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

Percentage Accurate: 69.2% → 90.3%

Time: 21.7s

Alternatives: 25

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.2% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-232}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\left(t - \frac{y \cdot \left(t - x\right)}{z}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -1e-232)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ (- t (/ (* y (- t x)) z)) (/ (* (- t x) a) z))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e-232) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = (t - ((y * (t - x)) / z)) + (((t - x) * a) / z);
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-232)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - Float64(Float64(y * Float64(t - x)) / z)) + Float64(Float64(Float64(t - x) * a) / z));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	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[LessEqual[t$95$1, -1e-232], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-232

   1. Initial program 72.0%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*l/ 72.0%

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

      3. associate-*r/ 88.6%

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

      4. clear-num 88.5%

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

      5. un-div-inv 88.8%

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

   6. Applied egg-rr 88.8%

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

   if -1.00000000000000002e-232 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 15.1%

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

      1. associate-/l* 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. mul-1-neg 89.7%

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

      4. mul-1-neg 89.7%

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

   7. Simplified 89.7%

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

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

   1. Initial program 71.1%

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

      1. +-commutative 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-/l* 89.9%

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

      4. fma-define 89.9%

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

   3. Simplified 89.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-232}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y \cdot \left(t - x\right)}{z}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-232)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- y a) (- x t)) z))
         (if (<= t_2 2e+162) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-232) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 2e+162) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-232) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 2e+162) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-232:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((y - a) * (x - t)) / z)
	elif t_2 <= 2e+162:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-232)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (t_2 <= 2e+162)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-232)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (t_2 <= 2e+162)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-232], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+162], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 1.9999999999999999e162 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 46.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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))) < -1.00000000000000002e-232 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.9999999999999999e162

   1. Initial program 97.2%

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

   if -1.00000000000000002e-232 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 15.1%

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

      1. associate-/l* 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate--l+ 89.7%

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

      2. associate-*r/ 89.7%

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

      3. associate-*r/ 89.7%

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

      4. mul-1-neg 89.7%

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

      5. div-sub 89.6%

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

      6. mul-1-neg 89.6%

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

      7. distribute-lft-out-- 89.6%

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

      8. associate-*r/ 89.6%

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

      9. mul-1-neg 89.6%

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

      10. unsub-neg 89.6%

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

      11. distribute-rgt-out-- 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-232}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 40.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-306}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* t (/ (- y z) a))))
   (if (<= z -3.2e+137)
     t_1
     (if (<= z -6.8e+67)
       (* x (/ (- y a) z))
       (if (<= z -2.55e+39)
         t_1
         (if (<= z -8.5e-22)
           t_2
           (if (<= z -2e-246)
             x
             (if (<= z -9.6e-291)
               t_2
               (if (<= z 3.8e-306)
                 x
                 (if (<= z 5.5e-55)
                   (* t (/ y (- a z)))
                   (if (<= z 2.5e+44) x t_1)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * ((y - z) / a);
	double tmp;
	if (z <= -3.2e+137) {
		tmp = t_1;
	} else if (z <= -6.8e+67) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.55e+39) {
		tmp = t_1;
	} else if (z <= -8.5e-22) {
		tmp = t_2;
	} else if (z <= -2e-246) {
		tmp = x;
	} else if (z <= -9.6e-291) {
		tmp = t_2;
	} else if (z <= 3.8e-306) {
		tmp = x;
	} else if (z <= 5.5e-55) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.5e+44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = t * ((y - z) / a)
    if (z <= (-3.2d+137)) then
        tmp = t_1
    else if (z <= (-6.8d+67)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-2.55d+39)) then
        tmp = t_1
    else if (z <= (-8.5d-22)) then
        tmp = t_2
    else if (z <= (-2d-246)) then
        tmp = x
    else if (z <= (-9.6d-291)) then
        tmp = t_2
    else if (z <= 3.8d-306) then
        tmp = x
    else if (z <= 5.5d-55) then
        tmp = t * (y / (a - z))
    else if (z <= 2.5d+44) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * ((y - z) / a);
	double tmp;
	if (z <= -3.2e+137) {
		tmp = t_1;
	} else if (z <= -6.8e+67) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.55e+39) {
		tmp = t_1;
	} else if (z <= -8.5e-22) {
		tmp = t_2;
	} else if (z <= -2e-246) {
		tmp = x;
	} else if (z <= -9.6e-291) {
		tmp = t_2;
	} else if (z <= 3.8e-306) {
		tmp = x;
	} else if (z <= 5.5e-55) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.5e+44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = t * ((y - z) / a)
	tmp = 0
	if z <= -3.2e+137:
		tmp = t_1
	elif z <= -6.8e+67:
		tmp = x * ((y - a) / z)
	elif z <= -2.55e+39:
		tmp = t_1
	elif z <= -8.5e-22:
		tmp = t_2
	elif z <= -2e-246:
		tmp = x
	elif z <= -9.6e-291:
		tmp = t_2
	elif z <= 3.8e-306:
		tmp = x
	elif z <= 5.5e-55:
		tmp = t * (y / (a - z))
	elif z <= 2.5e+44:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -3.2e+137)
		tmp = t_1;
	elseif (z <= -6.8e+67)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -2.55e+39)
		tmp = t_1;
	elseif (z <= -8.5e-22)
		tmp = t_2;
	elseif (z <= -2e-246)
		tmp = x;
	elseif (z <= -9.6e-291)
		tmp = t_2;
	elseif (z <= 3.8e-306)
		tmp = x;
	elseif (z <= 5.5e-55)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.5e+44)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -3.2e+137)
		tmp = t_1;
	elseif (z <= -6.8e+67)
		tmp = x * ((y - a) / z);
	elseif (z <= -2.55e+39)
		tmp = t_1;
	elseif (z <= -8.5e-22)
		tmp = t_2;
	elseif (z <= -2e-246)
		tmp = x;
	elseif (z <= -9.6e-291)
		tmp = t_2;
	elseif (z <= 3.8e-306)
		tmp = x;
	elseif (z <= 5.5e-55)
		tmp = t * (y / (a - z));
	elseif (z <= 2.5e+44)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+137], t$95$1, If[LessEqual[z, -6.8e+67], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.55e+39], t$95$1, If[LessEqual[z, -8.5e-22], t$95$2, If[LessEqual[z, -2e-246], x, If[LessEqual[z, -9.6e-291], t$95$2, If[LessEqual[z, 3.8e-306], x, If[LessEqual[z, 5.5e-55], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+44], x, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.20000000000000019e137 or -6.8000000000000003e67 < z < -2.5499999999999999e39 or 2.4999999999999998e44 < z

   1. Initial program 40.4%

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

      1. associate-/l* 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in a around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. associate-/l* 49.4%

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

      4. div-sub 49.5%

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

      5. sub-neg 49.5%

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

      6. *-inverses 49.5%

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

      7. metadata-eval 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in t around inf 57.5%

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

   if -3.20000000000000019e137 < z < -6.8000000000000003e67

   1. Initial program 50.9%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 46.5%

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

      1. associate-*r/ 46.5%

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

      2. associate-*r* 46.5%

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

      3. mul-1-neg 46.5%

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

      4. mul-1-neg 46.5%

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

   7. Simplified 46.5%

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

   8. Taylor expanded in z around 0 38.5%

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

      1. cancel-sign-sub 38.5%

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

      2. neg-mul-1 38.5%

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

      3. associate-*r* 38.5%

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

      4. distribute-lft-out-- 38.5%

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

      5. associate-*r/ 38.5%

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

      6. mul-1-neg 38.5%

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

      7. distribute-frac-neg2 38.5%

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

      8. distribute-rgt-out-- 38.5%

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

      9. neg-mul-1 38.5%

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

      10. times-frac 50.8%

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

      11. metadata-eval 50.8%

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

      12. distribute-neg-frac2 50.8%

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

      13. /-rgt-identity 50.8%

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

   10. Simplified 50.8%

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

   11. Taylor expanded in t around 0 38.9%

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

       1. associate-/l* 51.2%

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

   13. Simplified 51.2%

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

   if -2.5499999999999999e39 < z < -8.5000000000000001e-22 or -1.99999999999999991e-246 < z < -9.60000000000000049e-291

   1. Initial program 82.0%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 54.0%

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

      1. associate-/l* 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in a around inf 59.3%

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

   if -8.5000000000000001e-22 < z < -1.99999999999999991e-246 or -9.60000000000000049e-291 < z < 3.8e-306 or 5.4999999999999999e-55 < z < 2.4999999999999998e44

   1. Initial program 84.5%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around inf 42.6%

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

   if 3.8e-306 < z < 5.4999999999999999e-55

   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* 92.3%

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

   3. Simplified 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-*l/ 87.7%

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

      3. associate-*r/ 97.0%

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

      4. clear-num 96.9%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

      1. div-sub 97.3%

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

   8. Applied egg-rr 97.3%

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

   9. Taylor expanded in x around 0 52.3%

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

   10. Taylor expanded in y around inf 40.6%

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

       1. associate-/l* 47.2%

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

   12. Simplified 47.2%

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

Alternative 4: 46.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -90.0)
     x
     (if (<= a -1.55e-272)
       t_1
       (if (<= a -9.5e-292)
         (/ (* x y) z)
         (if (<= a 2.35e-118)
           t_1
           (if (<= a 4.1e-56)
             (/ x (/ z y))
             (if (<= a 2.45e+57)
               t_1
               (if (<= a 7.5e+154)
                 x
                 (if (<= a 1.7e+170)
                   (* z (/ t (- a)))
                   (if (<= a 1.2e+203) (* t (/ y (- a z))) x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -90.0) {
		tmp = x;
	} else if (a <= -1.55e-272) {
		tmp = t_1;
	} else if (a <= -9.5e-292) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 4.1e-56) {
		tmp = x / (z / y);
	} else if (a <= 2.45e+57) {
		tmp = t_1;
	} else if (a <= 7.5e+154) {
		tmp = x;
	} else if (a <= 1.7e+170) {
		tmp = z * (t / -a);
	} else if (a <= 1.2e+203) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-90.0d0)) then
        tmp = x
    else if (a <= (-1.55d-272)) then
        tmp = t_1
    else if (a <= (-9.5d-292)) then
        tmp = (x * y) / z
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 4.1d-56) then
        tmp = x / (z / y)
    else if (a <= 2.45d+57) then
        tmp = t_1
    else if (a <= 7.5d+154) then
        tmp = x
    else if (a <= 1.7d+170) then
        tmp = z * (t / -a)
    else if (a <= 1.2d+203) then
        tmp = t * (y / (a - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -90.0) {
		tmp = x;
	} else if (a <= -1.55e-272) {
		tmp = t_1;
	} else if (a <= -9.5e-292) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 4.1e-56) {
		tmp = x / (z / y);
	} else if (a <= 2.45e+57) {
		tmp = t_1;
	} else if (a <= 7.5e+154) {
		tmp = x;
	} else if (a <= 1.7e+170) {
		tmp = z * (t / -a);
	} else if (a <= 1.2e+203) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -90.0:
		tmp = x
	elif a <= -1.55e-272:
		tmp = t_1
	elif a <= -9.5e-292:
		tmp = (x * y) / z
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 4.1e-56:
		tmp = x / (z / y)
	elif a <= 2.45e+57:
		tmp = t_1
	elif a <= 7.5e+154:
		tmp = x
	elif a <= 1.7e+170:
		tmp = z * (t / -a)
	elif a <= 1.2e+203:
		tmp = t * (y / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -90.0)
		tmp = x;
	elseif (a <= -1.55e-272)
		tmp = t_1;
	elseif (a <= -9.5e-292)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 4.1e-56)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.45e+57)
		tmp = t_1;
	elseif (a <= 7.5e+154)
		tmp = x;
	elseif (a <= 1.7e+170)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (a <= 1.2e+203)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -90.0)
		tmp = x;
	elseif (a <= -1.55e-272)
		tmp = t_1;
	elseif (a <= -9.5e-292)
		tmp = (x * y) / z;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 4.1e-56)
		tmp = x / (z / y);
	elseif (a <= 2.45e+57)
		tmp = t_1;
	elseif (a <= 7.5e+154)
		tmp = x;
	elseif (a <= 1.7e+170)
		tmp = z * (t / -a);
	elseif (a <= 1.2e+203)
		tmp = t * (y / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -90.0], x, If[LessEqual[a, -1.55e-272], t$95$1, If[LessEqual[a, -9.5e-292], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 4.1e-56], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+57], t$95$1, If[LessEqual[a, 7.5e+154], x, If[LessEqual[a, 1.7e+170], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+203], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -90 or 2.45e57 < a < 7.5000000000000004e154 or 1.2000000000000001e203 < a

   1. Initial program 69.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Taylor expanded in a around inf 46.5%

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

   if -90 < a < -1.55000000000000015e-272 or -9.4999999999999994e-292 < a < 2.34999999999999995e-118 or 4.1000000000000001e-56 < a < 2.45e57

   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* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in a around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

      3. associate-/l* 52.2%

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

      4. div-sub 52.2%

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

      5. sub-neg 52.2%

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

      6. *-inverses 52.2%

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

      7. metadata-eval 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in t around inf 52.8%

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

   if -1.55000000000000015e-272 < a < -9.4999999999999994e-292

   1. Initial program 75.5%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 76.4%

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

      4. div-sub 76.4%

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

      5. sub-neg 76.4%

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

      6. *-inverses 76.4%

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

      7. metadata-eval 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in x around -inf 63.6%

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

      1. *-commutative 63.6%

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

   10. Simplified 63.6%

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

   if 2.34999999999999995e-118 < a < 4.1000000000000001e-56

   1. Initial program 63.4%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. associate-*r* 73.8%

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

      3. mul-1-neg 73.8%

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

      4. mul-1-neg 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in z around 0 65.4%

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

      1. cancel-sign-sub 65.4%

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

      2. neg-mul-1 65.4%

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

      3. associate-*r* 65.4%

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

      4. distribute-lft-out-- 65.4%

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

      5. associate-*r/ 65.4%

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

      6. mul-1-neg 65.4%

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

      7. distribute-frac-neg2 65.4%

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

      8. distribute-rgt-out-- 65.4%

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

      9. neg-mul-1 65.4%

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

      10. times-frac 65.0%

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

      11. metadata-eval 65.0%

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

      12. distribute-neg-frac2 65.0%

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

      13. /-rgt-identity 65.0%

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

   10. Simplified 65.0%

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

   11. Taylor expanded in y around inf 56.6%

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

   12. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 56.8%

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

   14. Simplified 56.8%

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

       1. clear-num 56.6%

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

       2. un-div-inv 56.9%

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

   16. Applied egg-rr 56.9%

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

   if 7.5000000000000004e154 < a < 1.7000000000000001e170

   1. Initial program 75.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 74.1%

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

      1. associate-/l* 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in a around inf 73.5%

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

   9. Taylor expanded in y around 0 73.4%

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

       1. mul-1-neg 73.4%

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

       2. *-commutative 73.4%

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

       3. associate-*r/ 73.9%

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

       4. distribute-rgt-neg-in 73.9%

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

       5. distribute-neg-frac2 73.9%

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

   11. Simplified 73.9%

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

   if 1.7000000000000001e170 < a < 1.2000000000000001e203

   1. Initial program 35.9%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*l/ 35.9%

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

      3. associate-*r/ 83.8%

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

      4. clear-num 83.8%

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

      5. un-div-inv 83.8%

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

   6. Applied egg-rr 83.8%

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

      1. div-sub 83.8%

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

   8. Applied egg-rr 83.8%

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

   9. Taylor expanded in x around 0 67.7%

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

   10. Taylor expanded in y around inf 36.2%

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

       1. associate-/l* 67.8%

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

   12. Simplified 67.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-232} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y \cdot \left(t - x\right)}{z}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-232) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ (- t (/ (* y (- t x)) z)) (/ (* (- t x) 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 <= -1e-232) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - ((y * (t - x)) / z)) + (((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 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-232)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = (t - ((y * (t - x)) / z)) + (((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 - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-232) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - ((y * (t - x)) / z)) + (((t - x) * 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 <= -1e-232) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = (t - ((y * (t - x)) / z)) + (((t - x) * 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 <= -1e-232) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t - Float64(Float64(y * Float64(t - x)) / z)) + Float64(Float64(Float64(t - x) * 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 <= -1e-232) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = (t - ((y * (t - x)) / z)) + (((t - x) * 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[Or[LessEqual[t$95$1, -1e-232], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-232 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.5%

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

      1. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 71.5%

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

      3. associate-*r/ 89.3%

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

      4. clear-num 89.2%

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

      5. un-div-inv 89.3%

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

   6. Applied egg-rr 89.3%

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

   if -1.00000000000000002e-232 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 15.1%

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

      1. associate-/l* 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. mul-1-neg 89.7%

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

      4. mul-1-neg 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-232} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y \cdot \left(t - x\right)}{z}\right) + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -25500:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+274}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -25500.0)
     x
     (if (<= a -1.25e-272)
       t_1
       (if (<= a -2.85e-292)
         (/ (* x y) z)
         (if (<= a 2.35e-118)
           t_1
           (if (<= a 4.8e-55)
             (* x (/ y (- z a)))
             (if (<= a 1.28e+57)
               t_1
               (if (<= a 4.2e+154)
                 x
                 (if (<= a 1.2e+203)
                   (* t (/ (- y z) a))
                   (if (<= a 8.2e+274) x (* t (/ y a)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -25500.0) {
		tmp = x;
	} else if (a <= -1.25e-272) {
		tmp = t_1;
	} else if (a <= -2.85e-292) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 4.8e-55) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.28e+57) {
		tmp = t_1;
	} else if (a <= 4.2e+154) {
		tmp = x;
	} else if (a <= 1.2e+203) {
		tmp = t * ((y - z) / a);
	} else if (a <= 8.2e+274) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-25500.0d0)) then
        tmp = x
    else if (a <= (-1.25d-272)) then
        tmp = t_1
    else if (a <= (-2.85d-292)) then
        tmp = (x * y) / z
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 4.8d-55) then
        tmp = x * (y / (z - a))
    else if (a <= 1.28d+57) then
        tmp = t_1
    else if (a <= 4.2d+154) then
        tmp = x
    else if (a <= 1.2d+203) then
        tmp = t * ((y - z) / a)
    else if (a <= 8.2d+274) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -25500.0) {
		tmp = x;
	} else if (a <= -1.25e-272) {
		tmp = t_1;
	} else if (a <= -2.85e-292) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 4.8e-55) {
		tmp = x * (y / (z - a));
	} else if (a <= 1.28e+57) {
		tmp = t_1;
	} else if (a <= 4.2e+154) {
		tmp = x;
	} else if (a <= 1.2e+203) {
		tmp = t * ((y - z) / a);
	} else if (a <= 8.2e+274) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -25500.0:
		tmp = x
	elif a <= -1.25e-272:
		tmp = t_1
	elif a <= -2.85e-292:
		tmp = (x * y) / z
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 4.8e-55:
		tmp = x * (y / (z - a))
	elif a <= 1.28e+57:
		tmp = t_1
	elif a <= 4.2e+154:
		tmp = x
	elif a <= 1.2e+203:
		tmp = t * ((y - z) / a)
	elif a <= 8.2e+274:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -25500.0)
		tmp = x;
	elseif (a <= -1.25e-272)
		tmp = t_1;
	elseif (a <= -2.85e-292)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 4.8e-55)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 1.28e+57)
		tmp = t_1;
	elseif (a <= 4.2e+154)
		tmp = x;
	elseif (a <= 1.2e+203)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (a <= 8.2e+274)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -25500.0)
		tmp = x;
	elseif (a <= -1.25e-272)
		tmp = t_1;
	elseif (a <= -2.85e-292)
		tmp = (x * y) / z;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 4.8e-55)
		tmp = x * (y / (z - a));
	elseif (a <= 1.28e+57)
		tmp = t_1;
	elseif (a <= 4.2e+154)
		tmp = x;
	elseif (a <= 1.2e+203)
		tmp = t * ((y - z) / a);
	elseif (a <= 8.2e+274)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -25500.0], x, If[LessEqual[a, -1.25e-272], t$95$1, If[LessEqual[a, -2.85e-292], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 4.8e-55], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.28e+57], t$95$1, If[LessEqual[a, 4.2e+154], x, If[LessEqual[a, 1.2e+203], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+274], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -25500 or 1.28000000000000001e57 < a < 4.19999999999999989e154 or 1.2000000000000001e203 < a < 8.2e274

   1. Initial program 69.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 47.3%

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

   if -25500 < a < -1.24999999999999995e-272 or -2.8499999999999998e-292 < a < 2.34999999999999995e-118 or 4.79999999999999983e-55 < a < 1.28000000000000001e57

   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* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in a around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

      3. associate-/l* 52.2%

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

      4. div-sub 52.2%

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

      5. sub-neg 52.2%

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

      6. *-inverses 52.2%

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

      7. metadata-eval 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in t around inf 52.8%

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

   if -1.24999999999999995e-272 < a < -2.8499999999999998e-292

   1. Initial program 75.5%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 76.4%

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

      4. div-sub 76.4%

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

      5. sub-neg 76.4%

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

      6. *-inverses 76.4%

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

      7. metadata-eval 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in x around -inf 63.6%

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

      1. *-commutative 63.6%

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

   10. Simplified 63.6%

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

   if 2.34999999999999995e-118 < a < 4.79999999999999983e-55

   1. Initial program 63.4%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. div-sub 74.3%

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

   7. Simplified 74.3%

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

      1. clear-num 73.9%

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

      2. un-div-inv 76.5%

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

   9. Applied egg-rr 76.5%

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

   10. Taylor expanded in t around 0 56.5%

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

       1. mul-1-neg 56.5%

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

       2. associate-/l* 64.9%

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

       3. distribute-rgt-neg-in 64.9%

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

       4. distribute-neg-frac2 64.9%

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

       5. neg-sub0 64.9%

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

       6. associate-+l- 64.9%

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

       7. neg-sub0 64.9%

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

       8. +-commutative 64.9%

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

       9. unsub-neg 64.9%

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

   12. Simplified 64.9%

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

   if 4.19999999999999989e154 < a < 1.2000000000000001e203

   1. Initial program 51.7%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 51.3%

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

      1. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in a around inf 70.0%

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

   if 8.2e274 < a

   1. Initial program 52.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 52.6%

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

      1. associate-/l* 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. associate-/l* 99.2%

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

   10. Simplified 99.2%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -25500:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+274}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -55:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+267}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -55.0)
     x
     (if (<= a -7.2e-269)
       t_1
       (if (<= a -1.65e-291)
         (/ (* x y) z)
         (if (<= a 2.35e-118)
           t_1
           (if (<= a 3.4e-56)
             (/ x (/ z y))
             (if (<= a 1.3e+57)
               t_1
               (if (<= a 6.8e+154)
                 x
                 (if (<= a 9.5e+243)
                   (* t (/ (- y z) a))
                   (if (<= a 8.6e+267) x (/ t (/ a y)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -55.0) {
		tmp = x;
	} else if (a <= -7.2e-269) {
		tmp = t_1;
	} else if (a <= -1.65e-291) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 1.3e+57) {
		tmp = t_1;
	} else if (a <= 6.8e+154) {
		tmp = x;
	} else if (a <= 9.5e+243) {
		tmp = t * ((y - z) / a);
	} else if (a <= 8.6e+267) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-55.0d0)) then
        tmp = x
    else if (a <= (-7.2d-269)) then
        tmp = t_1
    else if (a <= (-1.65d-291)) then
        tmp = (x * y) / z
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 3.4d-56) then
        tmp = x / (z / y)
    else if (a <= 1.3d+57) then
        tmp = t_1
    else if (a <= 6.8d+154) then
        tmp = x
    else if (a <= 9.5d+243) then
        tmp = t * ((y - z) / a)
    else if (a <= 8.6d+267) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -55.0) {
		tmp = x;
	} else if (a <= -7.2e-269) {
		tmp = t_1;
	} else if (a <= -1.65e-291) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 1.3e+57) {
		tmp = t_1;
	} else if (a <= 6.8e+154) {
		tmp = x;
	} else if (a <= 9.5e+243) {
		tmp = t * ((y - z) / a);
	} else if (a <= 8.6e+267) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -55.0:
		tmp = x
	elif a <= -7.2e-269:
		tmp = t_1
	elif a <= -1.65e-291:
		tmp = (x * y) / z
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 3.4e-56:
		tmp = x / (z / y)
	elif a <= 1.3e+57:
		tmp = t_1
	elif a <= 6.8e+154:
		tmp = x
	elif a <= 9.5e+243:
		tmp = t * ((y - z) / a)
	elif a <= 8.6e+267:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -55.0)
		tmp = x;
	elseif (a <= -7.2e-269)
		tmp = t_1;
	elseif (a <= -1.65e-291)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 1.3e+57)
		tmp = t_1;
	elseif (a <= 6.8e+154)
		tmp = x;
	elseif (a <= 9.5e+243)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (a <= 8.6e+267)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -55.0)
		tmp = x;
	elseif (a <= -7.2e-269)
		tmp = t_1;
	elseif (a <= -1.65e-291)
		tmp = (x * y) / z;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = x / (z / y);
	elseif (a <= 1.3e+57)
		tmp = t_1;
	elseif (a <= 6.8e+154)
		tmp = x;
	elseif (a <= 9.5e+243)
		tmp = t * ((y - z) / a);
	elseif (a <= 8.6e+267)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -55.0], x, If[LessEqual[a, -7.2e-269], t$95$1, If[LessEqual[a, -1.65e-291], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 3.4e-56], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+57], t$95$1, If[LessEqual[a, 6.8e+154], x, If[LessEqual[a, 9.5e+243], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+267], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -55 or 1.3e57 < a < 6.79999999999999948e154 or 9.49999999999999957e243 < a < 8.5999999999999994e267

   1. Initial program 69.4%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in a around inf 47.9%

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

   if -55 < a < -7.19999999999999996e-269 or -1.6499999999999999e-291 < a < 2.34999999999999995e-118 or 3.39999999999999982e-56 < a < 1.3e57

   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* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in a around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

      3. associate-/l* 52.2%

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

      4. div-sub 52.2%

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

      5. sub-neg 52.2%

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

      6. *-inverses 52.2%

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

      7. metadata-eval 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in t around inf 52.8%

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

   if -7.19999999999999996e-269 < a < -1.6499999999999999e-291

   1. Initial program 75.5%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 76.4%

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

      4. div-sub 76.4%

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

      5. sub-neg 76.4%

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

      6. *-inverses 76.4%

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

      7. metadata-eval 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in x around -inf 63.6%

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

      1. *-commutative 63.6%

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

   10. Simplified 63.6%

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

   if 2.34999999999999995e-118 < a < 3.39999999999999982e-56

   1. Initial program 63.4%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. associate-*r* 73.8%

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

      3. mul-1-neg 73.8%

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

      4. mul-1-neg 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in z around 0 65.4%

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

      1. cancel-sign-sub 65.4%

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

      2. neg-mul-1 65.4%

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

      3. associate-*r* 65.4%

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

      4. distribute-lft-out-- 65.4%

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

      5. associate-*r/ 65.4%

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

      6. mul-1-neg 65.4%

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

      7. distribute-frac-neg2 65.4%

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

      8. distribute-rgt-out-- 65.4%

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

      9. neg-mul-1 65.4%

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

      10. times-frac 65.0%

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

      11. metadata-eval 65.0%

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

      12. distribute-neg-frac2 65.0%

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

      13. /-rgt-identity 65.0%

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

   10. Simplified 65.0%

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

   11. Taylor expanded in y around inf 56.6%

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

   12. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 56.8%

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

   14. Simplified 56.8%

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

       1. clear-num 56.6%

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

       2. un-div-inv 56.9%

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

   16. Applied egg-rr 56.9%

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

   if 6.79999999999999948e154 < a < 9.49999999999999957e243

   1. Initial program 59.2%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around 0 48.5%

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

      1. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in a around inf 58.5%

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

   if 8.5999999999999994e267 < a

   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 37.5%

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

      1. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around 0 37.5%

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

      1. associate-/l* 68.6%

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

   10. Simplified 68.6%

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

       1. clear-num 68.6%

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

       2. un-div-inv 68.6%

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

   12. Applied egg-rr 68.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -55:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+267}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -2.26 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-233}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-281}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-244}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 125:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (* t (/ y a))))
        (t_3 (* y (/ (- x t) z))))
   (if (<= a -2.26e-85)
     t_2
     (if (<= a -1.6e-233)
       (- t (/ (* y t) z))
       (if (<= a -1.95e-281)
         t_3
         (if (<= a -7.8e-289)
           (/ (* y (- x t)) z)
           (if (<= a 1.35e-244)
             t_3
             (if (<= a 3.9e-139)
               t_1
               (if (<= a 4e-37)
                 (* x (/ y (- z a)))
                 (if (<= a 125.0) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -2.26e-85) {
		tmp = t_2;
	} else if (a <= -1.6e-233) {
		tmp = t - ((y * t) / z);
	} else if (a <= -1.95e-281) {
		tmp = t_3;
	} else if (a <= -7.8e-289) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.35e-244) {
		tmp = t_3;
	} else if (a <= 3.9e-139) {
		tmp = t_1;
	} else if (a <= 4e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 125.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t * (y / a))
    t_3 = y * ((x - t) / z)
    if (a <= (-2.26d-85)) then
        tmp = t_2
    else if (a <= (-1.6d-233)) then
        tmp = t - ((y * t) / z)
    else if (a <= (-1.95d-281)) then
        tmp = t_3
    else if (a <= (-7.8d-289)) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.35d-244) then
        tmp = t_3
    else if (a <= 3.9d-139) then
        tmp = t_1
    else if (a <= 4d-37) then
        tmp = x * (y / (z - a))
    else if (a <= 125.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -2.26e-85) {
		tmp = t_2;
	} else if (a <= -1.6e-233) {
		tmp = t - ((y * t) / z);
	} else if (a <= -1.95e-281) {
		tmp = t_3;
	} else if (a <= -7.8e-289) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.35e-244) {
		tmp = t_3;
	} else if (a <= 3.9e-139) {
		tmp = t_1;
	} else if (a <= 4e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 125.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t * (y / a))
	t_3 = y * ((x - t) / z)
	tmp = 0
	if a <= -2.26e-85:
		tmp = t_2
	elif a <= -1.6e-233:
		tmp = t - ((y * t) / z)
	elif a <= -1.95e-281:
		tmp = t_3
	elif a <= -7.8e-289:
		tmp = (y * (x - t)) / z
	elif a <= 1.35e-244:
		tmp = t_3
	elif a <= 3.9e-139:
		tmp = t_1
	elif a <= 4e-37:
		tmp = x * (y / (z - a))
	elif a <= 125.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	t_3 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -2.26e-85)
		tmp = t_2;
	elseif (a <= -1.6e-233)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= -1.95e-281)
		tmp = t_3;
	elseif (a <= -7.8e-289)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.35e-244)
		tmp = t_3;
	elseif (a <= 3.9e-139)
		tmp = t_1;
	elseif (a <= 4e-37)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 125.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t * (y / a));
	t_3 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -2.26e-85)
		tmp = t_2;
	elseif (a <= -1.6e-233)
		tmp = t - ((y * t) / z);
	elseif (a <= -1.95e-281)
		tmp = t_3;
	elseif (a <= -7.8e-289)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.35e-244)
		tmp = t_3;
	elseif (a <= 3.9e-139)
		tmp = t_1;
	elseif (a <= 4e-37)
		tmp = x * (y / (z - a));
	elseif (a <= 125.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.26e-85], t$95$2, If[LessEqual[a, -1.6e-233], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-281], t$95$3, If[LessEqual[a, -7.8e-289], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.35e-244], t$95$3, If[LessEqual[a, 3.9e-139], t$95$1, If[LessEqual[a, 4e-37], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 125.0], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.25999999999999997e-85 or 125 < a

   1. Initial program 66.5%

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

      1. associate-/l* 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. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 62.4%

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

   10. Simplified 62.4%

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

   if -2.25999999999999997e-85 < a < -1.5999999999999999e-233

   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* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around inf 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-*r* 70.0%

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

      3. mul-1-neg 70.0%

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

      4. mul-1-neg 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in a around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. associate-*r/ 72.5%

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

      3. sub-neg 72.5%

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

   10. Simplified 72.5%

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

   11. Taylor expanded in t around inf 60.2%

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

   if -1.5999999999999999e-233 < a < -1.9500000000000001e-281 or -7.7999999999999997e-289 < a < 1.35e-244

   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* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. associate-*r/ 87.3%

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

      2. associate-*r* 87.3%

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

      3. mul-1-neg 87.3%

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

      4. mul-1-neg 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in z around 0 68.7%

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

      1. cancel-sign-sub 68.7%

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

      2. neg-mul-1 68.7%

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

      3. associate-*r* 68.7%

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

      4. distribute-lft-out-- 68.7%

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

      5. associate-*r/ 68.7%

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

      6. mul-1-neg 68.7%

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

      7. distribute-frac-neg2 68.7%

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

      8. distribute-rgt-out-- 68.7%

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

      9. neg-mul-1 68.7%

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

      10. times-frac 69.2%

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

      11. metadata-eval 69.2%

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

      12. distribute-neg-frac2 69.2%

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

      13. /-rgt-identity 69.2%

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

   10. Simplified 69.2%

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

   11. Taylor expanded in y around inf 65.4%

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

       1. associate-/l* 73.8%

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

   13. Simplified 73.8%

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

   if -1.9500000000000001e-281 < a < -7.7999999999999997e-289

   1. Initial program 80.4%

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

      1. associate-/l* 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

      4. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 80.4%

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

      1. cancel-sign-sub 80.4%

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

      2. neg-mul-1 80.4%

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

      3. associate-*r* 80.4%

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

      4. distribute-lft-out-- 80.4%

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

      5. associate-*r/ 80.4%

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

      6. mul-1-neg 80.4%

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

      7. distribute-frac-neg2 80.4%

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

      8. distribute-rgt-out-- 80.4%

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

      9. neg-mul-1 80.4%

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

      10. times-frac 80.4%

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

      11. metadata-eval 80.4%

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

      12. distribute-neg-frac2 80.4%

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

      13. /-rgt-identity 80.4%

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

   10. Simplified 80.4%

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

   11. Taylor expanded in y around inf 80.4%

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

   if 1.35e-244 < a < 3.9000000000000001e-139 or 4.00000000000000027e-37 < a < 125

   1. Initial program 68.8%

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

      1. associate-/l* 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in a around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. unsub-neg 38.7%

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

      3. associate-/l* 46.8%

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

      4. div-sub 46.8%

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

      5. sub-neg 46.8%

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

      6. *-inverses 46.8%

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

      7. metadata-eval 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in t around inf 53.7%

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

   if 3.9000000000000001e-139 < a < 4.00000000000000027e-37

   1. Initial program 58.1%

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

      1. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

   7. Simplified 64.0%

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

      1. clear-num 63.7%

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

      2. un-div-inv 65.2%

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

   9. Applied egg-rr 65.2%

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

   10. Taylor expanded in t around 0 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-/l* 53.6%

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

       3. distribute-rgt-neg-in 53.6%

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

       4. distribute-neg-frac2 53.6%

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

       5. neg-sub0 53.6%

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

       6. associate-+l- 53.6%

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

       7. neg-sub0 53.6%

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

       8. +-commutative 53.6%

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

       9. unsub-neg 53.6%

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

   12. Simplified 53.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.26 \cdot 10^{-85}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-233}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 125:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-228}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-297}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-245}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 490:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (* t (/ y a))))
        (t_3 (* y (/ (- x t) z))))
   (if (<= a -7.2e-86)
     t_2
     (if (<= a -1.8e-228)
       (- t (/ (* y t) z))
       (if (<= a -7.5e-297)
         t_3
         (if (<= a 4.2e-299)
           t_1
           (if (<= a 6.7e-245)
             t_3
             (if (<= a 4.2e-139)
               t_1
               (if (<= a 2.2e-37)
                 (* x (/ y (- z a)))
                 (if (<= a 490.0) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -7.2e-86) {
		tmp = t_2;
	} else if (a <= -1.8e-228) {
		tmp = t - ((y * t) / z);
	} else if (a <= -7.5e-297) {
		tmp = t_3;
	} else if (a <= 4.2e-299) {
		tmp = t_1;
	} else if (a <= 6.7e-245) {
		tmp = t_3;
	} else if (a <= 4.2e-139) {
		tmp = t_1;
	} else if (a <= 2.2e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 490.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t * (y / a))
    t_3 = y * ((x - t) / z)
    if (a <= (-7.2d-86)) then
        tmp = t_2
    else if (a <= (-1.8d-228)) then
        tmp = t - ((y * t) / z)
    else if (a <= (-7.5d-297)) then
        tmp = t_3
    else if (a <= 4.2d-299) then
        tmp = t_1
    else if (a <= 6.7d-245) then
        tmp = t_3
    else if (a <= 4.2d-139) then
        tmp = t_1
    else if (a <= 2.2d-37) then
        tmp = x * (y / (z - a))
    else if (a <= 490.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -7.2e-86) {
		tmp = t_2;
	} else if (a <= -1.8e-228) {
		tmp = t - ((y * t) / z);
	} else if (a <= -7.5e-297) {
		tmp = t_3;
	} else if (a <= 4.2e-299) {
		tmp = t_1;
	} else if (a <= 6.7e-245) {
		tmp = t_3;
	} else if (a <= 4.2e-139) {
		tmp = t_1;
	} else if (a <= 2.2e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 490.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t * (y / a))
	t_3 = y * ((x - t) / z)
	tmp = 0
	if a <= -7.2e-86:
		tmp = t_2
	elif a <= -1.8e-228:
		tmp = t - ((y * t) / z)
	elif a <= -7.5e-297:
		tmp = t_3
	elif a <= 4.2e-299:
		tmp = t_1
	elif a <= 6.7e-245:
		tmp = t_3
	elif a <= 4.2e-139:
		tmp = t_1
	elif a <= 2.2e-37:
		tmp = x * (y / (z - a))
	elif a <= 490.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	t_3 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -7.2e-86)
		tmp = t_2;
	elseif (a <= -1.8e-228)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= -7.5e-297)
		tmp = t_3;
	elseif (a <= 4.2e-299)
		tmp = t_1;
	elseif (a <= 6.7e-245)
		tmp = t_3;
	elseif (a <= 4.2e-139)
		tmp = t_1;
	elseif (a <= 2.2e-37)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 490.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t * (y / a));
	t_3 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -7.2e-86)
		tmp = t_2;
	elseif (a <= -1.8e-228)
		tmp = t - ((y * t) / z);
	elseif (a <= -7.5e-297)
		tmp = t_3;
	elseif (a <= 4.2e-299)
		tmp = t_1;
	elseif (a <= 6.7e-245)
		tmp = t_3;
	elseif (a <= 4.2e-139)
		tmp = t_1;
	elseif (a <= 2.2e-37)
		tmp = x * (y / (z - a));
	elseif (a <= 490.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e-86], t$95$2, If[LessEqual[a, -1.8e-228], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-297], t$95$3, If[LessEqual[a, 4.2e-299], t$95$1, If[LessEqual[a, 6.7e-245], t$95$3, If[LessEqual[a, 4.2e-139], t$95$1, If[LessEqual[a, 2.2e-37], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 490.0], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.19999999999999932e-86 or 490 < a

   1. Initial program 66.5%

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

      1. associate-/l* 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. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 62.4%

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

   10. Simplified 62.4%

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

   if -7.19999999999999932e-86 < a < -1.8000000000000001e-228

   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* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around inf 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-*r* 70.0%

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

      3. mul-1-neg 70.0%

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

      4. mul-1-neg 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in a around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. associate-*r/ 72.5%

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

      3. sub-neg 72.5%

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

   10. Simplified 72.5%

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

   11. Taylor expanded in t around inf 60.2%

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

   if -1.8000000000000001e-228 < a < -7.4999999999999994e-297 or 4.2000000000000002e-299 < a < 6.7e-245

   1. Initial program 71.0%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 92.1%

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

      1. associate-*r/ 92.1%

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

      2. associate-*r* 92.1%

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

      3. mul-1-neg 92.1%

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

      4. mul-1-neg 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 71.1%

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

      1. cancel-sign-sub 71.1%

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

      2. neg-mul-1 71.1%

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

      3. associate-*r* 71.1%

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

      4. distribute-lft-out-- 71.1%

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

      5. associate-*r/ 71.1%

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

      6. mul-1-neg 71.1%

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

      7. distribute-frac-neg2 71.1%

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

      8. distribute-rgt-out-- 71.1%

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

      9. neg-mul-1 71.1%

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

      10. times-frac 71.5%

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

      11. metadata-eval 71.5%

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

      12. distribute-neg-frac2 71.5%

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

      13. /-rgt-identity 71.5%

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

   10. Simplified 71.5%

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

   11. Taylor expanded in y around inf 68.0%

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

       1. associate-/l* 72.0%

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

   13. Simplified 72.0%

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

   if -7.4999999999999994e-297 < a < 4.2000000000000002e-299 or 6.7e-245 < a < 4.20000000000000016e-139 or 2.20000000000000002e-37 < a < 490

   1. Initial program 68.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around 0 42.2%

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

      1. mul-1-neg 42.2%

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

      2. unsub-neg 42.2%

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

      3. associate-/l* 53.0%

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

      4. div-sub 53.0%

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

      5. sub-neg 53.0%

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

      6. *-inverses 53.0%

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

      7. metadata-eval 53.0%

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

   7. Simplified 53.0%

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

   8. Taylor expanded in t around inf 59.0%

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

   if 4.20000000000000016e-139 < a < 2.20000000000000002e-37

   1. Initial program 58.1%

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

      1. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

   7. Simplified 64.0%

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

      1. clear-num 63.7%

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

      2. un-div-inv 65.2%

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

   9. Applied egg-rr 65.2%

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

   10. Taylor expanded in t around 0 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-/l* 53.6%

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

       3. distribute-rgt-neg-in 53.6%

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

       4. distribute-neg-frac2 53.6%

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

       5. neg-sub0 53.6%

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

       6. associate-+l- 53.6%

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

       7. neg-sub0 53.6%

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

       8. +-commutative 53.6%

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

       9. unsub-neg 53.6%

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

   12. Simplified 53.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-86}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-228}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 490:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-300}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-243}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;a \leq 120:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z))))
        (t_2 (+ x (* t (/ y a))))
        (t_3 (* y (/ (- x t) z))))
   (if (<= a -5.5e-86)
     t_2
     (if (<= a -2e-230)
       t_1
       (if (<= a -2.15e-300)
         t_3
         (if (<= a 5.2e-296)
           t_1
           (if (<= a 4.2e-243)
             t_3
             (if (<= a 4.2e-139)
               t_1
               (if (<= a 4.2e-37)
                 (* x (/ y (- z a)))
                 (if (<= a 120.0) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -5.5e-86) {
		tmp = t_2;
	} else if (a <= -2e-230) {
		tmp = t_1;
	} else if (a <= -2.15e-300) {
		tmp = t_3;
	} else if (a <= 5.2e-296) {
		tmp = t_1;
	} else if (a <= 4.2e-243) {
		tmp = t_3;
	} else if (a <= 4.2e-139) {
		tmp = t_1;
	} else if (a <= 4.2e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 120.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t * (y / a))
    t_3 = y * ((x - t) / z)
    if (a <= (-5.5d-86)) then
        tmp = t_2
    else if (a <= (-2d-230)) then
        tmp = t_1
    else if (a <= (-2.15d-300)) then
        tmp = t_3
    else if (a <= 5.2d-296) then
        tmp = t_1
    else if (a <= 4.2d-243) then
        tmp = t_3
    else if (a <= 4.2d-139) then
        tmp = t_1
    else if (a <= 4.2d-37) then
        tmp = x * (y / (z - a))
    else if (a <= 120.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -5.5e-86) {
		tmp = t_2;
	} else if (a <= -2e-230) {
		tmp = t_1;
	} else if (a <= -2.15e-300) {
		tmp = t_3;
	} else if (a <= 5.2e-296) {
		tmp = t_1;
	} else if (a <= 4.2e-243) {
		tmp = t_3;
	} else if (a <= 4.2e-139) {
		tmp = t_1;
	} else if (a <= 4.2e-37) {
		tmp = x * (y / (z - a));
	} else if (a <= 120.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t * (y / a))
	t_3 = y * ((x - t) / z)
	tmp = 0
	if a <= -5.5e-86:
		tmp = t_2
	elif a <= -2e-230:
		tmp = t_1
	elif a <= -2.15e-300:
		tmp = t_3
	elif a <= 5.2e-296:
		tmp = t_1
	elif a <= 4.2e-243:
		tmp = t_3
	elif a <= 4.2e-139:
		tmp = t_1
	elif a <= 4.2e-37:
		tmp = x * (y / (z - a))
	elif a <= 120.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	t_3 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -5.5e-86)
		tmp = t_2;
	elseif (a <= -2e-230)
		tmp = t_1;
	elseif (a <= -2.15e-300)
		tmp = t_3;
	elseif (a <= 5.2e-296)
		tmp = t_1;
	elseif (a <= 4.2e-243)
		tmp = t_3;
	elseif (a <= 4.2e-139)
		tmp = t_1;
	elseif (a <= 4.2e-37)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	elseif (a <= 120.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t * (y / a));
	t_3 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -5.5e-86)
		tmp = t_2;
	elseif (a <= -2e-230)
		tmp = t_1;
	elseif (a <= -2.15e-300)
		tmp = t_3;
	elseif (a <= 5.2e-296)
		tmp = t_1;
	elseif (a <= 4.2e-243)
		tmp = t_3;
	elseif (a <= 4.2e-139)
		tmp = t_1;
	elseif (a <= 4.2e-37)
		tmp = x * (y / (z - a));
	elseif (a <= 120.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e-86], t$95$2, If[LessEqual[a, -2e-230], t$95$1, If[LessEqual[a, -2.15e-300], t$95$3, If[LessEqual[a, 5.2e-296], t$95$1, If[LessEqual[a, 4.2e-243], t$95$3, If[LessEqual[a, 4.2e-139], t$95$1, If[LessEqual[a, 4.2e-37], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 120.0], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.5e-86 or 120 < a

   1. Initial program 66.5%

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

      1. associate-/l* 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. Taylor expanded in z around 0 55.2%

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

      1. associate-/l* 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 62.4%

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

   10. Simplified 62.4%

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

   if -5.5e-86 < a < -2.00000000000000009e-230 or -2.15e-300 < a < 5.2000000000000001e-296 or 4.2000000000000002e-243 < a < 4.20000000000000016e-139 or 4.2000000000000002e-37 < a < 120

   1. Initial program 71.2%

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

      1. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in a around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

      3. associate-/l* 57.6%

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

      4. div-sub 57.8%

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

      5. sub-neg 57.8%

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

      6. *-inverses 57.8%

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

      7. metadata-eval 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in t around inf 59.7%

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

   if -2.00000000000000009e-230 < a < -2.15e-300 or 5.2000000000000001e-296 < a < 4.2000000000000002e-243

   1. Initial program 71.0%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 92.1%

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

      1. associate-*r/ 92.1%

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

      2. associate-*r* 92.1%

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

      3. mul-1-neg 92.1%

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

      4. mul-1-neg 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in z around 0 71.1%

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

      1. cancel-sign-sub 71.1%

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

      2. neg-mul-1 71.1%

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

      3. associate-*r* 71.1%

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

      4. distribute-lft-out-- 71.1%

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

      5. associate-*r/ 71.1%

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

      6. mul-1-neg 71.1%

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

      7. distribute-frac-neg2 71.1%

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

      8. distribute-rgt-out-- 71.1%

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

      9. neg-mul-1 71.1%

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

      10. times-frac 71.5%

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

      11. metadata-eval 71.5%

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

      12. distribute-neg-frac2 71.5%

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

      13. /-rgt-identity 71.5%

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

   10. Simplified 71.5%

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

   11. Taylor expanded in y around inf 68.0%

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

       1. associate-/l* 72.0%

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

   13. Simplified 72.0%

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

   if 4.20000000000000016e-139 < a < 4.2000000000000002e-37

   1. Initial program 58.1%

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

      1. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. div-sub 64.0%

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

   7. Simplified 64.0%

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

      1. clear-num 63.7%

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

      2. un-div-inv 65.2%

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

   9. Applied egg-rr 65.2%

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

   10. Taylor expanded in t around 0 44.6%

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

       1. mul-1-neg 44.6%

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

       2. associate-/l* 53.6%

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

       3. distribute-rgt-neg-in 53.6%

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

       4. distribute-neg-frac2 53.6%

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

       5. neg-sub0 53.6%

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

       6. associate-+l- 53.6%

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

       7. neg-sub0 53.6%

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

       8. +-commutative 53.6%

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

       9. unsub-neg 53.6%

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

   12. Simplified 53.6%

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

Alternative 11: 42.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* t (/ (- y z) a))))
   (if (<= z -2.25e+136)
     t_1
     (if (<= z -1.3e+73)
       (* x (/ (- y a) z))
       (if (<= z -4.15e+43)
         t_1
         (if (<= z -8e-19)
           t_2
           (if (<= z -2.15e-246)
             x
             (if (<= z -1.06e-291)
               t_2
               (if (<= z 5.5e-55)
                 (* y (/ (- t x) a))
                 (if (<= z 2.8e+44) x t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.25e+136) {
		tmp = t_1;
	} else if (z <= -1.3e+73) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.15e+43) {
		tmp = t_1;
	} else if (z <= -8e-19) {
		tmp = t_2;
	} else if (z <= -2.15e-246) {
		tmp = x;
	} else if (z <= -1.06e-291) {
		tmp = t_2;
	} else if (z <= 5.5e-55) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.8e+44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = t * ((y - z) / a)
    if (z <= (-2.25d+136)) then
        tmp = t_1
    else if (z <= (-1.3d+73)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-4.15d+43)) then
        tmp = t_1
    else if (z <= (-8d-19)) then
        tmp = t_2
    else if (z <= (-2.15d-246)) then
        tmp = x
    else if (z <= (-1.06d-291)) then
        tmp = t_2
    else if (z <= 5.5d-55) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.8d+44) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.25e+136) {
		tmp = t_1;
	} else if (z <= -1.3e+73) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.15e+43) {
		tmp = t_1;
	} else if (z <= -8e-19) {
		tmp = t_2;
	} else if (z <= -2.15e-246) {
		tmp = x;
	} else if (z <= -1.06e-291) {
		tmp = t_2;
	} else if (z <= 5.5e-55) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.8e+44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = t * ((y - z) / a)
	tmp = 0
	if z <= -2.25e+136:
		tmp = t_1
	elif z <= -1.3e+73:
		tmp = x * ((y - a) / z)
	elif z <= -4.15e+43:
		tmp = t_1
	elif z <= -8e-19:
		tmp = t_2
	elif z <= -2.15e-246:
		tmp = x
	elif z <= -1.06e-291:
		tmp = t_2
	elif z <= 5.5e-55:
		tmp = y * ((t - x) / a)
	elif z <= 2.8e+44:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -2.25e+136)
		tmp = t_1;
	elseif (z <= -1.3e+73)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -4.15e+43)
		tmp = t_1;
	elseif (z <= -8e-19)
		tmp = t_2;
	elseif (z <= -2.15e-246)
		tmp = x;
	elseif (z <= -1.06e-291)
		tmp = t_2;
	elseif (z <= 5.5e-55)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.8e+44)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -2.25e+136)
		tmp = t_1;
	elseif (z <= -1.3e+73)
		tmp = x * ((y - a) / z);
	elseif (z <= -4.15e+43)
		tmp = t_1;
	elseif (z <= -8e-19)
		tmp = t_2;
	elseif (z <= -2.15e-246)
		tmp = x;
	elseif (z <= -1.06e-291)
		tmp = t_2;
	elseif (z <= 5.5e-55)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.8e+44)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+136], t$95$1, If[LessEqual[z, -1.3e+73], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.15e+43], t$95$1, If[LessEqual[z, -8e-19], t$95$2, If[LessEqual[z, -2.15e-246], x, If[LessEqual[z, -1.06e-291], t$95$2, If[LessEqual[z, 5.5e-55], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+44], x, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.25e136 or -1.3e73 < z < -4.14999999999999979e43 or 2.8000000000000001e44 < z

   1. Initial program 40.4%

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

      1. associate-/l* 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in a around 0 30.0%

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

      1. mul-1-neg 30.0%

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

      2. unsub-neg 30.0%

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

      3. associate-/l* 49.4%

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

      4. div-sub 49.5%

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

      5. sub-neg 49.5%

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

      6. *-inverses 49.5%

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

      7. metadata-eval 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in t around inf 57.5%

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

   if -2.25e136 < z < -1.3e73

   1. Initial program 50.9%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 46.5%

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

      1. associate-*r/ 46.5%

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

      2. associate-*r* 46.5%

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

      3. mul-1-neg 46.5%

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

      4. mul-1-neg 46.5%

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

   7. Simplified 46.5%

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

   8. Taylor expanded in z around 0 38.5%

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

      1. cancel-sign-sub 38.5%

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

      2. neg-mul-1 38.5%

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

      3. associate-*r* 38.5%

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

      4. distribute-lft-out-- 38.5%

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

      5. associate-*r/ 38.5%

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

      6. mul-1-neg 38.5%

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

      7. distribute-frac-neg2 38.5%

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

      8. distribute-rgt-out-- 38.5%

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

      9. neg-mul-1 38.5%

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

      10. times-frac 50.8%

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

      11. metadata-eval 50.8%

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

      12. distribute-neg-frac2 50.8%

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

      13. /-rgt-identity 50.8%

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

   10. Simplified 50.8%

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

   11. Taylor expanded in t around 0 38.9%

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

       1. associate-/l* 51.2%

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

   13. Simplified 51.2%

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

   if -4.14999999999999979e43 < z < -7.9999999999999998e-19 or -2.14999999999999996e-246 < z < -1.05999999999999992e-291

   1. Initial program 82.0%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around 0 54.0%

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

      1. associate-/l* 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in a around inf 59.3%

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

   if -7.9999999999999998e-19 < z < -2.14999999999999996e-246 or 5.4999999999999999e-55 < z < 2.8000000000000001e44

   1. Initial program 83.9%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 41.5%

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

   if -1.05999999999999992e-291 < z < 5.4999999999999999e-55

   1. Initial program 88.2%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. div-sub 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in a around inf 43.8%

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

      1. associate-/l* 53.0%

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

   10. Simplified 53.0%

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

Alternative 12: 90.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-232} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-232) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-232) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-232)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-232) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-232) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-232) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-232) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-232], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000002e-232 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.5%

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

      1. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 71.5%

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

      3. associate-*r/ 89.3%

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

      4. clear-num 89.2%

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

      5. un-div-inv 89.3%

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

   6. Applied egg-rr 89.3%

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

   if -1.00000000000000002e-232 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 15.1%

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

      1. associate-/l* 14.8%

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

   3. Simplified 14.8%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. associate--l+ 89.7%

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

      2. associate-*r/ 89.7%

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

      3. associate-*r/ 89.7%

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

      4. mul-1-neg 89.7%

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

      5. div-sub 89.6%

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

      6. mul-1-neg 89.6%

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

      7. distribute-lft-out-- 89.6%

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

      8. associate-*r/ 89.6%

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

      9. mul-1-neg 89.6%

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

      10. unsub-neg 89.6%

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

      11. distribute-rgt-out-- 89.6%

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

   7. Simplified 89.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-232} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -50000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+159}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -50000.0)
     x
     (if (<= a -9e-272)
       t_1
       (if (<= a -1.38e-291)
         (/ (* x y) z)
         (if (<= a 2.35e-118)
           t_1
           (if (<= a 3.4e-56)
             (/ x (/ z y))
             (if (<= a 1.48e+57)
               t_1
               (if (<= a 7.6e+154)
                 x
                 (if (<= a 1.5e+159) (* z (/ t (- a))) (/ t (/ a y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -50000.0) {
		tmp = x;
	} else if (a <= -9e-272) {
		tmp = t_1;
	} else if (a <= -1.38e-291) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 1.48e+57) {
		tmp = t_1;
	} else if (a <= 7.6e+154) {
		tmp = x;
	} else if (a <= 1.5e+159) {
		tmp = z * (t / -a);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-50000.0d0)) then
        tmp = x
    else if (a <= (-9d-272)) then
        tmp = t_1
    else if (a <= (-1.38d-291)) then
        tmp = (x * y) / z
    else if (a <= 2.35d-118) then
        tmp = t_1
    else if (a <= 3.4d-56) then
        tmp = x / (z / y)
    else if (a <= 1.48d+57) then
        tmp = t_1
    else if (a <= 7.6d+154) then
        tmp = x
    else if (a <= 1.5d+159) then
        tmp = z * (t / -a)
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -50000.0) {
		tmp = x;
	} else if (a <= -9e-272) {
		tmp = t_1;
	} else if (a <= -1.38e-291) {
		tmp = (x * y) / z;
	} else if (a <= 2.35e-118) {
		tmp = t_1;
	} else if (a <= 3.4e-56) {
		tmp = x / (z / y);
	} else if (a <= 1.48e+57) {
		tmp = t_1;
	} else if (a <= 7.6e+154) {
		tmp = x;
	} else if (a <= 1.5e+159) {
		tmp = z * (t / -a);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -50000.0:
		tmp = x
	elif a <= -9e-272:
		tmp = t_1
	elif a <= -1.38e-291:
		tmp = (x * y) / z
	elif a <= 2.35e-118:
		tmp = t_1
	elif a <= 3.4e-56:
		tmp = x / (z / y)
	elif a <= 1.48e+57:
		tmp = t_1
	elif a <= 7.6e+154:
		tmp = x
	elif a <= 1.5e+159:
		tmp = z * (t / -a)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -50000.0)
		tmp = x;
	elseif (a <= -9e-272)
		tmp = t_1;
	elseif (a <= -1.38e-291)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 1.48e+57)
		tmp = t_1;
	elseif (a <= 7.6e+154)
		tmp = x;
	elseif (a <= 1.5e+159)
		tmp = Float64(z * Float64(t / Float64(-a)));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -50000.0)
		tmp = x;
	elseif (a <= -9e-272)
		tmp = t_1;
	elseif (a <= -1.38e-291)
		tmp = (x * y) / z;
	elseif (a <= 2.35e-118)
		tmp = t_1;
	elseif (a <= 3.4e-56)
		tmp = x / (z / y);
	elseif (a <= 1.48e+57)
		tmp = t_1;
	elseif (a <= 7.6e+154)
		tmp = x;
	elseif (a <= 1.5e+159)
		tmp = z * (t / -a);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -50000.0], x, If[LessEqual[a, -9e-272], t$95$1, If[LessEqual[a, -1.38e-291], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.35e-118], t$95$1, If[LessEqual[a, 3.4e-56], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.48e+57], t$95$1, If[LessEqual[a, 7.6e+154], x, If[LessEqual[a, 1.5e+159], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -5e4 or 1.47999999999999999e57 < a < 7.5999999999999996e154

   1. Initial program 69.7%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in a around inf 46.2%

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

   if -5e4 < a < -8.9999999999999995e-272 or -1.37999999999999994e-291 < a < 2.34999999999999995e-118 or 3.39999999999999982e-56 < a < 1.47999999999999999e57

   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* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in a around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. unsub-neg 43.0%

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

      3. associate-/l* 52.2%

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

      4. div-sub 52.2%

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

      5. sub-neg 52.2%

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

      6. *-inverses 52.2%

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

      7. metadata-eval 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in t around inf 52.8%

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

   if -8.9999999999999995e-272 < a < -1.37999999999999994e-291

   1. Initial program 75.5%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 76.4%

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

      4. div-sub 76.4%

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

      5. sub-neg 76.4%

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

      6. *-inverses 76.4%

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

      7. metadata-eval 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in x around -inf 63.6%

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

      1. *-commutative 63.6%

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

   10. Simplified 63.6%

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

   if 2.34999999999999995e-118 < a < 3.39999999999999982e-56

   1. Initial program 63.4%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in z around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. associate-*r* 73.8%

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

      3. mul-1-neg 73.8%

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

      4. mul-1-neg 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in z around 0 65.4%

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

      1. cancel-sign-sub 65.4%

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

      2. neg-mul-1 65.4%

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

      3. associate-*r* 65.4%

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

      4. distribute-lft-out-- 65.4%

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

      5. associate-*r/ 65.4%

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

      6. mul-1-neg 65.4%

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

      7. distribute-frac-neg2 65.4%

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

      8. distribute-rgt-out-- 65.4%

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

      9. neg-mul-1 65.4%

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

      10. times-frac 65.0%

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

      11. metadata-eval 65.0%

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

      12. distribute-neg-frac2 65.0%

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

      13. /-rgt-identity 65.0%

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

   10. Simplified 65.0%

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

   11. Taylor expanded in y around inf 56.6%

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

   12. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 56.8%

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

   14. Simplified 56.8%

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

       1. clear-num 56.6%

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

       2. un-div-inv 56.9%

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

   16. Applied egg-rr 56.9%

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

   if 7.5999999999999996e154 < a < 1.5000000000000001e159

   1. Initial program 67.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 66.0%

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

      1. associate-/l* 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in a around inf 65.2%

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

   9. Taylor expanded in y around 0 65.1%

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

       1. mul-1-neg 65.1%

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

       2. *-commutative 65.1%

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

       3. associate-*r/ 65.3%

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

       4. distribute-rgt-neg-in 65.3%

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

       5. distribute-neg-frac2 65.3%

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

   11. Simplified 65.3%

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

   if 1.5000000000000001e159 < a

   1. Initial program 59.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 35.6%

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

      1. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in z around 0 27.8%

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

      1. associate-/l* 43.6%

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

   10. Simplified 43.6%

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

       1. clear-num 43.6%

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

       2. un-div-inv 43.6%

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

   12. Applied egg-rr 43.6%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -50000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+159}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+105} \lor \neg \left(x \leq 9.5 \cdot 10^{+181}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (+ x (* y (/ t a)))))
   (if (<= x -4.7e+117)
     t_1
     (if (<= x -2.8e+73)
       (+ t (* y (/ x z)))
       (if (<= x -4.8e+25)
         (/ (* x y) (- z a))
         (if (<= x -1.76e-40)
           t_2
           (if (<= x 1.8e+61)
             (* t (/ (- y z) (- a z)))
             (if (or (<= x 3.9e+105) (not (<= x 9.5e+181))) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (x <= -4.7e+117) {
		tmp = t_1;
	} else if (x <= -2.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -4.8e+25) {
		tmp = (x * y) / (z - a);
	} else if (x <= -1.76e-40) {
		tmp = t_2;
	} else if (x <= 1.8e+61) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 3.9e+105) || !(x <= 9.5e+181)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = x + (y * (t / a))
    if (x <= (-4.7d+117)) then
        tmp = t_1
    else if (x <= (-2.8d+73)) then
        tmp = t + (y * (x / z))
    else if (x <= (-4.8d+25)) then
        tmp = (x * y) / (z - a)
    else if (x <= (-1.76d-40)) then
        tmp = t_2
    else if (x <= 1.8d+61) then
        tmp = t * ((y - z) / (a - z))
    else if ((x <= 3.9d+105) .or. (.not. (x <= 9.5d+181))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (x <= -4.7e+117) {
		tmp = t_1;
	} else if (x <= -2.8e+73) {
		tmp = t + (y * (x / z));
	} else if (x <= -4.8e+25) {
		tmp = (x * y) / (z - a);
	} else if (x <= -1.76e-40) {
		tmp = t_2;
	} else if (x <= 1.8e+61) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 3.9e+105) || !(x <= 9.5e+181)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = x + (y * (t / a))
	tmp = 0
	if x <= -4.7e+117:
		tmp = t_1
	elif x <= -2.8e+73:
		tmp = t + (y * (x / z))
	elif x <= -4.8e+25:
		tmp = (x * y) / (z - a)
	elif x <= -1.76e-40:
		tmp = t_2
	elif x <= 1.8e+61:
		tmp = t * ((y - z) / (a - z))
	elif (x <= 3.9e+105) or not (x <= 9.5e+181):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (x <= -4.7e+117)
		tmp = t_1;
	elseif (x <= -2.8e+73)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (x <= -4.8e+25)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (x <= -1.76e-40)
		tmp = t_2;
	elseif (x <= 1.8e+61)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((x <= 3.9e+105) || !(x <= 9.5e+181))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (x <= -4.7e+117)
		tmp = t_1;
	elseif (x <= -2.8e+73)
		tmp = t + (y * (x / z));
	elseif (x <= -4.8e+25)
		tmp = (x * y) / (z - a);
	elseif (x <= -1.76e-40)
		tmp = t_2;
	elseif (x <= 1.8e+61)
		tmp = t * ((y - z) / (a - z));
	elseif ((x <= 3.9e+105) || ~((x <= 9.5e+181)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.7e+117], t$95$1, If[LessEqual[x, -2.8e+73], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e+25], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.76e-40], t$95$2, If[LessEqual[x, 1.8e+61], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.9e+105], N[Not[LessEqual[x, 9.5e+181]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.70000000000000006e117 or 1.80000000000000005e61 < x < 3.89999999999999978e105 or 9.50000000000000032e181 < x

   1. Initial program 54.4%

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

      1. associate-/l* 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in z around 0 47.5%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in t around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 57.6%

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

      3. distribute-rgt-neg-in 57.6%

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

      4. distribute-frac-neg2 57.6%

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

   10. Simplified 57.6%

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

   if -4.70000000000000006e117 < x < -2.80000000000000008e73

   1. Initial program 36.1%

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

      1. associate-/l* 36.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.1%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 84.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 84.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 84.1%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 68.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.9%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 53.9%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around 0 84.6%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 84.6%

          \[\leadsto t - \color{blue}{\left(-\frac{x \cdot y}{z}\right)} \]

       2. *-commutative 84.6%

          \[\leadsto t - \left(-\frac{\color{blue}{y \cdot x}}{z}\right) \]

       3. associate-/l* 68.8%

          \[\leadsto t - \left(-\color{blue}{y \cdot \frac{x}{z}}\right) \]

       4. distribute-rgt-neg-in 68.8%

          \[\leadsto t - \color{blue}{y \cdot \left(-\frac{x}{z}\right)} \]

       5. distribute-neg-frac2 68.8%

          \[\leadsto t - y \cdot \color{blue}{\frac{x}{-z}} \]

   13. Simplified 68.8%

       \[\leadsto t - \color{blue}{y \cdot \frac{x}{-z}} \]

   if -2.80000000000000008e73 < x < -4.79999999999999992e25

   1. Initial program 83.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 72.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

   6. Taylor expanded in t around 0 58.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{a - z} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.6%

         \[\leadsto \frac{\color{blue}{-x \cdot y}}{a - z} \]

      2. distribute-rgt-neg-in 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{a - z} \]

   8. Simplified 58.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{a - z} \]

   if -4.79999999999999992e25 < x < -1.76e-40 or 3.89999999999999978e105 < x < 9.50000000000000032e181

   1. Initial program 59.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 48.8%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in t around inf 50.9%

      \[\leadsto x + y \cdot \color{blue}{\frac{t}{a}} \]

   if -1.76e-40 < x < 1.80000000000000005e61

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 82.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 57.2%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.6%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 71.6%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+117}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+105} \lor \neg \left(x \leq 9.5 \cdot 10^{+181}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+153}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-129}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -9e+270)
     t_1
     (if (<= t -5.2e+153)
       t
       (if (<= t -3.2e+120)
         x
         (if (<= t -5.2e-129)
           t
           (if (<= t -1.32e-253)
             x
             (if (<= t -5.2e-294)
               (* x (/ y z))
               (if (<= t 6.6e-16) x t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -9e+270) {
		tmp = t_1;
	} else if (t <= -5.2e+153) {
		tmp = t;
	} else if (t <= -3.2e+120) {
		tmp = x;
	} else if (t <= -5.2e-129) {
		tmp = t;
	} else if (t <= -1.32e-253) {
		tmp = x;
	} else if (t <= -5.2e-294) {
		tmp = x * (y / z);
	} else if (t <= 6.6e-16) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-9d+270)) then
        tmp = t_1
    else if (t <= (-5.2d+153)) then
        tmp = t
    else if (t <= (-3.2d+120)) then
        tmp = x
    else if (t <= (-5.2d-129)) then
        tmp = t
    else if (t <= (-1.32d-253)) then
        tmp = x
    else if (t <= (-5.2d-294)) then
        tmp = x * (y / z)
    else if (t <= 6.6d-16) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -9e+270) {
		tmp = t_1;
	} else if (t <= -5.2e+153) {
		tmp = t;
	} else if (t <= -3.2e+120) {
		tmp = x;
	} else if (t <= -5.2e-129) {
		tmp = t;
	} else if (t <= -1.32e-253) {
		tmp = x;
	} else if (t <= -5.2e-294) {
		tmp = x * (y / z);
	} else if (t <= 6.6e-16) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -9e+270:
		tmp = t_1
	elif t <= -5.2e+153:
		tmp = t
	elif t <= -3.2e+120:
		tmp = x
	elif t <= -5.2e-129:
		tmp = t
	elif t <= -1.32e-253:
		tmp = x
	elif t <= -5.2e-294:
		tmp = x * (y / z)
	elif t <= 6.6e-16:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -9e+270)
		tmp = t_1;
	elseif (t <= -5.2e+153)
		tmp = t;
	elseif (t <= -3.2e+120)
		tmp = x;
	elseif (t <= -5.2e-129)
		tmp = t;
	elseif (t <= -1.32e-253)
		tmp = x;
	elseif (t <= -5.2e-294)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 6.6e-16)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -9e+270)
		tmp = t_1;
	elseif (t <= -5.2e+153)
		tmp = t;
	elseif (t <= -3.2e+120)
		tmp = x;
	elseif (t <= -5.2e-129)
		tmp = t;
	elseif (t <= -1.32e-253)
		tmp = x;
	elseif (t <= -5.2e-294)
		tmp = x * (y / z);
	elseif (t <= 6.6e-16)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+270], t$95$1, If[LessEqual[t, -5.2e+153], t, If[LessEqual[t, -3.2e+120], x, If[LessEqual[t, -5.2e-129], t, If[LessEqual[t, -1.32e-253], x, If[LessEqual[t, -5.2e-294], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-16], x, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.0000000000000009e270 or 6.59999999999999976e-16 < t

   1. Initial program 70.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 81.9%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 81.9%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   8. Taylor expanded in z around 0 37.7%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 49.3%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   10. Simplified 49.3%

       \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if -9.0000000000000009e270 < t < -5.1999999999999998e153 or -3.19999999999999982e120 < t < -5.2000000000000001e-129

   1. Initial program 64.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 73.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 31.4%

      \[\leadsto \color{blue}{t} \]

   if -5.1999999999999998e153 < t < -3.19999999999999982e120 or -5.2000000000000001e-129 < t < -1.32000000000000007e-253 or -5.1999999999999999e-294 < t < 6.59999999999999976e-16

   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* 73.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 41.6%

      \[\leadsto \color{blue}{x} \]

   if -1.32000000000000007e-253 < t < -5.1999999999999999e-294

   1. Initial program 59.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 62.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 51.3%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 51.3%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 51.3%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 51.3%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 51.3%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in z around 0 51.3%

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) + a \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. cancel-sign-sub 51.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a\right) \cdot \left(t - x\right)}}{z} \]

      2. neg-mul-1 51.3%

         \[\leadsto \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(t - x\right)}{z} \]

      3. associate-*r* 51.3%

         \[\leadsto \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      4. distribute-lft-out-- 51.3%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      5. associate-*r/ 51.3%

         \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      6. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. distribute-frac-neg2 51.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{-z}} \]

      8. distribute-rgt-out-- 51.3%

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{-z} \]

      9. neg-mul-1 51.3%

         \[\leadsto \frac{\left(t - x\right) \cdot \left(y - a\right)}{\color{blue}{-1 \cdot z}} \]

      10. times-frac 70.2%

          \[\leadsto \color{blue}{\frac{t - x}{-1} \cdot \frac{y - a}{z}} \]

      11. metadata-eval 70.2%

          \[\leadsto \frac{t - x}{\color{blue}{-1}} \cdot \frac{y - a}{z} \]

      12. distribute-neg-frac2 70.2%

          \[\leadsto \color{blue}{\left(-\frac{t - x}{1}\right)} \cdot \frac{y - a}{z} \]

      13. /-rgt-identity 70.2%

          \[\leadsto \left(-\color{blue}{\left(t - x\right)}\right) \cdot \frac{y - a}{z} \]

   10. Simplified 70.2%

       \[\leadsto \color{blue}{\left(-\left(t - x\right)\right) \cdot \frac{y - a}{z}} \]

   11. Taylor expanded in y around inf 52.6%

       \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z}} \]

   12. Taylor expanded in x around inf 52.6%

       \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   13. Step-by-step derivation

       1. associate-/l* 60.9%

          \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   14. Simplified 60.9%

       \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x - y \cdot \frac{x - t}{a}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))) (t_2 (- x (* y (/ (- x t) a)))))
   (if (<= z -2e+120)
     t_1
     (if (<= z -3.6e-7)
       (* t (/ (- y z) (- a z)))
       (if (<= z -2.1e-50)
         t_2
         (if (<= z -2.05e-50) t (if (<= z 1.7e-50) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (z <= -2e+120) {
		tmp = t_1;
	} else if (z <= -3.6e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2.1e-50) {
		tmp = t_2;
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= 1.7e-50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    t_2 = x - (y * ((x - t) / a))
    if (z <= (-2d+120)) then
        tmp = t_1
    else if (z <= (-3.6d-7)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-2.1d-50)) then
        tmp = t_2
    else if (z <= (-2.05d-50)) then
        tmp = t
    else if (z <= 1.7d-50) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x - (y * ((x - t) / a));
	double tmp;
	if (z <= -2e+120) {
		tmp = t_1;
	} else if (z <= -3.6e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -2.1e-50) {
		tmp = t_2;
	} else if (z <= -2.05e-50) {
		tmp = t;
	} else if (z <= 1.7e-50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	t_2 = x - (y * ((x - t) / a))
	tmp = 0
	if z <= -2e+120:
		tmp = t_1
	elif z <= -3.6e-7:
		tmp = t * ((y - z) / (a - z))
	elif z <= -2.1e-50:
		tmp = t_2
	elif z <= -2.05e-50:
		tmp = t
	elif z <= 1.7e-50:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	t_2 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	tmp = 0.0
	if (z <= -2e+120)
		tmp = t_1;
	elseif (z <= -3.6e-7)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -2.1e-50)
		tmp = t_2;
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= 1.7e-50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	t_2 = x - (y * ((x - t) / a));
	tmp = 0.0;
	if (z <= -2e+120)
		tmp = t_1;
	elseif (z <= -3.6e-7)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -2.1e-50)
		tmp = t_2;
	elseif (z <= -2.05e-50)
		tmp = t;
	elseif (z <= 1.7e-50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+120], t$95$1, If[LessEqual[z, -3.6e-7], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-50], t$95$2, If[LessEqual[z, -2.05e-50], t, If[LessEqual[z, 1.7e-50], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e120 or 1.70000000000000007e-50 < z

   1. Initial program 42.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 63.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 59.1%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 59.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 59.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 59.1%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 56.5%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 67.7%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 67.7%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 67.7%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   if -2e120 < z < -3.59999999999999994e-7

   1. Initial program 75.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 78.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 51.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 56.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 56.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.59999999999999994e-7 < z < -2.1000000000000001e-50 or -2.04999999999999993e-50 < z < 1.70000000000000007e-50

   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* 91.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 68.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 77.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 77.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if -2.1000000000000001e-50 < z < -2.04999999999999993e-50

   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* 7.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 7.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+74}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= x -1.85e+117)
     t_1
     (if (<= x -2.2e+74)
       (+ t (* y (/ x z)))
       (if (<= x -2.1e-72)
         t_2
         (if (<= x 9e+53)
           (* t (/ (- y z) (- a z)))
           (if (<= x 4.3e+152) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -1.85e+117) {
		tmp = t_1;
	} else if (x <= -2.2e+74) {
		tmp = t + (y * (x / z));
	} else if (x <= -2.1e-72) {
		tmp = t_2;
	} else if (x <= 9e+53) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 4.3e+152) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = y * ((t - x) / (a - z))
    if (x <= (-1.85d+117)) then
        tmp = t_1
    else if (x <= (-2.2d+74)) then
        tmp = t + (y * (x / z))
    else if (x <= (-2.1d-72)) then
        tmp = t_2
    else if (x <= 9d+53) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 4.3d+152) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -1.85e+117) {
		tmp = t_1;
	} else if (x <= -2.2e+74) {
		tmp = t + (y * (x / z));
	} else if (x <= -2.1e-72) {
		tmp = t_2;
	} else if (x <= 9e+53) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 4.3e+152) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = y * ((t - x) / (a - z))
	tmp = 0
	if x <= -1.85e+117:
		tmp = t_1
	elif x <= -2.2e+74:
		tmp = t + (y * (x / z))
	elif x <= -2.1e-72:
		tmp = t_2
	elif x <= 9e+53:
		tmp = t * ((y - z) / (a - z))
	elif x <= 4.3e+152:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (x <= -1.85e+117)
		tmp = t_1;
	elseif (x <= -2.2e+74)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (x <= -2.1e-72)
		tmp = t_2;
	elseif (x <= 9e+53)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 4.3e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (x <= -1.85e+117)
		tmp = t_1;
	elseif (x <= -2.2e+74)
		tmp = t + (y * (x / z));
	elseif (x <= -2.1e-72)
		tmp = t_2;
	elseif (x <= 9e+53)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 4.3e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e+117], t$95$1, If[LessEqual[x, -2.2e+74], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-72], t$95$2, If[LessEqual[x, 9e+53], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+152], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8499999999999999e117 or 4.29999999999999994e152 < x

   1. Initial program 52.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 70.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 50.2%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 60.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in t around 0 44.2%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 44.2%

         \[\leadsto x + \color{blue}{\left(-\frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 55.9%

         \[\leadsto x + \left(-\color{blue}{x \cdot \frac{y}{a}}\right) \]

      3. distribute-rgt-neg-in 55.9%

         \[\leadsto x + \color{blue}{x \cdot \left(-\frac{y}{a}\right)} \]

      4. distribute-frac-neg2 55.9%

         \[\leadsto x + x \cdot \color{blue}{\frac{y}{-a}} \]

   10. Simplified 55.9%

       \[\leadsto x + \color{blue}{x \cdot \frac{y}{-a}} \]

   if -1.8499999999999999e117 < x < -2.2000000000000001e74

   1. Initial program 36.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 36.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.1%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 84.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 84.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 84.1%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 68.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 53.9%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 53.9%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 53.9%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around 0 84.6%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 84.6%

          \[\leadsto t - \color{blue}{\left(-\frac{x \cdot y}{z}\right)} \]

       2. *-commutative 84.6%

          \[\leadsto t - \left(-\frac{\color{blue}{y \cdot x}}{z}\right) \]

       3. associate-/l* 68.8%

          \[\leadsto t - \left(-\color{blue}{y \cdot \frac{x}{z}}\right) \]

       4. distribute-rgt-neg-in 68.8%

          \[\leadsto t - \color{blue}{y \cdot \left(-\frac{x}{z}\right)} \]

       5. distribute-neg-frac2 68.8%

          \[\leadsto t - y \cdot \color{blue}{\frac{x}{-z}} \]

   13. Simplified 68.8%

       \[\leadsto t - \color{blue}{y \cdot \frac{x}{-z}} \]

   if -2.2000000000000001e74 < x < -2.1e-72 or 9.0000000000000004e53 < x < 4.29999999999999994e152

   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* 83.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 60.4%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -2.1e-72 < x < 9.0000000000000004e53

   1. Initial program 75.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 81.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 60.0%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 75.4%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 75.4%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+117}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+74}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -1.9e+153)
     t_1
     (if (<= z 6.6e+94)
       (+ x (* t (/ y a)))
       (if (<= z 3.05e+140)
         t_1
         (if (<= z 4.2e+187)
           (* t (- 1.0 (/ y z)))
           (if (<= z 2.25e+253) t_1 (/ t (/ z (- z y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.9e+153) {
		tmp = t_1;
	} else if (z <= 6.6e+94) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.05e+140) {
		tmp = t_1;
	} else if (z <= 4.2e+187) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2.25e+253) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-1.9d+153)) then
        tmp = t_1
    else if (z <= 6.6d+94) then
        tmp = x + (t * (y / a))
    else if (z <= 3.05d+140) then
        tmp = t_1
    else if (z <= 4.2d+187) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 2.25d+253) then
        tmp = t_1
    else
        tmp = t / (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.9e+153) {
		tmp = t_1;
	} else if (z <= 6.6e+94) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.05e+140) {
		tmp = t_1;
	} else if (z <= 4.2e+187) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2.25e+253) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -1.9e+153:
		tmp = t_1
	elif z <= 6.6e+94:
		tmp = x + (t * (y / a))
	elif z <= 3.05e+140:
		tmp = t_1
	elif z <= 4.2e+187:
		tmp = t * (1.0 - (y / z))
	elif z <= 2.25e+253:
		tmp = t_1
	else:
		tmp = t / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.9e+153)
		tmp = t_1;
	elseif (z <= 6.6e+94)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.05e+140)
		tmp = t_1;
	elseif (z <= 4.2e+187)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 2.25e+253)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -1.9e+153)
		tmp = t_1;
	elseif (z <= 6.6e+94)
		tmp = x + (t * (y / a));
	elseif (z <= 3.05e+140)
		tmp = t_1;
	elseif (z <= 4.2e+187)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 2.25e+253)
		tmp = t_1;
	else
		tmp = t / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+153], t$95$1, If[LessEqual[z, 6.6e+94], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+140], t$95$1, If[LessEqual[z, 4.2e+187], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+253], t$95$1, N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.89999999999999983e153 or 6.6e94 < z < 3.0499999999999998e140 or 4.2e187 < z < 2.24999999999999986e253

   1. Initial program 30.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 58.3%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 58.3%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 59.1%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 59.1%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 59.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 59.1%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 59.1%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 56.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 56.7%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 74.3%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 74.3%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 74.3%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around 0 57.1%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 57.1%

          \[\leadsto t - \color{blue}{\left(-\frac{x \cdot y}{z}\right)} \]

       2. *-commutative 57.1%

          \[\leadsto t - \left(-\frac{\color{blue}{y \cdot x}}{z}\right) \]

       3. associate-/l* 66.3%

          \[\leadsto t - \left(-\color{blue}{y \cdot \frac{x}{z}}\right) \]

       4. distribute-rgt-neg-in 66.3%

          \[\leadsto t - \color{blue}{y \cdot \left(-\frac{x}{z}\right)} \]

       5. distribute-neg-frac2 66.3%

          \[\leadsto t - y \cdot \color{blue}{\frac{x}{-z}} \]

   13. Simplified 66.3%

       \[\leadsto t - \color{blue}{y \cdot \frac{x}{-z}} \]

   if -1.89999999999999983e153 < z < 6.6e94

   1. Initial program 82.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around 0 58.6%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 66.9%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in t around inf 52.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   10. Simplified 57.8%

       \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   if 3.0499999999999998e140 < z < 4.2e187

   1. Initial program 64.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 76.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 51.4%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)} \]

      2. unsub-neg 51.4%

         \[\leadsto \color{blue}{x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* 63.3%

         \[\leadsto x - \color{blue}{\left(t - x\right) \cdot \frac{y - z}{z}} \]

      4. div-sub 63.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg 63.3%

         \[\leadsto x - \left(t - x\right) \cdot \color{blue}{\left(\frac{y}{z} + \left(-\frac{z}{z}\right)\right)} \]

      6. *-inverses 63.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 63.3%

         \[\leadsto x - \left(t - x\right) \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{x - \left(t - x\right) \cdot \left(\frac{y}{z} + -1\right)} \]

   8. Taylor expanded in t around inf 63.3%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]

   if 2.24999999999999986e253 < z

   1. Initial program 14.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 24.7%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 24.7%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 24.7%

         \[\leadsto x + \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} \]

      2. associate-*l/ 14.5%

         \[\leadsto x + \color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}} \]

      3. associate-*r/ 35.9%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}} \]

      4. clear-num 35.9%

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \]

      5. un-div-inv 36.1%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]

   6. Applied egg-rr 36.1%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a - z}{y - z}}} \]
   7. Step-by-step derivation

      1. div-sub 36.1%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   8. Applied egg-rr 36.1%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   9. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y - z} - \frac{z}{y - z}}} \]

   10. Taylor expanded in a around 0 89.3%

       \[\leadsto \frac{t}{\color{blue}{-1 \cdot \frac{z}{y - z}}} \]
   11. Step-by-step derivation

       1. mul-1-neg 89.3%

          \[\leadsto \frac{t}{\color{blue}{-\frac{z}{y - z}}} \]

       2. distribute-frac-neg2 89.3%

          \[\leadsto \frac{t}{\color{blue}{\frac{z}{-\left(y - z\right)}}} \]

   12. Simplified 89.3%

       \[\leadsto \frac{t}{\color{blue}{\frac{z}{-\left(y - z\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+140}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+253}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+153}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-128}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -6.1e+268)
     t_1
     (if (<= t -4.2e+153)
       t
       (if (<= t -2.2e+120)
         x
         (if (<= t -1.75e-128) t (if (<= t 2.4e-44) x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -6.1e+268) {
		tmp = t_1;
	} else if (t <= -4.2e+153) {
		tmp = t;
	} else if (t <= -2.2e+120) {
		tmp = x;
	} else if (t <= -1.75e-128) {
		tmp = t;
	} else if (t <= 2.4e-44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-6.1d+268)) then
        tmp = t_1
    else if (t <= (-4.2d+153)) then
        tmp = t
    else if (t <= (-2.2d+120)) then
        tmp = x
    else if (t <= (-1.75d-128)) then
        tmp = t
    else if (t <= 2.4d-44) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -6.1e+268) {
		tmp = t_1;
	} else if (t <= -4.2e+153) {
		tmp = t;
	} else if (t <= -2.2e+120) {
		tmp = x;
	} else if (t <= -1.75e-128) {
		tmp = t;
	} else if (t <= 2.4e-44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -6.1e+268:
		tmp = t_1
	elif t <= -4.2e+153:
		tmp = t
	elif t <= -2.2e+120:
		tmp = x
	elif t <= -1.75e-128:
		tmp = t
	elif t <= 2.4e-44:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -6.1e+268)
		tmp = t_1;
	elseif (t <= -4.2e+153)
		tmp = t;
	elseif (t <= -2.2e+120)
		tmp = x;
	elseif (t <= -1.75e-128)
		tmp = t;
	elseif (t <= 2.4e-44)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -6.1e+268)
		tmp = t_1;
	elseif (t <= -4.2e+153)
		tmp = t;
	elseif (t <= -2.2e+120)
		tmp = x;
	elseif (t <= -1.75e-128)
		tmp = t;
	elseif (t <= 2.4e-44)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e+268], t$95$1, If[LessEqual[t, -4.2e+153], t, If[LessEqual[t, -2.2e+120], x, If[LessEqual[t, -1.75e-128], t, If[LessEqual[t, 2.4e-44], x, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.10000000000000002e268 or 2.40000000000000009e-44 < t

   1. Initial program 69.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 x around 0 54.1%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 78.1%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   8. Taylor expanded in z around 0 35.5%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 46.4%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   10. Simplified 46.4%

       \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if -6.10000000000000002e268 < t < -4.20000000000000033e153 or -2.2000000000000001e120 < t < -1.75e-128

   1. Initial program 64.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 73.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 31.4%

      \[\leadsto \color{blue}{t} \]

   if -4.20000000000000033e153 < t < -2.2000000000000001e120 or -1.75e-128 < t < 2.40000000000000009e-44

   1. Initial program 67.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+123} \lor \neg \left(z \leq 4.7 \cdot 10^{+168}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+123) (not (<= z 4.7e+168)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* (- y z) (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+123) || !(z <= 4.7e+168)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((y - z) * ((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 <= (-1.6d+123)) .or. (.not. (z <= 4.7d+168))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((y - z) * ((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 <= -1.6e+123) || !(z <= 4.7e+168)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+123) or not (z <= 4.7e+168):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+123) || !(z <= 4.7e+168))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+123) || ~((z <= 4.7e+168)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+123], N[Not[LessEqual[z, 4.7e+168]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000002e123 or 4.69999999999999961e168 < z

   1. Initial program 28.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 51.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 51.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 63.0%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 63.0%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 63.0%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 63.0%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 63.0%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 61.6%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 61.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 77.0%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 77.0%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 77.0%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   if -1.60000000000000002e123 < z < 4.69999999999999961e168

   1. Initial program 82.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.9%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+123} \lor \neg \left(z \leq 4.7 \cdot 10^{+168}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+123} \lor \neg \left(z \leq 2400\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+123) (not (<= z 2400.0)))
   (+ t (* y (/ (- x t) z)))
   (- x (* (- t x) (/ (- z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+123) || !(z <= 2400.0)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - ((t - x) * ((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 <= (-1.65d+123)) .or. (.not. (z <= 2400.0d0))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x - ((t - x) * ((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 <= -1.65e+123) || !(z <= 2400.0)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x - ((t - x) * ((z - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+123) or not (z <= 2400.0):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x - ((t - x) * ((z - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+123) || !(z <= 2400.0))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+123) || ~((z <= 2400.0)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x - ((t - x) * ((z - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+123], N[Not[LessEqual[z, 2400.0]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000001e123 or 2400 < z

   1. Initial program 38.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 62.2%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 62.2%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 62.2%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 62.2%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 62.2%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 62.2%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 59.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 70.7%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 70.7%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 70.7%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   if -1.65000000000000001e123 < z < 2400

   1. Initial program 85.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Taylor expanded in a around inf 67.1%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 77.8%

         \[\leadsto x + \color{blue}{\left(t - x\right) \cdot \frac{y - z}{a}} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{x + \left(t - x\right) \cdot \frac{y - z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+123} \lor \neg \left(z \leq 2400\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+39} \lor \neg \left(z \leq 2.05 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+39) (not (<= z 2.05e+71)))
   (* t (/ (- y z) (- a z)))
   (- x (* y (/ (- x t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+39) || !(z <= 2.05e+71)) {
		tmp = t * ((y - z) / (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 <= (-3.2d+39)) .or. (.not. (z <= 2.05d+71))) then
        tmp = t * ((y - z) / (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 <= -3.2e+39) || !(z <= 2.05e+71)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+39) or not (z <= 2.05e+71):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - (y * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+39) || !(z <= 2.05e+71))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(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 <= -3.2e+39) || ~((z <= 2.05e+71)))
		tmp = t * ((y - z) / (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, -3.2e+39], N[Not[LessEqual[z, 2.05e+71]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - 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 < -3.19999999999999993e39 or 2.0500000000000001e71 < z

   1. Initial program 40.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 61.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 61.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 41.3%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 62.3%

         \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   7. Simplified 62.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if -3.19999999999999993e39 < z < 2.0500000000000001e71

   1. Initial program 85.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+39} \lor \neg \left(z \leq 2.05 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 9.2 \cdot 10^{+17}\right):\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+153) (not (<= z 9.2e+17)))
   (+ t (* y (/ x z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 9.2e+17)) {
		tmp = t + (y * (x / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.9d+153)) .or. (.not. (z <= 9.2d+17))) then
        tmp = t + (y * (x / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 9.2e+17)) {
		tmp = t + (y * (x / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+153) or not (z <= 9.2e+17):
		tmp = t + (y * (x / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+153) || !(z <= 9.2e+17))
		tmp = Float64(t + Float64(y * Float64(x / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+153) || ~((z <= 9.2e+17)))
		tmp = t + (y * (x / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+153], N[Not[LessEqual[z, 9.2e+17]], $MachinePrecision]], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999983e153 or 9.2e17 < z

   1. Initial program 38.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 60.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 60.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 61.9%

         \[\leadsto \left(t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      2. associate-*r* 61.9%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-1 \cdot y\right) \cdot \left(t - x\right)}}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      3. mul-1-neg 61.9%

         \[\leadsto \left(t + \frac{\color{blue}{\left(-y\right)} \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]

      4. mul-1-neg 61.9%

         \[\leadsto \left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{\left(t + \frac{\left(-y\right) \cdot \left(t - x\right)}{z}\right) - \left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]

   8. Taylor expanded in a around 0 59.1%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 59.1%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 72.3%

         \[\leadsto t + \left(-\color{blue}{y \cdot \frac{t - x}{z}}\right) \]

      3. sub-neg 72.3%

         \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   10. Simplified 72.3%

       \[\leadsto \color{blue}{t - y \cdot \frac{t - x}{z}} \]

   11. Taylor expanded in t around 0 56.7%

       \[\leadsto t - \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 56.7%

          \[\leadsto t - \color{blue}{\left(-\frac{x \cdot y}{z}\right)} \]

       2. *-commutative 56.7%

          \[\leadsto t - \left(-\frac{\color{blue}{y \cdot x}}{z}\right) \]

       3. associate-/l* 63.0%

          \[\leadsto t - \left(-\color{blue}{y \cdot \frac{x}{z}}\right) \]

       4. distribute-rgt-neg-in 63.0%

          \[\leadsto t - \color{blue}{y \cdot \left(-\frac{x}{z}\right)} \]

       5. distribute-neg-frac2 63.0%

          \[\leadsto t - y \cdot \color{blue}{\frac{x}{-z}} \]

   13. Simplified 63.0%

       \[\leadsto t - \color{blue}{y \cdot \frac{x}{-z}} \]

   if -1.89999999999999983e153 < z < 9.2e17

   1. Initial program 82.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 59.1%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 67.4%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   8. Taylor expanded in t around inf 52.6%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 58.3%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   10. Simplified 58.3%

       \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 9.2 \cdot 10^{+17}\right):\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+137) t (if (<= z 7.8e+61) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+137) {
		tmp = t;
	} else if (z <= 7.8e+61) {
		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 <= (-2.6d+137)) then
        tmp = t
    else if (z <= 7.8d+61) 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 <= -2.6e+137) {
		tmp = t;
	} else if (z <= 7.8e+61) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+137:
		tmp = t
	elif z <= 7.8e+61:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+137)
		tmp = t;
	elseif (z <= 7.8e+61)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+137)
		tmp = t;
	elseif (z <= 7.8e+61)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+137], t, If[LessEqual[z, 7.8e+61], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999999e137 or 7.79999999999999975e61 < z

   1. Initial program 37.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around inf 47.2%

      \[\leadsto \color{blue}{t} \]

   if -2.5999999999999999e137 < z < 7.79999999999999975e61

   1. Initial program 82.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 32.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 24.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 67.3%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 78.3%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 78.3%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 21.3%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer target: 83.7% 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 2024107 
(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))))