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

Percentage Accurate: 68.8% → 86.7%

Time: 16.1s

Alternatives: 31

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (if (<= t_1 -5e-271)
       t_1
       (if (<= t_1 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_1 5e+306) t_1 (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= -5e-271) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else if (t_1 <= -5e-271) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	elif t_1 <= -5e-271:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_1 <= 5e+306:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	elseif (t_1 <= -5e-271)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	elseif (t_1 <= -5e-271)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-271], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 35.3%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

      1. clear-num 80.8%

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

      2. un-div-inv 80.9%

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

   6. Applied egg-rr 80.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000002e-271 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.99999999999999993e306

   1. Initial program 97.0%

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

   if -5.0000000000000002e-271 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.7%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 4.99999999999999993e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 30.6%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around 0 28.4%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-271}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-271} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-271) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-271) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-271) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-271], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000002e-271 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-/l* 87.4%

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

      4. fma-define 87.4%

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

   3. Simplified 87.4%

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

   if -5.0000000000000002e-271 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.7%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-271} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- y z) (/ (- x t) (- z a))))
     (if (<= t_1 -5e-271)
       t_1
       (if (<= t_1 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_1 5e+306) t_1 (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else if (t_1 <= -5e-271) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else if (t_1 <= -5e-271) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y - z) * ((x - t) / (z - a)))
	elif t_1 <= -5e-271:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_1 <= 5e+306:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(z - a))));
	elseif (t_1 <= -5e-271)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	elseif (t_1 <= -5e-271)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-271], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 35.3%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000002e-271 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.99999999999999993e306

   1. Initial program 97.0%

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

   if -5.0000000000000002e-271 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.7%

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

      1. associate-/l* 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   if 4.99999999999999993e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 30.6%

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

      1. associate-/l* 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around 0 28.4%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-271}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ t_3 := y \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;t + \frac{t\_3}{z}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{t\_3}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+81}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ x (/ (- y z) (/ a t))))
        (t_3 (* y (- x t))))
   (if (<= a -7e+81)
     t_2
     (if (<= a -3.7e-99)
       t_1
       (if (<= a 6.5e-191)
         (+ t (/ t_3 z))
         (if (<= a 9.4e-73)
           (/ y (/ (- a z) (- t x)))
           (if (<= a 2.15e+23)
             t_1
             (if (<= a 4.6e+52)
               (- x (/ t_3 a))
               (if (<= a 9.2e+81) (- t (* x (/ a z))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -7e+81) {
		tmp = t_2;
	} else if (a <= -3.7e-99) {
		tmp = t_1;
	} else if (a <= 6.5e-191) {
		tmp = t + (t_3 / z);
	} else if (a <= 9.4e-73) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 2.15e+23) {
		tmp = t_1;
	} else if (a <= 4.6e+52) {
		tmp = x - (t_3 / a);
	} else if (a <= 9.2e+81) {
		tmp = t - (x * (a / z));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) / (a / t))
    t_3 = y * (x - t)
    if (a <= (-7d+81)) then
        tmp = t_2
    else if (a <= (-3.7d-99)) then
        tmp = t_1
    else if (a <= 6.5d-191) then
        tmp = t + (t_3 / z)
    else if (a <= 9.4d-73) then
        tmp = y / ((a - z) / (t - x))
    else if (a <= 2.15d+23) then
        tmp = t_1
    else if (a <= 4.6d+52) then
        tmp = x - (t_3 / a)
    else if (a <= 9.2d+81) then
        tmp = t - (x * (a / z))
    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 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -7e+81) {
		tmp = t_2;
	} else if (a <= -3.7e-99) {
		tmp = t_1;
	} else if (a <= 6.5e-191) {
		tmp = t + (t_3 / z);
	} else if (a <= 9.4e-73) {
		tmp = y / ((a - z) / (t - x));
	} else if (a <= 2.15e+23) {
		tmp = t_1;
	} else if (a <= 4.6e+52) {
		tmp = x - (t_3 / a);
	} else if (a <= 9.2e+81) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) / (a / t))
	t_3 = y * (x - t)
	tmp = 0
	if a <= -7e+81:
		tmp = t_2
	elif a <= -3.7e-99:
		tmp = t_1
	elif a <= 6.5e-191:
		tmp = t + (t_3 / z)
	elif a <= 9.4e-73:
		tmp = y / ((a - z) / (t - x))
	elif a <= 2.15e+23:
		tmp = t_1
	elif a <= 4.6e+52:
		tmp = x - (t_3 / a)
	elif a <= 9.2e+81:
		tmp = t - (x * (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	t_3 = Float64(y * Float64(x - t))
	tmp = 0.0
	if (a <= -7e+81)
		tmp = t_2;
	elseif (a <= -3.7e-99)
		tmp = t_1;
	elseif (a <= 6.5e-191)
		tmp = Float64(t + Float64(t_3 / z));
	elseif (a <= 9.4e-73)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (a <= 2.15e+23)
		tmp = t_1;
	elseif (a <= 4.6e+52)
		tmp = Float64(x - Float64(t_3 / a));
	elseif (a <= 9.2e+81)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) / (a / t));
	t_3 = y * (x - t);
	tmp = 0.0;
	if (a <= -7e+81)
		tmp = t_2;
	elseif (a <= -3.7e-99)
		tmp = t_1;
	elseif (a <= 6.5e-191)
		tmp = t + (t_3 / z);
	elseif (a <= 9.4e-73)
		tmp = y / ((a - z) / (t - x));
	elseif (a <= 2.15e+23)
		tmp = t_1;
	elseif (a <= 4.6e+52)
		tmp = x - (t_3 / a);
	elseif (a <= 9.2e+81)
		tmp = t - (x * (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+81], t$95$2, If[LessEqual[a, -3.7e-99], t$95$1, If[LessEqual[a, 6.5e-191], N[(t + N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e-73], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+23], t$95$1, If[LessEqual[a, 4.6e+52], N[(x - N[(t$95$3 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+81], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.0000000000000001e81 or 9.1999999999999995e81 < a

   1. Initial program 70.3%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in t around inf 78.4%

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

   8. Taylor expanded in a around inf 75.0%

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

   if -7.0000000000000001e81 < a < -3.7e-99 or 9.39999999999999988e-73 < a < 2.1499999999999999e23

   1. Initial program 68.2%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. associate-/l* 69.8%

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

   7. Simplified 69.8%

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

   if -3.7e-99 < a < 6.4999999999999995e-191

   1. Initial program 60.2%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate--l+ 86.8%

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

      2. associate-*r/ 86.8%

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

      3. associate-*r/ 86.8%

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

      4. mul-1-neg 86.8%

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

      5. div-sub 86.8%

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

      6. mul-1-neg 86.8%

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

      7. distribute-lft-out-- 86.8%

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

      8. associate-*r/ 86.8%

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

      9. mul-1-neg 86.8%

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

      10. unsub-neg 86.8%

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

      11. distribute-rgt-out-- 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in y around inf 84.8%

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

   if 6.4999999999999995e-191 < a < 9.39999999999999988e-73

   1. Initial program 83.5%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. div-sub 76.8%

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

   7. Simplified 76.8%

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

      1. clear-num 76.8%

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

      2. div-inv 76.9%

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

   9. Applied egg-rr 76.9%

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

   if 2.1499999999999999e23 < a < 4.6e52

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.5%

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

   if 4.6e52 < a < 9.1999999999999995e81

   1. Initial program 36.5%

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

      1. associate-/l* 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. associate-*r/ 56.8%

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

      3. associate-*r/ 56.8%

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

      4. mul-1-neg 56.8%

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

      5. div-sub 56.8%

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

      6. mul-1-neg 56.8%

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

      7. distribute-lft-out-- 56.8%

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

      8. associate-*r/ 56.8%

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

      9. mul-1-neg 56.8%

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

      10. unsub-neg 56.8%

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

      11. distribute-rgt-out-- 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in t around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-/l* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. distribute-neg-frac2 78.2%

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

   10. Simplified 78.2%

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

   11. Taylor expanded in y around 0 79.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+81}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ t_3 := y \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;t + \frac{t\_3}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{t\_3}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+82}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ x (/ (- y z) (/ a t))))
        (t_3 (* y (- x t))))
   (if (<= a -6.2e+84)
     t_2
     (if (<= a -5.2e-97)
       t_1
       (if (<= a 1.06e-190)
         (+ t (/ t_3 z))
         (if (<= a 4.7e-86)
           (* y (/ (- x t) (- z a)))
           (if (<= a 1.45e+25)
             t_1
             (if (<= a 1.12e+53)
               (- x (/ t_3 a))
               (if (<= a 2.75e+82) (- t (* x (/ a z))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -6.2e+84) {
		tmp = t_2;
	} else if (a <= -5.2e-97) {
		tmp = t_1;
	} else if (a <= 1.06e-190) {
		tmp = t + (t_3 / z);
	} else if (a <= 4.7e-86) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 1.45e+25) {
		tmp = t_1;
	} else if (a <= 1.12e+53) {
		tmp = x - (t_3 / a);
	} else if (a <= 2.75e+82) {
		tmp = t - (x * (a / z));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) / (a / t))
    t_3 = y * (x - t)
    if (a <= (-6.2d+84)) then
        tmp = t_2
    else if (a <= (-5.2d-97)) then
        tmp = t_1
    else if (a <= 1.06d-190) then
        tmp = t + (t_3 / z)
    else if (a <= 4.7d-86) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 1.45d+25) then
        tmp = t_1
    else if (a <= 1.12d+53) then
        tmp = x - (t_3 / a)
    else if (a <= 2.75d+82) then
        tmp = t - (x * (a / z))
    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 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double t_3 = y * (x - t);
	double tmp;
	if (a <= -6.2e+84) {
		tmp = t_2;
	} else if (a <= -5.2e-97) {
		tmp = t_1;
	} else if (a <= 1.06e-190) {
		tmp = t + (t_3 / z);
	} else if (a <= 4.7e-86) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 1.45e+25) {
		tmp = t_1;
	} else if (a <= 1.12e+53) {
		tmp = x - (t_3 / a);
	} else if (a <= 2.75e+82) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) / (a / t))
	t_3 = y * (x - t)
	tmp = 0
	if a <= -6.2e+84:
		tmp = t_2
	elif a <= -5.2e-97:
		tmp = t_1
	elif a <= 1.06e-190:
		tmp = t + (t_3 / z)
	elif a <= 4.7e-86:
		tmp = y * ((x - t) / (z - a))
	elif a <= 1.45e+25:
		tmp = t_1
	elif a <= 1.12e+53:
		tmp = x - (t_3 / a)
	elif a <= 2.75e+82:
		tmp = t - (x * (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	t_3 = Float64(y * Float64(x - t))
	tmp = 0.0
	if (a <= -6.2e+84)
		tmp = t_2;
	elseif (a <= -5.2e-97)
		tmp = t_1;
	elseif (a <= 1.06e-190)
		tmp = Float64(t + Float64(t_3 / z));
	elseif (a <= 4.7e-86)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 1.45e+25)
		tmp = t_1;
	elseif (a <= 1.12e+53)
		tmp = Float64(x - Float64(t_3 / a));
	elseif (a <= 2.75e+82)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) / (a / t));
	t_3 = y * (x - t);
	tmp = 0.0;
	if (a <= -6.2e+84)
		tmp = t_2;
	elseif (a <= -5.2e-97)
		tmp = t_1;
	elseif (a <= 1.06e-190)
		tmp = t + (t_3 / z);
	elseif (a <= 4.7e-86)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 1.45e+25)
		tmp = t_1;
	elseif (a <= 1.12e+53)
		tmp = x - (t_3 / a);
	elseif (a <= 2.75e+82)
		tmp = t - (x * (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+84], t$95$2, If[LessEqual[a, -5.2e-97], t$95$1, If[LessEqual[a, 1.06e-190], N[(t + N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-86], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+25], t$95$1, If[LessEqual[a, 1.12e+53], N[(x - N[(t$95$3 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e+82], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -6.20000000000000006e84 or 2.74999999999999998e82 < a

   1. Initial program 70.3%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in t around inf 78.4%

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

   8. Taylor expanded in a around inf 75.0%

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

   if -6.20000000000000006e84 < a < -5.20000000000000014e-97 or 4.7000000000000001e-86 < a < 1.44999999999999995e25

   1. Initial program 68.2%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. associate-/l* 69.8%

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

   7. Simplified 69.8%

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

   if -5.20000000000000014e-97 < a < 1.05999999999999997e-190

   1. Initial program 60.2%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. associate--l+ 86.8%

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

      2. associate-*r/ 86.8%

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

      3. associate-*r/ 86.8%

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

      4. mul-1-neg 86.8%

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

      5. div-sub 86.8%

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

      6. mul-1-neg 86.8%

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

      7. distribute-lft-out-- 86.8%

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

      8. associate-*r/ 86.8%

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

      9. mul-1-neg 86.8%

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

      10. unsub-neg 86.8%

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

      11. distribute-rgt-out-- 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in y around inf 84.8%

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

   if 1.05999999999999997e-190 < a < 4.7000000000000001e-86

   1. Initial program 83.5%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. div-sub 76.8%

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

   7. Simplified 76.8%

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

   if 1.44999999999999995e25 < a < 1.12e53

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.5%

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

   if 1.12e53 < a < 2.74999999999999998e82

   1. Initial program 36.5%

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

      1. associate-/l* 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. associate-*r/ 56.8%

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

      3. associate-*r/ 56.8%

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

      4. mul-1-neg 56.8%

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

      5. div-sub 56.8%

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

      6. mul-1-neg 56.8%

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

      7. distribute-lft-out-- 56.8%

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

      8. associate-*r/ 56.8%

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

      9. mul-1-neg 56.8%

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

      10. unsub-neg 56.8%

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

      11. distribute-rgt-out-- 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in t around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-/l* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. distribute-neg-frac2 78.2%

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

   10. Simplified 78.2%

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

   11. Taylor expanded in y around 0 79.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-190}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+53}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{+82}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-191}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+82}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- y z) (/ a t)))))
   (if (<= a -1.3e+93)
     t_2
     (if (<= a -4.8e-170)
       t_1
       (if (<= a 1.35e-191)
         (+ t (* y (/ x z)))
         (if (<= a 3.15e-85)
           (* y (/ (- x t) (- z a)))
           (if (<= a 3.4e+24)
             t_1
             (if (<= a 1.04e+52)
               (- x (/ (* y (- x t)) a))
               (if (<= a 1.45e+82) (- t (* x (/ a z))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -1.3e+93) {
		tmp = t_2;
	} else if (a <= -4.8e-170) {
		tmp = t_1;
	} else if (a <= 1.35e-191) {
		tmp = t + (y * (x / z));
	} else if (a <= 3.15e-85) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 3.4e+24) {
		tmp = t_1;
	} else if (a <= 1.04e+52) {
		tmp = x - ((y * (x - t)) / a);
	} else if (a <= 1.45e+82) {
		tmp = t - (x * (a / z));
	} 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 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) / (a / t))
    if (a <= (-1.3d+93)) then
        tmp = t_2
    else if (a <= (-4.8d-170)) then
        tmp = t_1
    else if (a <= 1.35d-191) then
        tmp = t + (y * (x / z))
    else if (a <= 3.15d-85) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 3.4d+24) then
        tmp = t_1
    else if (a <= 1.04d+52) then
        tmp = x - ((y * (x - t)) / a)
    else if (a <= 1.45d+82) then
        tmp = t - (x * (a / z))
    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 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -1.3e+93) {
		tmp = t_2;
	} else if (a <= -4.8e-170) {
		tmp = t_1;
	} else if (a <= 1.35e-191) {
		tmp = t + (y * (x / z));
	} else if (a <= 3.15e-85) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 3.4e+24) {
		tmp = t_1;
	} else if (a <= 1.04e+52) {
		tmp = x - ((y * (x - t)) / a);
	} else if (a <= 1.45e+82) {
		tmp = t - (x * (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) / (a / t))
	tmp = 0
	if a <= -1.3e+93:
		tmp = t_2
	elif a <= -4.8e-170:
		tmp = t_1
	elif a <= 1.35e-191:
		tmp = t + (y * (x / z))
	elif a <= 3.15e-85:
		tmp = y * ((x - t) / (z - a))
	elif a <= 3.4e+24:
		tmp = t_1
	elif a <= 1.04e+52:
		tmp = x - ((y * (x - t)) / a)
	elif a <= 1.45e+82:
		tmp = t - (x * (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	tmp = 0.0
	if (a <= -1.3e+93)
		tmp = t_2;
	elseif (a <= -4.8e-170)
		tmp = t_1;
	elseif (a <= 1.35e-191)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (a <= 3.15e-85)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 3.4e+24)
		tmp = t_1;
	elseif (a <= 1.04e+52)
		tmp = Float64(x - Float64(Float64(y * Float64(x - t)) / a));
	elseif (a <= 1.45e+82)
		tmp = Float64(t - Float64(x * Float64(a / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) / (a / t));
	tmp = 0.0;
	if (a <= -1.3e+93)
		tmp = t_2;
	elseif (a <= -4.8e-170)
		tmp = t_1;
	elseif (a <= 1.35e-191)
		tmp = t + (y * (x / z));
	elseif (a <= 3.15e-85)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 3.4e+24)
		tmp = t_1;
	elseif (a <= 1.04e+52)
		tmp = x - ((y * (x - t)) / a);
	elseif (a <= 1.45e+82)
		tmp = t - (x * (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+93], t$95$2, If[LessEqual[a, -4.8e-170], t$95$1, If[LessEqual[a, 1.35e-191], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.15e-85], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+24], t$95$1, If[LessEqual[a, 1.04e+52], N[(x - N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+82], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.3e93 or 1.4500000000000001e82 < a

   1. Initial program 70.3%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in t around inf 78.4%

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

   8. Taylor expanded in a around inf 75.0%

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

   if -1.3e93 < a < -4.7999999999999999e-170 or 3.15e-85 < a < 3.4000000000000001e24

   1. Initial program 68.5%

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

      1. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. associate-/l* 68.7%

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

   7. Simplified 68.7%

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

   if -4.7999999999999999e-170 < a < 1.34999999999999999e-191

   1. Initial program 56.8%

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

      1. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate--l+ 89.8%

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

      2. associate-*r/ 89.8%

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

      3. associate-*r/ 89.8%

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

      4. mul-1-neg 89.8%

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

      5. div-sub 89.8%

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

      6. mul-1-neg 89.8%

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

      7. distribute-lft-out-- 89.8%

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

      8. associate-*r/ 89.8%

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

      9. mul-1-neg 89.8%

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

      10. unsub-neg 89.8%

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

      11. distribute-rgt-out-- 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in t around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. associate-/l* 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

      4. distribute-neg-frac2 78.7%

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

   10. Simplified 78.7%

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

   11. Taylor expanded in y around inf 81.2%

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

       1. associate-*r/ 81.2%

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

       2. *-commutative 81.2%

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

       3. neg-mul-1 81.2%

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

       4. distribute-rgt-neg-in 81.2%

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

       5. associate-*r/ 81.1%

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

   13. Simplified 81.1%

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

   if 1.34999999999999999e-191 < a < 3.15e-85

   1. Initial program 83.5%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. div-sub 76.8%

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

   7. Simplified 76.8%

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

   if 3.4000000000000001e24 < a < 1.04e52

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.5%

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

   if 1.04e52 < a < 1.4500000000000001e82

   1. Initial program 36.5%

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

      1. associate-/l* 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in z around inf 56.8%

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

      1. associate--l+ 56.8%

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

      2. associate-*r/ 56.8%

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

      3. associate-*r/ 56.8%

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

      4. mul-1-neg 56.8%

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

      5. div-sub 56.8%

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

      6. mul-1-neg 56.8%

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

      7. distribute-lft-out-- 56.8%

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

      8. associate-*r/ 56.8%

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

      9. mul-1-neg 56.8%

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

      10. unsub-neg 56.8%

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

      11. distribute-rgt-out-- 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in t around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-/l* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. distribute-neg-frac2 78.2%

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

   10. Simplified 78.2%

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

   11. Taylor expanded in y around 0 79.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-191}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+82}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-191}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44} \lor \neg \left(a \leq 1.2 \cdot 10^{+84}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.65e+86)
     (+ x (* y (/ t a)))
     (if (<= a -3e-170)
       t_1
       (if (<= a 6.2e-191)
         (+ t (* y (/ x z)))
         (if (<= a 3.1e-82)
           (* y (/ (- x t) (- z a)))
           (if (<= a 2.5e+24)
             t_1
             (if (or (<= a 2.7e+44) (not (<= a 1.2e+84)))
               (- x (/ x (/ a y)))
               (- t (* x (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.65e+86) {
		tmp = x + (y * (t / a));
	} else if (a <= -3e-170) {
		tmp = t_1;
	} else if (a <= 6.2e-191) {
		tmp = t + (y * (x / z));
	} else if (a <= 3.1e-82) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 2.5e+24) {
		tmp = t_1;
	} else if ((a <= 2.7e+44) || !(a <= 1.2e+84)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-1.65d+86)) then
        tmp = x + (y * (t / a))
    else if (a <= (-3d-170)) then
        tmp = t_1
    else if (a <= 6.2d-191) then
        tmp = t + (y * (x / z))
    else if (a <= 3.1d-82) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= 2.5d+24) then
        tmp = t_1
    else if ((a <= 2.7d+44) .or. (.not. (a <= 1.2d+84))) then
        tmp = x - (x / (a / y))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.65e+86) {
		tmp = x + (y * (t / a));
	} else if (a <= -3e-170) {
		tmp = t_1;
	} else if (a <= 6.2e-191) {
		tmp = t + (y * (x / z));
	} else if (a <= 3.1e-82) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= 2.5e+24) {
		tmp = t_1;
	} else if ((a <= 2.7e+44) || !(a <= 1.2e+84)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.65e+86:
		tmp = x + (y * (t / a))
	elif a <= -3e-170:
		tmp = t_1
	elif a <= 6.2e-191:
		tmp = t + (y * (x / z))
	elif a <= 3.1e-82:
		tmp = y * ((x - t) / (z - a))
	elif a <= 2.5e+24:
		tmp = t_1
	elif (a <= 2.7e+44) or not (a <= 1.2e+84):
		tmp = x - (x / (a / y))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.65e+86)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= -3e-170)
		tmp = t_1;
	elseif (a <= 6.2e-191)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (a <= 3.1e-82)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= 2.5e+24)
		tmp = t_1;
	elseif ((a <= 2.7e+44) || !(a <= 1.2e+84))
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.65e+86)
		tmp = x + (y * (t / a));
	elseif (a <= -3e-170)
		tmp = t_1;
	elseif (a <= 6.2e-191)
		tmp = t + (y * (x / z));
	elseif (a <= 3.1e-82)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= 2.5e+24)
		tmp = t_1;
	elseif ((a <= 2.7e+44) || ~((a <= 1.2e+84)))
		tmp = x - (x / (a / y));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+86], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-170], t$95$1, If[LessEqual[a, 6.2e-191], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-82], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+24], t$95$1, If[Or[LessEqual[a, 2.7e+44], N[Not[LessEqual[a, 1.2e+84]], $MachinePrecision]], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.65e86

   1. Initial program 72.3%

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

      1. associate-/l* 82.8%

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

   3. Simplified 82.8%

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

      1. clear-num 82.7%

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

      2. un-div-inv 82.7%

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

   6. Applied egg-rr 82.7%

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

   7. Taylor expanded in t around inf 77.8%

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

   8. Taylor expanded in z around 0 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-/l* 63.5%

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

   10. Simplified 63.5%

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

   if -1.65e86 < a < -3.00000000000000013e-170 or 3.1e-82 < a < 2.50000000000000023e24

   1. Initial program 68.5%

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

      1. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. associate-/l* 68.7%

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

   7. Simplified 68.7%

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

   if -3.00000000000000013e-170 < a < 6.2000000000000004e-191

   1. Initial program 56.8%

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

      1. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate--l+ 89.8%

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

      2. associate-*r/ 89.8%

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

      3. associate-*r/ 89.8%

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

      4. mul-1-neg 89.8%

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

      5. div-sub 89.8%

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

      6. mul-1-neg 89.8%

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

      7. distribute-lft-out-- 89.8%

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

      8. associate-*r/ 89.8%

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

      9. mul-1-neg 89.8%

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

      10. unsub-neg 89.8%

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

      11. distribute-rgt-out-- 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in t around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. associate-/l* 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

      4. distribute-neg-frac2 78.7%

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

   10. Simplified 78.7%

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

   11. Taylor expanded in y around inf 81.2%

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

       1. associate-*r/ 81.2%

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

       2. *-commutative 81.2%

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

       3. neg-mul-1 81.2%

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

       4. distribute-rgt-neg-in 81.2%

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

       5. associate-*r/ 81.1%

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

   13. Simplified 81.1%

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

   if 6.2000000000000004e-191 < a < 3.1e-82

   1. Initial program 83.5%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. div-sub 76.8%

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

   7. Simplified 76.8%

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

   if 2.50000000000000023e24 < a < 2.7e44 or 1.2e84 < a

   1. Initial program 70.8%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. mul-1-neg 61.0%

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

      3. distribute-lft-neg-out 61.0%

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

      4. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

      3. associate-/l* 67.8%

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

   10. Simplified 67.8%

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

       1. clear-num 67.8%

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

       2. un-div-inv 67.9%

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

   12. Applied egg-rr 67.9%

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

   if 2.7e44 < a < 1.2e84

   1. Initial program 42.7%

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

      1. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 51.1%

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

      1. associate--l+ 51.1%

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

      2. associate-*r/ 51.1%

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

      3. associate-*r/ 51.1%

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

      4. mul-1-neg 51.1%

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

      5. div-sub 51.1%

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

      6. mul-1-neg 51.1%

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

      7. distribute-lft-out-- 51.1%

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

      8. associate-*r/ 51.1%

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

      9. mul-1-neg 51.1%

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

      10. unsub-neg 51.1%

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

      11. distribute-rgt-out-- 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in t around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

      4. distribute-neg-frac2 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around 0 72.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-191}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44} \lor \neg \left(a \leq 1.2 \cdot 10^{+84}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+42} \lor \neg \left(a \leq 3.2 \cdot 10^{+84}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* t (/ y z)))))
   (if (<= a -4.5e+70)
     (+ x (* y (/ t a)))
     (if (<= a -6e-283)
       t_1
       (if (<= a 1.15e-79)
         (* y (/ x (- z a)))
         (if (<= a 4.9e+23)
           t_1
           (if (or (<= a 2.4e+42) (not (<= a 3.2e+84)))
             (- x (/ x (/ a y)))
             (- t (* x (/ a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double tmp;
	if (a <= -4.5e+70) {
		tmp = x + (y * (t / a));
	} else if (a <= -6e-283) {
		tmp = t_1;
	} else if (a <= 1.15e-79) {
		tmp = y * (x / (z - a));
	} else if (a <= 4.9e+23) {
		tmp = t_1;
	} else if ((a <= 2.4e+42) || !(a <= 3.2e+84)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (y / z))
    if (a <= (-4.5d+70)) then
        tmp = x + (y * (t / a))
    else if (a <= (-6d-283)) then
        tmp = t_1
    else if (a <= 1.15d-79) then
        tmp = y * (x / (z - a))
    else if (a <= 4.9d+23) then
        tmp = t_1
    else if ((a <= 2.4d+42) .or. (.not. (a <= 3.2d+84))) then
        tmp = x - (x / (a / y))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t * (y / z));
	double tmp;
	if (a <= -4.5e+70) {
		tmp = x + (y * (t / a));
	} else if (a <= -6e-283) {
		tmp = t_1;
	} else if (a <= 1.15e-79) {
		tmp = y * (x / (z - a));
	} else if (a <= 4.9e+23) {
		tmp = t_1;
	} else if ((a <= 2.4e+42) || !(a <= 3.2e+84)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t * (y / z))
	tmp = 0
	if a <= -4.5e+70:
		tmp = x + (y * (t / a))
	elif a <= -6e-283:
		tmp = t_1
	elif a <= 1.15e-79:
		tmp = y * (x / (z - a))
	elif a <= 4.9e+23:
		tmp = t_1
	elif (a <= 2.4e+42) or not (a <= 3.2e+84):
		tmp = x - (x / (a / y))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (a <= -4.5e+70)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= -6e-283)
		tmp = t_1;
	elseif (a <= 1.15e-79)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (a <= 4.9e+23)
		tmp = t_1;
	elseif ((a <= 2.4e+42) || !(a <= 3.2e+84))
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t * (y / z));
	tmp = 0.0;
	if (a <= -4.5e+70)
		tmp = x + (y * (t / a));
	elseif (a <= -6e-283)
		tmp = t_1;
	elseif (a <= 1.15e-79)
		tmp = y * (x / (z - a));
	elseif (a <= 4.9e+23)
		tmp = t_1;
	elseif ((a <= 2.4e+42) || ~((a <= 3.2e+84)))
		tmp = x - (x / (a / y));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+70], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-283], t$95$1, If[LessEqual[a, 1.15e-79], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+23], t$95$1, If[Or[LessEqual[a, 2.4e+42], N[Not[LessEqual[a, 3.2e+84]], $MachinePrecision]], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.4999999999999999e70

   1. Initial program 72.9%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. un-div-inv 83.1%

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

   6. Applied egg-rr 83.1%

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

   7. Taylor expanded in t around inf 78.3%

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

   8. Taylor expanded in z around 0 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 62.2%

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

   10. Simplified 62.2%

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

   if -4.4999999999999999e70 < a < -5.99999999999999992e-283 or 1.15000000000000006e-79 < a < 4.9000000000000003e23

   1. Initial program 66.7%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around 0 55.4%

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

   6. Taylor expanded in a around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. associate-*r* 41.5%

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

      3. neg-mul-1 41.5%

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

      4. *-commutative 41.5%

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

   8. Simplified 41.5%

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

   9. Taylor expanded in y around 0 49.7%

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

       1. mul-1-neg 49.7%

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

       2. unsub-neg 49.7%

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

       3. associate-/l* 55.7%

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

   11. Simplified 55.7%

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

   if -5.99999999999999992e-283 < a < 1.15000000000000006e-79

   1. Initial program 69.9%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. div-sub 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in t around 0 59.9%

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

      1. neg-mul-1 59.9%

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

      2. distribute-neg-frac2 59.9%

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

   10. Simplified 59.9%

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

   if 4.9000000000000003e23 < a < 2.3999999999999999e42 or 3.2000000000000001e84 < a

   1. Initial program 70.8%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. mul-1-neg 61.0%

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

      3. distribute-lft-neg-out 61.0%

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

      4. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in z around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

      3. associate-/l* 67.8%

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

   10. Simplified 67.8%

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

       1. clear-num 67.8%

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

       2. un-div-inv 67.9%

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

   12. Applied egg-rr 67.9%

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

   if 2.3999999999999999e42 < a < 3.2000000000000001e84

   1. Initial program 42.7%

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

      1. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 51.1%

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

      1. associate--l+ 51.1%

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

      2. associate-*r/ 51.1%

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

      3. associate-*r/ 51.1%

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

      4. mul-1-neg 51.1%

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

      5. div-sub 51.1%

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

      6. mul-1-neg 51.1%

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

      7. distribute-lft-out-- 51.1%

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

      8. associate-*r/ 51.1%

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

      9. mul-1-neg 51.1%

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

      10. unsub-neg 51.1%

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

      11. distribute-rgt-out-- 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in t around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

      4. distribute-neg-frac2 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around 0 72.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-283}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+23}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+42} \lor \neg \left(a \leq 3.2 \cdot 10^{+84}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := t - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-170}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (- t (* t (/ y z)))))
   (if (<= z -5.8e+121)
     t_2
     (if (<= z -1.85e+82)
       t_1
       (if (<= z -1.9e+70)
         t_2
         (if (<= z -4.8e-9)
           (* y (/ (- x t) z))
           (if (<= z -3.8e-170)
             (- x (* x (/ y a)))
             (if (<= z 1.05e+97) t_1 (- t (* x (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -5.8e+121) {
		tmp = t_2;
	} else if (z <= -1.85e+82) {
		tmp = t_1;
	} else if (z <= -1.9e+70) {
		tmp = t_2;
	} else if (z <= -4.8e-9) {
		tmp = y * ((x - t) / z);
	} else if (z <= -3.8e-170) {
		tmp = x - (x * (y / a));
	} else if (z <= 1.05e+97) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    t_2 = t - (t * (y / z))
    if (z <= (-5.8d+121)) then
        tmp = t_2
    else if (z <= (-1.85d+82)) then
        tmp = t_1
    else if (z <= (-1.9d+70)) then
        tmp = t_2
    else if (z <= (-4.8d-9)) then
        tmp = y * ((x - t) / z)
    else if (z <= (-3.8d-170)) then
        tmp = x - (x * (y / a))
    else if (z <= 1.05d+97) then
        tmp = t_1
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = t - (t * (y / z));
	double tmp;
	if (z <= -5.8e+121) {
		tmp = t_2;
	} else if (z <= -1.85e+82) {
		tmp = t_1;
	} else if (z <= -1.9e+70) {
		tmp = t_2;
	} else if (z <= -4.8e-9) {
		tmp = y * ((x - t) / z);
	} else if (z <= -3.8e-170) {
		tmp = x - (x * (y / a));
	} else if (z <= 1.05e+97) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = t - (t * (y / z))
	tmp = 0
	if z <= -5.8e+121:
		tmp = t_2
	elif z <= -1.85e+82:
		tmp = t_1
	elif z <= -1.9e+70:
		tmp = t_2
	elif z <= -4.8e-9:
		tmp = y * ((x - t) / z)
	elif z <= -3.8e-170:
		tmp = x - (x * (y / a))
	elif z <= 1.05e+97:
		tmp = t_1
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(t - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -5.8e+121)
		tmp = t_2;
	elseif (z <= -1.85e+82)
		tmp = t_1;
	elseif (z <= -1.9e+70)
		tmp = t_2;
	elseif (z <= -4.8e-9)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= -3.8e-170)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 1.05e+97)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = t - (t * (y / z));
	tmp = 0.0;
	if (z <= -5.8e+121)
		tmp = t_2;
	elseif (z <= -1.85e+82)
		tmp = t_1;
	elseif (z <= -1.9e+70)
		tmp = t_2;
	elseif (z <= -4.8e-9)
		tmp = y * ((x - t) / z);
	elseif (z <= -3.8e-170)
		tmp = x - (x * (y / a));
	elseif (z <= 1.05e+97)
		tmp = t_1;
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+121], t$95$2, If[LessEqual[z, -1.85e+82], t$95$1, If[LessEqual[z, -1.9e+70], t$95$2, If[LessEqual[z, -4.8e-9], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-170], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+97], t$95$1, N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.7999999999999998e121 or -1.8500000000000001e82 < z < -1.8999999999999999e70

   1. Initial program 31.6%

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

      1. associate-/l* 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in x around 0 39.7%

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

   6. Taylor expanded in a around 0 34.7%

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

      1. associate-*r/ 34.7%

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

      2. associate-*r* 34.7%

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

      3. neg-mul-1 34.7%

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

      4. *-commutative 34.7%

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

   8. Simplified 34.7%

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

   9. Taylor expanded in y around 0 50.4%

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

       1. mul-1-neg 50.4%

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

       2. unsub-neg 50.4%

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

       3. associate-/l* 62.8%

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

   11. Simplified 62.8%

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

   if -5.7999999999999998e121 < z < -1.8500000000000001e82 or -3.7999999999999998e-170 < z < 1.05000000000000006e97

   1. Initial program 83.6%

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

      1. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

      1. clear-num 86.6%

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

      2. un-div-inv 86.7%

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

   6. Applied egg-rr 86.7%

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

   7. Taylor expanded in t around inf 73.1%

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

   8. Taylor expanded in z around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-/l* 64.0%

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

   10. Simplified 64.0%

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

   if -1.8999999999999999e70 < z < -4.8e-9

   1. Initial program 89.0%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in y around inf 60.3%

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

      1. div-sub 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in a around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. associate-/l* 48.8%

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

      3. distribute-rgt-neg-in 48.8%

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

      4. distribute-neg-frac2 48.8%

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

   10. Simplified 48.8%

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

   if -4.8e-9 < z < -3.7999999999999998e-170

   1. Initial program 91.3%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in t around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. mul-1-neg 72.7%

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

      3. distribute-lft-neg-out 72.7%

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

      4. *-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in z around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

      3. associate-/l* 59.8%

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

   10. Simplified 59.8%

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

   if 1.05000000000000006e97 < z

   1. Initial program 28.2%

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

      1. associate-/l* 59.3%

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

   3. Simplified 59.3%

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

   5. Taylor expanded in z around inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. associate-*r/ 59.0%

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

      3. associate-*r/ 59.0%

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

      4. mul-1-neg 59.0%

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

      5. div-sub 59.0%

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

      6. mul-1-neg 59.0%

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

      7. distribute-lft-out-- 59.0%

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

      8. associate-*r/ 59.0%

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

      9. mul-1-neg 59.0%

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

      10. unsub-neg 59.0%

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

      11. distribute-rgt-out-- 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in t around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

      4. distribute-neg-frac2 79.5%

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

   10. Simplified 79.5%

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

   11. Taylor expanded in y around 0 67.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+121}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-170}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+97}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-299}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= y -4.3e+39)
     (* y (/ (- t x) a))
     (if (<= y -1.4e-66)
       t_1
       (if (<= y 3.6e-299)
         x
         (if (<= y 1.66e+16)
           t
           (if (<= y 3.7e+169) t_1 (* t (/ y (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (y <= -4.3e+39) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.4e-66) {
		tmp = t_1;
	} else if (y <= 3.6e-299) {
		tmp = x;
	} else if (y <= 1.66e+16) {
		tmp = t;
	} else if (y <= 3.7e+169) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (y <= (-4.3d+39)) then
        tmp = y * ((t - x) / a)
    else if (y <= (-1.4d-66)) then
        tmp = t_1
    else if (y <= 3.6d-299) then
        tmp = x
    else if (y <= 1.66d+16) then
        tmp = t
    else if (y <= 3.7d+169) then
        tmp = t_1
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (y <= -4.3e+39) {
		tmp = y * ((t - x) / a);
	} else if (y <= -1.4e-66) {
		tmp = t_1;
	} else if (y <= 3.6e-299) {
		tmp = x;
	} else if (y <= 1.66e+16) {
		tmp = t;
	} else if (y <= 3.7e+169) {
		tmp = t_1;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if y <= -4.3e+39:
		tmp = y * ((t - x) / a)
	elif y <= -1.4e-66:
		tmp = t_1
	elif y <= 3.6e-299:
		tmp = x
	elif y <= 1.66e+16:
		tmp = t
	elif y <= 3.7e+169:
		tmp = t_1
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (y <= -4.3e+39)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (y <= -1.4e-66)
		tmp = t_1;
	elseif (y <= 3.6e-299)
		tmp = x;
	elseif (y <= 1.66e+16)
		tmp = t;
	elseif (y <= 3.7e+169)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (y <= -4.3e+39)
		tmp = y * ((t - x) / a);
	elseif (y <= -1.4e-66)
		tmp = t_1;
	elseif (y <= 3.6e-299)
		tmp = x;
	elseif (y <= 1.66e+16)
		tmp = t;
	elseif (y <= 3.7e+169)
		tmp = t_1;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+39], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-66], t$95$1, If[LessEqual[y, 3.6e-299], x, If[LessEqual[y, 1.66e+16], t, If[LessEqual[y, 3.7e+169], t$95$1, N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.3e39

   1. Initial program 72.9%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in y around inf 66.4%

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

      1. div-sub 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in a around inf 47.1%

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

   if -4.3e39 < y < -1.4e-66 or 1.66e16 < y < 3.70000000000000001e169

   1. Initial program 60.9%

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

      1. associate-/l* 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in z around inf 56.3%

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

      1. associate--l+ 56.3%

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

      2. associate-*r/ 56.3%

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

      3. associate-*r/ 56.3%

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

      4. mul-1-neg 56.3%

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

      5. div-sub 56.3%

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

      6. mul-1-neg 56.3%

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

      7. distribute-lft-out-- 56.3%

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

      8. associate-*r/ 56.3%

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

      9. mul-1-neg 56.3%

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

      10. unsub-neg 56.3%

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

      11. distribute-rgt-out-- 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in t around 0 38.1%

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

      1. associate-/l* 41.1%

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

   10. Simplified 41.1%

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

   if -1.4e-66 < y < 3.6e-299

   1. Initial program 82.2%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 58.4%

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

   if 3.6e-299 < y < 1.66e16

   1. Initial program 53.8%

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

      1. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in z around inf 35.7%

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

   if 3.70000000000000001e169 < y

   1. Initial program 73.4%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around 0 45.0%

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

   6. Taylor expanded in y around inf 42.2%

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

      1. associate-/l* 52.1%

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

   8. Simplified 52.1%

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

Alternative 11: 35.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-276}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+83}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= a -2.85e+205)
     t_1
     (if (<= a -6.6e+100)
       x
       (if (<= a -1.8e-71)
         t_1
         (if (<= a -3.9e-276)
           t
           (if (<= a 1.15e-64)
             (* x (/ (- y a) z))
             (if (<= a 4.1e+83) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -2.85e+205) {
		tmp = t_1;
	} else if (a <= -6.6e+100) {
		tmp = x;
	} else if (a <= -1.8e-71) {
		tmp = t_1;
	} else if (a <= -3.9e-276) {
		tmp = t;
	} else if (a <= 1.15e-64) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4.1e+83) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (a <= (-2.85d+205)) then
        tmp = t_1
    else if (a <= (-6.6d+100)) then
        tmp = x
    else if (a <= (-1.8d-71)) then
        tmp = t_1
    else if (a <= (-3.9d-276)) then
        tmp = t
    else if (a <= 1.15d-64) then
        tmp = x * ((y - a) / z)
    else if (a <= 4.1d+83) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -2.85e+205) {
		tmp = t_1;
	} else if (a <= -6.6e+100) {
		tmp = x;
	} else if (a <= -1.8e-71) {
		tmp = t_1;
	} else if (a <= -3.9e-276) {
		tmp = t;
	} else if (a <= 1.15e-64) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4.1e+83) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if a <= -2.85e+205:
		tmp = t_1
	elif a <= -6.6e+100:
		tmp = x
	elif a <= -1.8e-71:
		tmp = t_1
	elif a <= -3.9e-276:
		tmp = t
	elif a <= 1.15e-64:
		tmp = x * ((y - a) / z)
	elif a <= 4.1e+83:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (a <= -2.85e+205)
		tmp = t_1;
	elseif (a <= -6.6e+100)
		tmp = x;
	elseif (a <= -1.8e-71)
		tmp = t_1;
	elseif (a <= -3.9e-276)
		tmp = t;
	elseif (a <= 1.15e-64)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 4.1e+83)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (a <= -2.85e+205)
		tmp = t_1;
	elseif (a <= -6.6e+100)
		tmp = x;
	elseif (a <= -1.8e-71)
		tmp = t_1;
	elseif (a <= -3.9e-276)
		tmp = t;
	elseif (a <= 1.15e-64)
		tmp = x * ((y - a) / z);
	elseif (a <= 4.1e+83)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e+205], t$95$1, If[LessEqual[a, -6.6e+100], x, If[LessEqual[a, -1.8e-71], t$95$1, If[LessEqual[a, -3.9e-276], t, If[LessEqual[a, 1.15e-64], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+83], t, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.84999999999999981e205 or -6.6000000000000002e100 < a < -1.8e-71

   1. Initial program 72.1%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 43.5%

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

   6. Taylor expanded in a around inf 34.9%

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

      1. associate-/l* 48.8%

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

   8. Simplified 48.8%

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

   if -2.84999999999999981e205 < a < -6.6000000000000002e100 or 4.1000000000000001e83 < a

   1. Initial program 72.1%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 56.6%

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

   if -1.8e-71 < a < -3.9e-276 or 1.1500000000000001e-64 < a < 4.1000000000000001e83

   1. Initial program 61.7%

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

      1. associate-/l* 70.5%

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

   3. Simplified 70.5%

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

   5. Taylor expanded in z around inf 41.0%

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

   if -3.9e-276 < a < 1.1500000000000001e-64

   1. Initial program 68.6%

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

      1. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in z around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. associate-*r/ 68.8%

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

      3. associate-*r/ 68.8%

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

      4. mul-1-neg 68.8%

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

      5. div-sub 68.8%

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

      6. mul-1-neg 68.8%

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

      7. distribute-lft-out-- 68.8%

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

      8. associate-*r/ 68.8%

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

      9. mul-1-neg 68.8%

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

      10. unsub-neg 68.8%

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

      11. distribute-rgt-out-- 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in t around 0 49.8%

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

      1. associate-/l* 48.0%

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

   10. Simplified 48.0%

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

Alternative 12: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -6.5e+130)
     t
     (if (<= z -1.55e-125)
       x
       (if (<= z -2.5e-296)
         t_1
         (if (<= z 4e+19) x (if (<= z 7e+59) t_1 (if (<= z 3.1e+90) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -6.5e+130) {
		tmp = t;
	} else if (z <= -1.55e-125) {
		tmp = x;
	} else if (z <= -2.5e-296) {
		tmp = t_1;
	} else if (z <= 4e+19) {
		tmp = x;
	} else if (z <= 7e+59) {
		tmp = t_1;
	} else if (z <= 3.1e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-6.5d+130)) then
        tmp = t
    else if (z <= (-1.55d-125)) then
        tmp = x
    else if (z <= (-2.5d-296)) then
        tmp = t_1
    else if (z <= 4d+19) then
        tmp = x
    else if (z <= 7d+59) then
        tmp = t_1
    else if (z <= 3.1d+90) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -6.5e+130) {
		tmp = t;
	} else if (z <= -1.55e-125) {
		tmp = x;
	} else if (z <= -2.5e-296) {
		tmp = t_1;
	} else if (z <= 4e+19) {
		tmp = x;
	} else if (z <= 7e+59) {
		tmp = t_1;
	} else if (z <= 3.1e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -6.5e+130:
		tmp = t
	elif z <= -1.55e-125:
		tmp = x
	elif z <= -2.5e-296:
		tmp = t_1
	elif z <= 4e+19:
		tmp = x
	elif z <= 7e+59:
		tmp = t_1
	elif z <= 3.1e+90:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.5e+130)
		tmp = t;
	elseif (z <= -1.55e-125)
		tmp = x;
	elseif (z <= -2.5e-296)
		tmp = t_1;
	elseif (z <= 4e+19)
		tmp = x;
	elseif (z <= 7e+59)
		tmp = t_1;
	elseif (z <= 3.1e+90)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -6.5e+130)
		tmp = t;
	elseif (z <= -1.55e-125)
		tmp = x;
	elseif (z <= -2.5e-296)
		tmp = t_1;
	elseif (z <= 4e+19)
		tmp = x;
	elseif (z <= 7e+59)
		tmp = t_1;
	elseif (z <= 3.1e+90)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+130], t, If[LessEqual[z, -1.55e-125], x, If[LessEqual[z, -2.5e-296], t$95$1, If[LessEqual[z, 4e+19], x, If[LessEqual[z, 7e+59], t$95$1, If[LessEqual[z, 3.1e+90], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e130 or 3.09999999999999988e90 < z

   1. Initial program 28.5%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in z around inf 52.1%

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

   if -6.5e130 < z < -1.55000000000000006e-125 or -2.50000000000000015e-296 < z < 4e19 or 7e59 < z < 3.09999999999999988e90

   1. Initial program 83.0%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in a around inf 38.8%

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

   if -1.55000000000000006e-125 < z < -2.50000000000000015e-296 or 4e19 < z < 7e59

   1. Initial program 89.0%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around 0 52.4%

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

   6. Taylor expanded in y around inf 46.5%

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

      1. associate-/l* 51.0%

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

   8. Simplified 51.0%

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

Alternative 13: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+197}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\left(y - a\right) \cdot \frac{1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.26e+197)
   (+ t (* x (/ (- y a) z)))
   (if (<= z -1.76e+93)
     (+ x (/ (- y z) (/ (- a z) t)))
     (if (<= z -3.7e+38)
       (+ t (* (- y a) (/ x z)))
       (if (<= z 2.6e+95)
         (+ x (* (- x t) (/ (- z y) a)))
         (+ t (* x (* (- y a) (/ 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+197) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -1.76e+93) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= -3.7e+38) {
		tmp = t + ((y - a) * (x / z));
	} else if (z <= 2.6e+95) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) * (1.0 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.26d+197)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= (-1.76d+93)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (z <= (-3.7d+38)) then
        tmp = t + ((y - a) * (x / z))
    else if (z <= 2.6d+95) then
        tmp = x + ((x - t) * ((z - y) / a))
    else
        tmp = t + (x * ((y - a) * (1.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.26e+197) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= -1.76e+93) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= -3.7e+38) {
		tmp = t + ((y - a) * (x / z));
	} else if (z <= 2.6e+95) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) * (1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.26e+197:
		tmp = t + (x * ((y - a) / z))
	elif z <= -1.76e+93:
		tmp = x + ((y - z) / ((a - z) / t))
	elif z <= -3.7e+38:
		tmp = t + ((y - a) * (x / z))
	elif z <= 2.6e+95:
		tmp = x + ((x - t) * ((z - y) / a))
	else:
		tmp = t + (x * ((y - a) * (1.0 / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.26e+197)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= -1.76e+93)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (z <= -3.7e+38)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	elseif (z <= 2.6e+95)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) * Float64(1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.26e+197)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= -1.76e+93)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (z <= -3.7e+38)
		tmp = t + ((y - a) * (x / z));
	elseif (z <= 2.6e+95)
		tmp = x + ((x - t) * ((z - y) / a));
	else
		tmp = t + (x * ((y - a) * (1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.26e+197], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e+93], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e+38], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+95], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.26e197

   1. Initial program 23.2%

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

      1. associate-/l* 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in z around inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. associate-*r/ 66.0%

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

      3. associate-*r/ 66.0%

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

      4. mul-1-neg 66.0%

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

      5. div-sub 66.0%

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

      6. mul-1-neg 66.0%

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

      7. distribute-lft-out-- 66.0%

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

      8. associate-*r/ 66.0%

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

      9. mul-1-neg 66.0%

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

      10. unsub-neg 66.0%

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

      11. distribute-rgt-out-- 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in t around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/l* 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

      4. distribute-neg-frac2 90.5%

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

   10. Simplified 90.5%

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

   if -1.26e197 < z < -1.75999999999999994e93

   1. Initial program 40.3%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

      1. clear-num 79.4%

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

      2. un-div-inv 79.4%

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

   6. Applied egg-rr 79.4%

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

   7. Taylor expanded in t around inf 67.6%

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

   if -1.75999999999999994e93 < z < -3.7000000000000001e38

   1. Initial program 50.5%

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

      1. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in z around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. mul-1-neg 68.6%

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

      5. div-sub 68.6%

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

      6. mul-1-neg 68.6%

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

      7. distribute-lft-out-- 68.6%

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

      8. associate-*r/ 68.6%

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

      9. mul-1-neg 68.6%

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

      10. unsub-neg 68.6%

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

      11. distribute-rgt-out-- 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 70.4%

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

      3. distribute-rgt-neg-in 70.4%

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

      4. distribute-neg-frac2 70.4%

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

   10. Simplified 70.4%

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

   11. Taylor expanded in x around 0 68.3%

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

       1. mul-1-neg 68.3%

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

       2. distribute-neg-frac2 68.3%

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

       3. *-commutative 68.3%

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

       4. neg-mul-1 68.3%

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

       5. *-commutative 68.3%

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

       6. associate-/l* 70.4%

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

       7. *-commutative 70.4%

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

       8. neg-mul-1 70.4%

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

       9. distribute-neg-frac2 70.4%

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

       10. distribute-frac-neg 70.4%

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

   13. Simplified 70.4%

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

   if -3.7000000000000001e38 < z < 2.5999999999999999e95

   1. Initial program 88.9%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around inf 72.9%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

   if 2.5999999999999999e95 < z

   1. Initial program 28.2%

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

      1. associate-/l* 59.3%

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

   3. Simplified 59.3%

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

   5. Taylor expanded in z around inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. associate-*r/ 59.0%

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

      3. associate-*r/ 59.0%

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

      4. mul-1-neg 59.0%

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

      5. div-sub 59.0%

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

      6. mul-1-neg 59.0%

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

      7. distribute-lft-out-- 59.0%

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

      8. associate-*r/ 59.0%

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

      9. mul-1-neg 59.0%

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

      10. unsub-neg 59.0%

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

      11. distribute-rgt-out-- 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in t around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

      4. distribute-neg-frac2 79.5%

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

   10. Simplified 79.5%

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

       1. frac-2neg 79.5%

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

       2. div-inv 79.5%

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

       3. remove-double-neg 79.5%

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

   12. Applied egg-rr 79.5%

       \[\leadsto t - x \cdot \color{blue}{\left(\left(-\left(y - a\right)\right) \cdot \frac{1}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+197}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\left(y - a\right) \cdot \frac{1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+39}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -4.1e+203)
     t_1
     (if (<= z -3.3e+93)
       (+ x (/ (- y z) (/ (- a z) t)))
       (if (<= z -1.65e+39)
         (+ t (* (- y a) (/ x z)))
         (if (<= z 2.3e+97) (+ x (* (- x t) (/ (- z y) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.1e+203) {
		tmp = t_1;
	} else if (z <= -3.3e+93) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= -1.65e+39) {
		tmp = t + ((y - a) * (x / z));
	} else if (z <= 2.3e+97) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    if (z <= (-4.1d+203)) then
        tmp = t_1
    else if (z <= (-3.3d+93)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (z <= (-1.65d+39)) then
        tmp = t + ((y - a) * (x / z))
    else if (z <= 2.3d+97) then
        tmp = x + ((x - t) * ((z - y) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.1e+203) {
		tmp = t_1;
	} else if (z <= -3.3e+93) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= -1.65e+39) {
		tmp = t + ((y - a) * (x / z));
	} else if (z <= 2.3e+97) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -4.1e+203:
		tmp = t_1
	elif z <= -3.3e+93:
		tmp = x + ((y - z) / ((a - z) / t))
	elif z <= -1.65e+39:
		tmp = t + ((y - a) * (x / z))
	elif z <= 2.3e+97:
		tmp = x + ((x - t) * ((z - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -4.1e+203)
		tmp = t_1;
	elseif (z <= -3.3e+93)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (z <= -1.65e+39)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	elseif (z <= 2.3e+97)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -4.1e+203)
		tmp = t_1;
	elseif (z <= -3.3e+93)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (z <= -1.65e+39)
		tmp = t + ((y - a) * (x / z));
	elseif (z <= 2.3e+97)
		tmp = x + ((x - t) * ((z - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+203], t$95$1, If[LessEqual[z, -3.3e+93], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e+39], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+97], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.10000000000000016e203 or 2.30000000000000006e97 < z

   1. Initial program 26.4%

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

      1. associate-/l* 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. mul-1-neg 61.4%

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

      5. div-sub 61.4%

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

      6. mul-1-neg 61.4%

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

      7. distribute-lft-out-- 61.4%

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

      8. associate-*r/ 61.4%

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

      9. mul-1-neg 61.4%

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

      10. unsub-neg 61.4%

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

      11. distribute-rgt-out-- 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in t around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-/l* 83.3%

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

      3. distribute-rgt-neg-in 83.3%

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

      4. distribute-neg-frac2 83.3%

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

   10. Simplified 83.3%

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

   if -4.10000000000000016e203 < z < -3.30000000000000009e93

   1. Initial program 40.3%

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

      1. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

      1. clear-num 79.4%

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

      2. un-div-inv 79.4%

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

   6. Applied egg-rr 79.4%

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

   7. Taylor expanded in t around inf 67.6%

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

   if -3.30000000000000009e93 < z < -1.6500000000000001e39

   1. Initial program 50.5%

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

      1. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in z around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. mul-1-neg 68.6%

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

      5. div-sub 68.6%

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

      6. mul-1-neg 68.6%

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

      7. distribute-lft-out-- 68.6%

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

      8. associate-*r/ 68.6%

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

      9. mul-1-neg 68.6%

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

      10. unsub-neg 68.6%

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

      11. distribute-rgt-out-- 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-/l* 70.4%

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

      3. distribute-rgt-neg-in 70.4%

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

      4. distribute-neg-frac2 70.4%

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

   10. Simplified 70.4%

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

   11. Taylor expanded in x around 0 68.3%

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

       1. mul-1-neg 68.3%

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

       2. distribute-neg-frac2 68.3%

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

       3. *-commutative 68.3%

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

       4. neg-mul-1 68.3%

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

       5. *-commutative 68.3%

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

       6. associate-/l* 70.4%

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

       7. *-commutative 70.4%

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

       8. neg-mul-1 70.4%

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

       9. distribute-neg-frac2 70.4%

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

       10. distribute-frac-neg 70.4%

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

   13. Simplified 70.4%

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

   if -1.6500000000000001e39 < z < 2.30000000000000006e97

   1. Initial program 88.9%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around inf 72.9%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+203}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+39}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -1.35e+70)
     t_1
     (if (<= z -7.5e-81)
       (* x (+ (/ (- y z) (- z a)) 1.0))
       (if (<= z 2.5e-97)
         (+ x (/ (* (- y z) (- t x)) a))
         (if (<= z 3.6e+95) (+ x (* (- x t) (/ (- z y) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.35e+70) {
		tmp = t_1;
	} else if (z <= -7.5e-81) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 2.5e-97) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 3.6e+95) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    if (z <= (-1.35d+70)) then
        tmp = t_1
    else if (z <= (-7.5d-81)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (z <= 2.5d-97) then
        tmp = x + (((y - z) * (t - x)) / a)
    else if (z <= 3.6d+95) then
        tmp = x + ((x - t) * ((z - y) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.35e+70) {
		tmp = t_1;
	} else if (z <= -7.5e-81) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 2.5e-97) {
		tmp = x + (((y - z) * (t - x)) / a);
	} else if (z <= 3.6e+95) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -1.35e+70:
		tmp = t_1
	elif z <= -7.5e-81:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif z <= 2.5e-97:
		tmp = x + (((y - z) * (t - x)) / a)
	elif z <= 3.6e+95:
		tmp = x + ((x - t) * ((z - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -1.35e+70)
		tmp = t_1;
	elseif (z <= -7.5e-81)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (z <= 2.5e-97)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / a));
	elseif (z <= 3.6e+95)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -1.35e+70)
		tmp = t_1;
	elseif (z <= -7.5e-81)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (z <= 2.5e-97)
		tmp = x + (((y - z) * (t - x)) / a);
	elseif (z <= 3.6e+95)
		tmp = x + ((x - t) * ((z - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+70], t$95$1, If[LessEqual[z, -7.5e-81], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-97], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+95], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e70 or 3.59999999999999978e95 < z

   1. Initial program 30.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 60.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 60.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 54.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 54.7%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 54.7%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 54.7%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 54.7%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 54.7%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 54.7%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 54.7%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 54.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 54.7%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 55.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 55.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 61.3%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 61.3%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 73.0%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 73.0%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 73.0%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 73.0%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -1.35e70 < z < -7.50000000000000018e-81

   1. Initial program 86.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 67.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 67.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   if -7.50000000000000018e-81 < z < 2.4999999999999998e-97

   1. Initial program 96.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 94.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-define 94.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 94.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 94.0%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 96.0%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 92.2%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   6. Applied egg-rr 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   7. Taylor expanded in a around inf 86.6%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]

   if 2.4999999999999998e-97 < z < 3.59999999999999978e95

   1. Initial program 71.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 57.3%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.4%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 68.4%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ t_2 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))) (t_2 (+ t (* y (/ x z)))))
   (if (<= z -1.4e+120)
     t_2
     (if (<= z -6.9e+81)
       t_1
       (if (<= z -1.35e-13)
         t_2
         (if (<= z 1.8e+15) t_1 (* t (/ (- y z) (- a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t + (y * (x / z));
	double tmp;
	if (z <= -1.4e+120) {
		tmp = t_2;
	} else if (z <= -6.9e+81) {
		tmp = t_1;
	} else if (z <= -1.35e-13) {
		tmp = t_2;
	} else if (z <= 1.8e+15) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    t_2 = t + (y * (x / z))
    if (z <= (-1.4d+120)) then
        tmp = t_2
    else if (z <= (-6.9d+81)) then
        tmp = t_1
    else if (z <= (-1.35d-13)) then
        tmp = t_2
    else if (z <= 1.8d+15) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t + (y * (x / z));
	double tmp;
	if (z <= -1.4e+120) {
		tmp = t_2;
	} else if (z <= -6.9e+81) {
		tmp = t_1;
	} else if (z <= -1.35e-13) {
		tmp = t_2;
	} else if (z <= 1.8e+15) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	t_2 = t + (y * (x / z))
	tmp = 0
	if z <= -1.4e+120:
		tmp = t_2
	elif z <= -6.9e+81:
		tmp = t_1
	elif z <= -1.35e-13:
		tmp = t_2
	elif z <= 1.8e+15:
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	t_2 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.4e+120)
		tmp = t_2;
	elseif (z <= -6.9e+81)
		tmp = t_1;
	elseif (z <= -1.35e-13)
		tmp = t_2;
	elseif (z <= 1.8e+15)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	t_2 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -1.4e+120)
		tmp = t_2;
	elseif (z <= -6.9e+81)
		tmp = t_1;
	elseif (z <= -1.35e-13)
		tmp = t_2;
	elseif (z <= 1.8e+15)
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+120], t$95$2, If[LessEqual[z, -6.9e+81], t$95$1, If[LessEqual[z, -1.35e-13], t$95$2, If[LessEqual[z, 1.8e+15], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e120 or -6.8999999999999996e81 < z < -1.35000000000000005e-13

   1. Initial program 49.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 70.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 55.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 55.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 55.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 55.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 55.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 55.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 55.9%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 55.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 55.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 55.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 55.9%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 56.2%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 59.4%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 67.4%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 67.4%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 67.4%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 67.4%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around inf 58.6%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 58.6%

          \[\leadsto t - \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. *-commutative 58.6%

          \[\leadsto t - \frac{-1 \cdot \color{blue}{\left(y \cdot x\right)}}{z} \]

       3. neg-mul-1 58.6%

          \[\leadsto t - \frac{\color{blue}{-y \cdot x}}{z} \]

       4. distribute-rgt-neg-in 58.6%

          \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

       5. associate-*r/ 64.1%

          \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   13. Simplified 64.1%

       \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   if -1.4e120 < z < -6.8999999999999996e81 or -1.35000000000000005e-13 < z < 1.8e15

   1. Initial program 87.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 88.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-define 88.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 88.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 88.4%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 86.9%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 88.5%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   6. Applied egg-rr 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   7. Taylor expanded in z around 0 72.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 75.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   9. Simplified 75.2%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if 1.8e15 < z

   1. Initial program 44.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 67.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 38.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+120}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{+81}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -2.35e+70)
     t_1
     (if (<= z -1.25e-77)
       (* x (+ (/ (- y z) (- z a)) 1.0))
       (if (<= z 1.2e+95) (- x (* y (/ (- x t) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -2.35e+70) {
		tmp = t_1;
	} else if (z <= -1.25e-77) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 1.2e+95) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    if (z <= (-2.35d+70)) then
        tmp = t_1
    else if (z <= (-1.25d-77)) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else if (z <= 1.2d+95) then
        tmp = x - (y * ((x - t) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -2.35e+70) {
		tmp = t_1;
	} else if (z <= -1.25e-77) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else if (z <= 1.2e+95) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -2.35e+70:
		tmp = t_1
	elif z <= -1.25e-77:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	elif z <= 1.2e+95:
		tmp = x - (y * ((x - t) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -2.35e+70)
		tmp = t_1;
	elseif (z <= -1.25e-77)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	elseif (z <= 1.2e+95)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -2.35e+70)
		tmp = t_1;
	elseif (z <= -1.25e-77)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	elseif (z <= 1.2e+95)
		tmp = x - (y * ((x - t) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+70], t$95$1, If[LessEqual[z, -1.25e-77], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+95], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e70 or 1.2e95 < z

   1. Initial program 30.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 60.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 60.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.7%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 54.7%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 54.7%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 54.7%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 54.7%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 54.7%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 54.7%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 54.7%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 54.7%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 54.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 54.7%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 55.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 55.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 61.3%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 61.3%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 73.0%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 73.0%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 73.0%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 73.0%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -2.3499999999999999e70 < z < -1.24999999999999991e-77

   1. Initial program 86.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 67.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y - z}{a - z}\right)}\right) \]

      2. unsub-neg 67.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - z}{a - z}\right)} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]

   if -1.24999999999999991e-77 < z < 1.2e95

   1. Initial program 89.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 88.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-define 88.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 88.3%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 88.3%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 88.3%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 89.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   6. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   7. Taylor expanded in z around 0 72.0%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 72.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   9. Simplified 72.7%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+70}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+95}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 58.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-167}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e-10)
   (+ t (* y (/ x z)))
   (if (<= z -5.6e-167)
     (- x (* x (/ y a)))
     (if (<= z 4.7e+14) (+ x (* y (/ t a))) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e-10) {
		tmp = t + (y * (x / z));
	} else if (z <= -5.6e-167) {
		tmp = x - (x * (y / a));
	} else if (z <= 4.7e+14) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d-10)) then
        tmp = t + (y * (x / z))
    else if (z <= (-5.6d-167)) then
        tmp = x - (x * (y / a))
    else if (z <= 4.7d+14) then
        tmp = x + (y * (t / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e-10) {
		tmp = t + (y * (x / z));
	} else if (z <= -5.6e-167) {
		tmp = x - (x * (y / a));
	} else if (z <= 4.7e+14) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e-10:
		tmp = t + (y * (x / z))
	elif z <= -5.6e-167:
		tmp = x - (x * (y / a))
	elif z <= 4.7e+14:
		tmp = x + (y * (t / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e-10)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (z <= -5.6e-167)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 4.7e+14)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e-10)
		tmp = t + (y * (x / z));
	elseif (z <= -5.6e-167)
		tmp = x - (x * (y / a));
	elseif (z <= 4.7e+14)
		tmp = x + (y * (t / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e-10], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-167], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+14], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e-10

   1. Initial program 47.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 69.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 53.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 53.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 53.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 53.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 53.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 53.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 53.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 53.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 53.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 53.4%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 56.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 56.1%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 63.1%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 63.1%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 63.1%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 63.1%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around inf 53.0%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 53.0%

          \[\leadsto t - \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. *-commutative 53.0%

          \[\leadsto t - \frac{-1 \cdot \color{blue}{\left(y \cdot x\right)}}{z} \]

       3. neg-mul-1 53.0%

          \[\leadsto t - \frac{\color{blue}{-y \cdot x}}{z} \]

       4. distribute-rgt-neg-in 53.0%

          \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

       5. associate-*r/ 57.8%

          \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   13. Simplified 57.8%

       \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   if -2.7e-10 < z < -5.59999999999999971e-167

   1. Initial program 91.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.8%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.8%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(y - z\right)\right)}{a - z}} \]

      2. mul-1-neg 74.8%

         \[\leadsto x + \frac{\color{blue}{-x \cdot \left(y - z\right)}}{a - z} \]

      3. distribute-lft-neg-out 74.8%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{a - z} \]

      4. *-commutative 74.8%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-x\right)}}{a - z} \]

   7. Simplified 74.8%

      \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(-x\right)}{a - z}} \]

   8. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 58.4%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 58.4%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 61.5%

         \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   10. Simplified 61.5%

       \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -5.59999999999999971e-167 < z < 4.7e14

   1. Initial program 91.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 90.5%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 90.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 90.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 76.4%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 69.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 70.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 70.2%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   if 4.7e14 < z

   1. Initial program 44.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 67.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 67.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 38.9%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-167}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+197}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+213}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\left(y - a\right) \cdot \frac{1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+197)
   (+ t (* x (/ (- y a) z)))
   (if (<= z 8.5e+213)
     (+ x (* (- y z) (/ (- x t) (- z a))))
     (+ t (* x (* (- y a) (/ 1.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+197) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 8.5e+213) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else {
		tmp = t + (x * ((y - a) * (1.0 / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d+197)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= 8.5d+213) then
        tmp = x + ((y - z) * ((x - t) / (z - a)))
    else
        tmp = t + (x * ((y - a) * (1.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+197) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 8.5e+213) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else {
		tmp = t + (x * ((y - a) * (1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+197:
		tmp = t + (x * ((y - a) / z))
	elif z <= 8.5e+213:
		tmp = x + ((y - z) * ((x - t) / (z - a)))
	else:
		tmp = t + (x * ((y - a) * (1.0 / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+197)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= 8.5e+213)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(z - a))));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) * Float64(1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+197)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= 8.5e+213)
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	else
		tmp = t + (x * ((y - a) * (1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+197], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+213], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000001e197

   1. Initial program 23.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 44.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 44.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 66.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 66.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 66.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 66.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 66.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 66.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 66.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 66.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 66.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 66.2%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 66.2%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 72.2%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 72.2%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 90.5%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 90.5%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 90.5%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 90.5%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -4.6000000000000001e197 < z < 8.4999999999999995e213

   1. Initial program 78.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   if 8.4999999999999995e213 < z

   1. Initial program 16.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 53.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 53.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 55.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 55.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 55.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 55.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 55.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 55.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 55.9%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 55.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 55.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 55.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 55.9%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 56.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 56.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 68.4%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 68.4%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 88.0%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 88.0%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 88.0%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 88.0%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]
   11. Step-by-step derivation

       1. frac-2neg 88.0%

          \[\leadsto t - x \cdot \color{blue}{\frac{-\left(y - a\right)}{-\left(-z\right)}} \]

       2. div-inv 88.2%

          \[\leadsto t - x \cdot \color{blue}{\left(\left(-\left(y - a\right)\right) \cdot \frac{1}{-\left(-z\right)}\right)} \]

       3. remove-double-neg 88.2%

          \[\leadsto t - x \cdot \left(\left(-\left(y - a\right)\right) \cdot \frac{1}{\color{blue}{z}}\right) \]

   12. Applied egg-rr 88.2%

       \[\leadsto t - x \cdot \color{blue}{\left(\left(-\left(y - a\right)\right) \cdot \frac{1}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+197}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+213}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\left(y - a\right) \cdot \frac{1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-163}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+98}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-12)
   (+ t (* y (/ x z)))
   (if (<= z -2.8e-163)
     (- x (* x (/ y a)))
     (if (<= z 3.3e+98) (+ x (* y (/ t a))) (- t (* x (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-12) {
		tmp = t + (y * (x / z));
	} else if (z <= -2.8e-163) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.3e+98) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d-12)) then
        tmp = t + (y * (x / z))
    else if (z <= (-2.8d-163)) then
        tmp = x - (x * (y / a))
    else if (z <= 3.3d+98) then
        tmp = x + (y * (t / a))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-12) {
		tmp = t + (y * (x / z));
	} else if (z <= -2.8e-163) {
		tmp = x - (x * (y / a));
	} else if (z <= 3.3e+98) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-12:
		tmp = t + (y * (x / z))
	elif z <= -2.8e-163:
		tmp = x - (x * (y / a))
	elif z <= 3.3e+98:
		tmp = x + (y * (t / a))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-12)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (z <= -2.8e-163)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 3.3e+98)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-12)
		tmp = t + (y * (x / z));
	elseif (z <= -2.8e-163)
		tmp = x - (x * (y / a));
	elseif (z <= 3.3e+98)
		tmp = x + (y * (t / a));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-12], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-163], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+98], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.4999999999999995e-12

   1. Initial program 47.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 69.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 53.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 53.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 53.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 53.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 53.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 53.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 53.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 53.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 53.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 53.4%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 56.1%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 56.1%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 63.1%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 63.1%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 63.1%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 63.1%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around inf 53.0%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 53.0%

          \[\leadsto t - \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. *-commutative 53.0%

          \[\leadsto t - \frac{-1 \cdot \color{blue}{\left(y \cdot x\right)}}{z} \]

       3. neg-mul-1 53.0%

          \[\leadsto t - \frac{\color{blue}{-y \cdot x}}{z} \]

       4. distribute-rgt-neg-in 53.0%

          \[\leadsto t - \frac{\color{blue}{y \cdot \left(-x\right)}}{z} \]

       5. associate-*r/ 57.8%

          \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   13. Simplified 57.8%

       \[\leadsto t - \color{blue}{y \cdot \frac{-x}{z}} \]

   if -9.4999999999999995e-12 < z < -2.8e-163

   1. Initial program 91.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.8%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.8%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(y - z\right)\right)}{a - z}} \]

      2. mul-1-neg 74.8%

         \[\leadsto x + \frac{\color{blue}{-x \cdot \left(y - z\right)}}{a - z} \]

      3. distribute-lft-neg-out 74.8%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{a - z} \]

      4. *-commutative 74.8%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-x\right)}}{a - z} \]

   7. Simplified 74.8%

      \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(-x\right)}{a - z}} \]

   8. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 58.4%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 58.4%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 61.5%

         \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   10. Simplified 61.5%

       \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -2.8e-163 < z < 3.30000000000000028e98

   1. Initial program 87.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 88.6%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 88.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 88.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 74.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 63.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 65.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 65.1%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   if 3.30000000000000028e98 < z

   1. Initial program 28.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 59.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 59.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 59.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 59.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 59.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 59.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 59.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 59.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 59.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 59.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 59.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 65.2%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 65.2%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 79.5%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 79.5%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 79.5%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 79.5%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around 0 67.6%

       \[\leadsto t - x \cdot \color{blue}{\frac{a}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-163}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+98}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+119}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-171}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+119)
   (- t (* t (/ y z)))
   (if (<= z -1.75e-171)
     (- x (* x (/ y a)))
     (if (<= z 2.15e+95) (+ x (* y (/ t a))) (- t (* x (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+119) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.75e-171) {
		tmp = x - (x * (y / a));
	} else if (z <= 2.15e+95) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9d+119)) then
        tmp = t - (t * (y / z))
    else if (z <= (-1.75d-171)) then
        tmp = x - (x * (y / a))
    else if (z <= 2.15d+95) then
        tmp = x + (y * (t / a))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+119) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.75e-171) {
		tmp = x - (x * (y / a));
	} else if (z <= 2.15e+95) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+119:
		tmp = t - (t * (y / z))
	elif z <= -1.75e-171:
		tmp = x - (x * (y / a))
	elif z <= 2.15e+95:
		tmp = x + (y * (t / a))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+119)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= -1.75e-171)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 2.15e+95)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+119)
		tmp = t - (t * (y / z));
	elseif (z <= -1.75e-171)
		tmp = x - (x * (y / a));
	elseif (z <= 2.15e+95)
		tmp = x + (y * (t / a));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+119], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-171], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+95], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.00000000000000039e119

   1. Initial program 27.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 56.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 56.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 33.8%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around 0 30.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 30.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(y - z\right)\right)}{z}} \]

      2. associate-*r* 30.8%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot \left(y - z\right)}}{z} \]

      3. neg-mul-1 30.8%

         \[\leadsto \frac{\color{blue}{\left(-t\right)} \cdot \left(y - z\right)}{z} \]

      4. *-commutative 30.8%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(-t\right)}}{z} \]

   8. Simplified 30.8%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(-t\right)}{z}} \]

   9. Taylor expanded in y around 0 49.0%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 49.0%

          \[\leadsto t + \color{blue}{\left(-\frac{t \cdot y}{z}\right)} \]

       2. unsub-neg 49.0%

          \[\leadsto \color{blue}{t - \frac{t \cdot y}{z}} \]

       3. associate-/l* 63.7%

          \[\leadsto t - \color{blue}{t \cdot \frac{y}{z}} \]

   11. Simplified 63.7%

       \[\leadsto \color{blue}{t - t \cdot \frac{y}{z}} \]

   if -9.00000000000000039e119 < z < -1.74999999999999997e-171

   1. Initial program 78.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 58.2%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 58.2%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(y - z\right)\right)}{a - z}} \]

      2. mul-1-neg 58.2%

         \[\leadsto x + \frac{\color{blue}{-x \cdot \left(y - z\right)}}{a - z} \]

      3. distribute-lft-neg-out 58.2%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{a - z} \]

      4. *-commutative 58.2%

         \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-x\right)}}{a - z} \]

   7. Simplified 58.2%

      \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(-x\right)}{a - z}} \]

   8. Taylor expanded in z around 0 43.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. unsub-neg 43.0%

         \[\leadsto \color{blue}{x - \frac{x \cdot y}{a}} \]

      3. associate-/l* 46.1%

         \[\leadsto x - \color{blue}{x \cdot \frac{y}{a}} \]

   10. Simplified 46.1%

       \[\leadsto \color{blue}{x - x \cdot \frac{y}{a}} \]

   if -1.74999999999999997e-171 < z < 2.15e95

   1. Initial program 87.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 88.6%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 88.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 88.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 74.9%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 63.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 65.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 65.1%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   if 2.15e95 < z

   1. Initial program 28.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 59.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 59.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 59.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 59.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 59.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 59.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 59.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 59.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 59.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 59.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 59.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 65.2%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 65.2%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 79.5%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 79.5%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 79.5%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 79.5%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around 0 67.6%

       \[\leadsto t - x \cdot \color{blue}{\frac{a}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 22: 34.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8e+89)
   (* t (/ y (- a z)))
   (if (<= y 6.5e-300) x (if (<= y 4.5e-41) t (* t (/ (- y z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8e+89) {
		tmp = t * (y / (a - z));
	} else if (y <= 6.5e-300) {
		tmp = x;
	} else if (y <= 4.5e-41) {
		tmp = t;
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-8d+89)) then
        tmp = t * (y / (a - z))
    else if (y <= 6.5d-300) then
        tmp = x
    else if (y <= 4.5d-41) then
        tmp = t
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8e+89) {
		tmp = t * (y / (a - z));
	} else if (y <= 6.5e-300) {
		tmp = x;
	} else if (y <= 4.5e-41) {
		tmp = t;
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8e+89:
		tmp = t * (y / (a - z))
	elif y <= 6.5e-300:
		tmp = x
	elif y <= 4.5e-41:
		tmp = t
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8e+89)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= 6.5e-300)
		tmp = x;
	elseif (y <= 4.5e-41)
		tmp = t;
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -8e+89)
		tmp = t * (y / (a - z));
	elseif (y <= 6.5e-300)
		tmp = x;
	elseif (y <= 4.5e-41)
		tmp = t;
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8e+89], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-300], x, If[LessEqual[y, 4.5e-41], t, N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.99999999999999996e89

   1. Initial program 67.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 44.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in y around inf 35.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   7. Step-by-step derivation

      1. associate-/l* 44.4%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   8. Simplified 44.4%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]

   if -7.99999999999999996e89 < y < 6.4999999999999997e-300

   1. Initial program 77.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 84.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.3%

      \[\leadsto \color{blue}{x} \]

   if 6.4999999999999997e-300 < y < 4.5e-41

   1. Initial program 49.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 62.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 39.7%

      \[\leadsto \color{blue}{t} \]

   if 4.5e-41 < y

   1. Initial program 68.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 81.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 35.4%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around inf 28.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 35.6%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.6e+123)
   t
   (if (<= z -1.45e-125)
     x
     (if (<= z -9.6e-297) (* t (/ y a)) (if (<= z 4e+89) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.6e+123) {
		tmp = t;
	} else if (z <= -1.45e-125) {
		tmp = x;
	} else if (z <= -9.6e-297) {
		tmp = t * (y / a);
	} else if (z <= 4e+89) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.6d+123)) then
        tmp = t
    else if (z <= (-1.45d-125)) then
        tmp = x
    else if (z <= (-9.6d-297)) then
        tmp = t * (y / a)
    else if (z <= 4d+89) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.6e+123) {
		tmp = t;
	} else if (z <= -1.45e-125) {
		tmp = x;
	} else if (z <= -9.6e-297) {
		tmp = t * (y / a);
	} else if (z <= 4e+89) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.6e+123:
		tmp = t
	elif z <= -1.45e-125:
		tmp = x
	elif z <= -9.6e-297:
		tmp = t * (y / a)
	elif z <= 4e+89:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.6e+123)
		tmp = t;
	elseif (z <= -1.45e-125)
		tmp = x;
	elseif (z <= -9.6e-297)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 4e+89)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.6e+123)
		tmp = t;
	elseif (z <= -1.45e-125)
		tmp = x;
	elseif (z <= -9.6e-297)
		tmp = t * (y / a);
	elseif (z <= 4e+89)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.6e+123], t, If[LessEqual[z, -1.45e-125], x, If[LessEqual[z, -9.6e-297], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+89], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.59999999999999989e123 or 3.99999999999999998e89 < z

   1. Initial program 28.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 58.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 52.1%

      \[\leadsto \color{blue}{t} \]

   if -7.59999999999999989e123 < z < -1.4500000000000001e-125 or -9.5999999999999998e-297 < z < 3.99999999999999998e89

   1. Initial program 82.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 85.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{x} \]

   if -1.4500000000000001e-125 < z < -9.5999999999999998e-297

   1. Initial program 91.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 97.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 47.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in z around 0 44.7%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 50.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+38} \lor \neg \left(z \leq 2.7 \cdot 10^{+95}\right):\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.4e+38) (not (<= z 2.7e+95)))
   (+ t (* x (/ (- y a) z)))
   (+ x (* (- x t) (/ (- z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e+38) || !(z <= 2.7e+95)) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x + ((x - t) * ((z - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.4d+38)) .or. (.not. (z <= 2.7d+95))) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = x + ((x - t) * ((z - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e+38) || !(z <= 2.7e+95)) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x + ((x - t) * ((z - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.4e+38) or not (z <= 2.7e+95):
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = x + ((x - t) * ((z - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.4e+38) || !(z <= 2.7e+95))
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.4e+38) || ~((z <= 2.7e+95)))
		tmp = t + (x * ((y - a) / z));
	else
		tmp = x + ((x - t) * ((z - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.4e+38], N[Not[LessEqual[z, 2.7e+95]], $MachinePrecision]], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.3999999999999998e38 or 2.7e95 < z

   1. Initial program 32.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 61.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 56.1%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 56.1%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 56.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 56.1%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 56.1%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 56.1%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 56.1%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 56.1%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 56.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 56.1%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 56.4%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 56.4%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 62.3%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.3%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 73.4%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 73.4%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 73.4%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 73.4%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -9.3999999999999998e38 < z < 2.7e95

   1. Initial program 88.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 72.9%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 75.9%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+38} \lor \neg \left(z \leq 2.7 \cdot 10^{+95}\right):\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-9} \lor \neg \left(z \leq 1.12 \cdot 10^{+95}\right):\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-9) (not (<= z 1.12e+95)))
   (+ t (* x (/ (- y a) z)))
   (- x (* y (/ (- x t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-9) || !(z <= 1.12e+95)) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - (y * ((x - 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 ((z <= (-1.15d-9)) .or. (.not. (z <= 1.12d+95))) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = x - (y * ((x - 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 ((z <= -1.15e-9) || !(z <= 1.12e+95)) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-9) or not (z <= 1.12e+95):
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = x - (y * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-9) || !(z <= 1.12e+95))
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e-9) || ~((z <= 1.12e+95)))
		tmp = t + (x * ((y - a) / z));
	else
		tmp = x - (y * ((x - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-9], N[Not[LessEqual[z, 1.12e+95]], $MachinePrecision]], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-9 or 1.11999999999999999e95 < z

   1. Initial program 40.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 66.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 66.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 55.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 55.2%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 55.2%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 55.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 55.2%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 55.2%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 55.2%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 55.2%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 55.2%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 55.2%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 55.2%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 55.6%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 55.6%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 59.5%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.5%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 69.2%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 69.2%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 69.2%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 69.2%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   if -1.15e-9 < z < 1.11999999999999999e95

   1. Initial program 88.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 88.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

      2. fma-define 88.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right)} \]

      3. pow2 88.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}, \sqrt[3]{x}, \left(y - z\right) \cdot \frac{t - x}{a - z}\right) \]

      4. *-commutative 88.5%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}\right) \]

      5. associate-*l/ 87.8%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}\right) \]

      6. associate-*r/ 89.9%

         \[\leadsto \mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right) \]

   6. Applied egg-rr 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{x}\right)}^{2}, \sqrt[3]{x}, \left(t - x\right) \cdot \frac{y - z}{a - z}\right)} \]

   7. Taylor expanded in z around 0 70.2%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 71.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   9. Simplified 71.5%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-9} \lor \neg \left(z \leq 1.12 \cdot 10^{+95}\right):\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+132} \lor \neg \left(z \leq 8.2 \cdot 10^{+89}\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+132) (not (<= z 8.2e+89)))
   (- t (* t (/ y z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+132) || !(z <= 8.2e+89)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d+132)) .or. (.not. (z <= 8.2d+89))) then
        tmp = t - (t * (y / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e+132) || !(z <= 8.2e+89)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e+132) or not (z <= 8.2e+89):
		tmp = t - (t * (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e+132) || !(z <= 8.2e+89))
		tmp = Float64(t - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+132) || ~((z <= 8.2e+89)))
		tmp = t - (t * (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e+132], N[Not[LessEqual[z, 8.2e+89]], $MachinePrecision]], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e132 or 8.1999999999999997e89 < z

   1. Initial program 28.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 58.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 33.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around 0 30.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 30.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(y - z\right)\right)}{z}} \]

      2. associate-*r* 30.6%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot \left(y - z\right)}}{z} \]

      3. neg-mul-1 30.6%

         \[\leadsto \frac{\color{blue}{\left(-t\right)} \cdot \left(y - z\right)}{z} \]

      4. *-commutative 30.6%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(-t\right)}}{z} \]

   8. Simplified 30.6%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(-t\right)}{z}} \]

   9. Taylor expanded in y around 0 47.6%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 47.6%

          \[\leadsto t + \color{blue}{\left(-\frac{t \cdot y}{z}\right)} \]

       2. unsub-neg 47.6%

          \[\leadsto \color{blue}{t - \frac{t \cdot y}{z}} \]

       3. associate-/l* 59.4%

          \[\leadsto t - \color{blue}{t \cdot \frac{y}{z}} \]

   11. Simplified 59.4%

       \[\leadsto \color{blue}{t - t \cdot \frac{y}{z}} \]

   if -2.5000000000000001e132 < z < 8.1999999999999997e89

   1. Initial program 84.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 87.6%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 87.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 87.7%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 67.3%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 53.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 55.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 55.3%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+132} \lor \neg \left(z \leq 8.2 \cdot 10^{+89}\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+121}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+121)
   (- t (* t (/ y z)))
   (if (<= z 5.1e+95) (+ x (* y (/ t a))) (- t (* x (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+121) {
		tmp = t - (t * (y / z));
	} else if (z <= 5.1e+95) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+121)) then
        tmp = t - (t * (y / z))
    else if (z <= 5.1d+95) then
        tmp = x + (y * (t / a))
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+121) {
		tmp = t - (t * (y / z));
	} else if (z <= 5.1e+95) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+121:
		tmp = t - (t * (y / z))
	elif z <= 5.1e+95:
		tmp = x + (y * (t / a))
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+121)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= 5.1e+95)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+121)
		tmp = t - (t * (y / z));
	elseif (z <= 5.1e+95)
		tmp = x + (y * (t / a));
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+121], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+95], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999999e121

   1. Initial program 27.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 57.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 57.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 34.8%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in a around 0 31.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 31.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(y - z\right)\right)}{z}} \]

      2. associate-*r* 31.6%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot t\right) \cdot \left(y - z\right)}}{z} \]

      3. neg-mul-1 31.6%

         \[\leadsto \frac{\color{blue}{\left(-t\right)} \cdot \left(y - z\right)}{z} \]

      4. *-commutative 31.6%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot \left(-t\right)}}{z} \]

   8. Simplified 31.6%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(-t\right)}{z}} \]

   9. Taylor expanded in y around 0 50.4%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 50.4%

          \[\leadsto t + \color{blue}{\left(-\frac{t \cdot y}{z}\right)} \]

       2. unsub-neg 50.4%

          \[\leadsto \color{blue}{t - \frac{t \cdot y}{z}} \]

       3. associate-/l* 65.6%

          \[\leadsto t - \color{blue}{t \cdot \frac{y}{z}} \]

   11. Simplified 65.6%

       \[\leadsto \color{blue}{t - t \cdot \frac{y}{z}} \]

   if -6.9999999999999999e121 < z < 5.10000000000000003e95

   1. Initial program 84.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 87.2%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 87.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 87.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 67.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 53.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 55.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 55.2%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   if 5.10000000000000003e95 < z

   1. Initial program 28.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 59.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 59.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 59.0%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 59.0%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 59.0%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 59.0%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 59.0%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 59.0%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 59.0%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 59.0%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 59.0%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 59.1%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in t around 0 65.2%

      \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot \left(y - a\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 65.2%

         \[\leadsto t - \color{blue}{\left(-\frac{x \cdot \left(y - a\right)}{z}\right)} \]

      2. associate-/l* 79.5%

         \[\leadsto t - \left(-\color{blue}{x \cdot \frac{y - a}{z}}\right) \]

      3. distribute-rgt-neg-in 79.5%

         \[\leadsto t - \color{blue}{x \cdot \left(-\frac{y - a}{z}\right)} \]

      4. distribute-neg-frac2 79.5%

         \[\leadsto t - x \cdot \color{blue}{\frac{y - a}{-z}} \]

   10. Simplified 79.5%

       \[\leadsto t - \color{blue}{x \cdot \frac{y - a}{-z}} \]

   11. Taylor expanded in y around 0 67.6%

       \[\leadsto t - x \cdot \color{blue}{\frac{a}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 28: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+129) t (if (<= z 6.5e+96) (+ x (* y (/ t a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+129) {
		tmp = t;
	} else if (z <= 6.5e+96) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+129)) then
        tmp = t
    else if (z <= 6.5d+96) then
        tmp = x + (y * (t / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+129) {
		tmp = t;
	} else if (z <= 6.5e+96) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+129:
		tmp = t
	elif z <= 6.5e+96:
		tmp = x + (y * (t / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+129)
		tmp = t;
	elseif (z <= 6.5e+96)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+129)
		tmp = t;
	elseif (z <= 6.5e+96)
		tmp = x + (y * (t / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+129], t, If[LessEqual[z, 6.5e+96], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e129 or 6.5e96 < z

   1. Initial program 27.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 58.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 58.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.5%

      \[\leadsto \color{blue}{t} \]

   if -2.3999999999999999e129 < z < 6.5e96

   1. Initial program 84.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 87.2%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 87.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 87.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in t around inf 67.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   8. Taylor expanded in z around 0 53.3%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-/l* 55.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]

   10. Simplified 55.2%

       \[\leadsto x + \color{blue}{y \cdot \frac{t}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+123) t (if (<= z 1.06e+89) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+123) {
		tmp = t;
	} else if (z <= 1.06e+89) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+123)) then
        tmp = t
    else if (z <= 1.06d+89) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+123) {
		tmp = t;
	} else if (z <= 1.06e+89) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+123:
		tmp = t
	elif z <= 1.06e+89:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+123)
		tmp = t;
	elseif (z <= 1.06e+89)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+123)
		tmp = t;
	elseif (z <= 1.06e+89)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+123], t, If[LessEqual[z, 1.06e+89], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999979e123 or 1.05999999999999997e89 < z

   1. Initial program 28.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 58.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 52.1%

      \[\leadsto \color{blue}{t} \]

   if -8.19999999999999979e123 < z < 1.05999999999999997e89

   1. Initial program 84.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 34.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 24.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 68.4%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 79.5%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 79.5%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 21.6%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 31: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 68.4%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 79.5%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 79.5%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 40.5%

   \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{a - z}} \]
6. Step-by-step derivation

   1. associate-*r/ 40.5%

      \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(x \cdot \left(y - z\right)\right)}{a - z}} \]

   2. mul-1-neg 40.5%

      \[\leadsto x + \frac{\color{blue}{-x \cdot \left(y - z\right)}}{a - z} \]

   3. distribute-lft-neg-out 40.5%

      \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{a - z} \]

   4. *-commutative 40.5%

      \[\leadsto x + \frac{\color{blue}{\left(y - z\right) \cdot \left(-x\right)}}{a - z} \]

7. Simplified 40.5%

   \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot \left(-x\right)}{a - z}} \]

8. Taylor expanded in z around inf 2.8%

   \[\leadsto \color{blue}{x + -1 \cdot x} \]
9. Step-by-step derivation

   1. distribute-rgt1-in 2.8%

      \[\leadsto \color{blue}{\left(-1 + 1\right) \cdot x} \]

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

10. Simplified 2.8%

    \[\leadsto \color{blue}{0} \]
11. Add Preprocessing

Developer target: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))