elseif (t <= 8.5e+124)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+98)
		tmp = y;
	elseif (t <= 7.4e+56)
		tmp = x;
	elseif (t <= 8e+90)
		tmp = a * ((y - x) / t);
	elseif (t <= 8.5e+124)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+98], y, If[LessEqual[t, 7.4e+56], x, If[LessEqual[t, 8e+90], N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+124], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999999e98 or 8.4999999999999997e124 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 49.7%

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

   if -3.7999999999999999e98 < t < 7.39999999999999994e56 or 7.99999999999999973e90 < t < 8.4999999999999997e124

   1. Initial program 84.1%

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

   3. Taylor expanded in a around inf 39.0%

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

   if 7.39999999999999994e56 < t < 7.99999999999999973e90

   1. Initial program 46.9%

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

      1. div-inv 48.1%

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

      2. *-commutative 48.1%

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

      3. associate-*l* 58.2%

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

   4. Applied egg-rr 58.2%

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

   5. Taylor expanded in t around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. associate-*r/ 77.6%

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

      3. associate-*r/ 77.6%

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

      4. mul-1-neg 77.6%

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

      5. div-sub 77.8%

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

      6. mul-1-neg 77.8%

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

      7. distribute-lft-out-- 77.8%

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

      8. associate-*r/ 77.8%

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

      9. mul-1-neg 77.8%

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

      10. unsub-neg 77.8%

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

      11. distribute-rgt-out-- 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in a around inf 52.3%

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

      1. associate-/l* 52.2%

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

   10. Simplified 52.2%

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

Alternative 20: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+62} \lor \neg \left(z \leq 4.9 \cdot 10^{+173}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+62) (not (<= z 4.9e+173)))
   (* z (/ (- y x) (- a t)))
   (+ x (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+62) || !(z <= 4.9e+173)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.5d+62)) .or. (.not. (z <= 4.9d+173))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (y / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+62) || !(z <= 4.9e+173)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+62) or not (z <= 4.9e+173):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+62) || !(z <= 4.9e+173))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+62) || ~((z <= 4.9e+173)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+62], N[Not[LessEqual[z, 4.9e+173]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999998e62 or 4.9000000000000001e173 < z

   1. Initial program 69.7%

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

      1. div-inv 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 81.8%

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

   4. Applied egg-rr 81.8%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. div-sub 80.3%

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

   7. Simplified 80.3%

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

   if -7.49999999999999998e62 < z < 4.9000000000000001e173

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around 0 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*r/ 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-/r/ 77.1%

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

   8. Simplified 77.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+62} \lor \neg \left(z \leq 4.9 \cdot 10^{+173}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+64} \lor \neg \left(z \leq 7 \cdot 10^{+172}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+64) (not (<= z 7e+172)))
   (* z (/ (- y x) (- a t)))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+64) || !(z <= 7e+172)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d+64)) .or. (.not. (z <= 7d+172))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+64) || !(z <= 7e+172)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+64) or not (z <= 7e+172):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+64) || !(z <= 7e+172))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e+64) || ~((z <= 7e+172)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+64], N[Not[LessEqual[z, 7e+172]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e64 or 6.99999999999999955e172 < z

   1. Initial program 69.7%

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

      1. div-inv 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 81.8%

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

   4. Applied egg-rr 81.8%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. div-sub 80.3%

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

   7. Simplified 80.3%

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

   if -2.7e64 < z < 6.99999999999999955e172

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+64} \lor \neg \left(z \leq 7 \cdot 10^{+172}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -14500:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 2.36 \cdot 10^{-85}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -14500.0)
   (+ x (* (- y x) (/ (- z t) a)))
   (if (<= a 2.36e-85)
     (+ y (* (/ (- x y) t) (- z a)))
     (+ x (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -14500.0) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (a <= 2.36e-85) {
		tmp = y + (((x - y) / t) * (z - a));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-14500.0d0)) then
        tmp = x + ((y - x) * ((z - t) / a))
    else if (a <= 2.36d-85) then
        tmp = y + (((x - y) / t) * (z - a))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -14500.0) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else if (a <= 2.36e-85) {
		tmp = y + (((x - y) / t) * (z - a));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -14500.0:
		tmp = x + ((y - x) * ((z - t) / a))
	elif a <= 2.36e-85:
		tmp = y + (((x - y) / t) * (z - a))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -14500.0)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	elseif (a <= 2.36e-85)
		tmp = Float64(y + Float64(Float64(Float64(x - y) / t) * Float64(z - a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -14500.0)
		tmp = x + ((y - x) * ((z - t) / a));
	elseif (a <= 2.36e-85)
		tmp = y + (((x - y) / t) * (z - a));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -14500.0], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.36e-85], N[(y + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -14500

   1. Initial program 74.5%

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

   3. Taylor expanded in a around inf 71.7%

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

      1. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   if -14500 < a < 2.35999999999999999e-85

   1. Initial program 60.0%

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

   3. Taylor expanded in t around inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. distribute-lft-out-- 73.8%

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

      3. div-sub 73.8%

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

      4. mul-1-neg 73.8%

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

      5. unsub-neg 73.8%

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

      6. div-sub 73.8%

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

      7. associate-/l* 78.2%

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

      8. associate-/l* 75.2%

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

      9. distribute-rgt-out-- 78.3%

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

   5. Simplified 78.3%

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

   if 2.35999999999999999e-85 < a

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14500:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 2.36 \cdot 10^{-85}:\\ \;\;\;\;y + \frac{x - y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e+96) y (if (<= t 1.3e+125) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+96) {
		tmp = y;
	} else if (t <= 1.3e+125) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.6d+96)) then
        tmp = y
    else if (t <= 1.3d+125) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+96) {
		tmp = y;
	} else if (t <= 1.3e+125) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e+96:
		tmp = y
	elif t <= 1.3e+125:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e+96)
		tmp = y;
	elseif (t <= 1.3e+125)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e+96)
		tmp = y;
	elseif (t <= 1.3e+125)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e+96], y, If[LessEqual[t, 1.3e+125], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000003e96 or 1.30000000000000002e125 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf 49.7%

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

   if -1.60000000000000003e96 < t < 1.30000000000000002e125

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 37.2%

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

Alternative 24: 25.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in a around inf 28.9%

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

Developer target: 86.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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