Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.6% → 94.7%

Time: 19.3s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.6% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \left(\frac{a}{t_2} - \left(\frac{y}{t_2} + \frac{a}{z} \cdot \frac{x - t}{\frac{z}{\mathsf{fma}\left(y, -1, a\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))) (t_2 (/ z (- t x))))
   (if (<= t_1 -1e-244)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+
        t
        (-
         (/ a t_2)
         (+ (/ y t_2) (* (/ a z) (/ (- x t) (/ z (fma y -1.0 a)))))))
       (fma (/ (- y z) (- a z)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -1e-244) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((a / t_2) - ((y / t_2) + ((a / z) * ((x - t) / (z / fma(y, -1.0, a))))));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_1 <= -1e-244)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(a / t_2) - Float64(Float64(y / t_2) + Float64(Float64(a / z) * Float64(Float64(x - t) / Float64(z / fma(y, -1.0, a)))))));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-244], 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[(t + N[(N[(a / t$95$2), $MachinePrecision] - N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z / N[(y * -1.0 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245

   1. Initial program 90.6%

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

      1. associate-*r/ 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 64.3%

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

   4. Simplified 99.7%

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

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

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. remove-double-neg 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-*r/ 80.1%

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

      5. associate-/l* 91.3%

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

      6. associate-/r/ 97.7%

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

      7. fma-neg 97.7%

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

      8. remove-double-neg 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \left(\frac{a}{\frac{z}{t - x}} - \left(\frac{y}{\frac{z}{t - x}} + \frac{a}{z} \cdot \frac{x - t}{\frac{z}{\mathsf{fma}\left(y, -1, a\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]

Alternative 2: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t - {\left(\frac{\frac{z}{y - a}}{t - x}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-244)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (- t (pow (/ (/ z (- y a)) (- t x)) -1.0))
       (fma (/ (- y z) (- a z)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-244) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t - pow(((z / (y - a)) / (t - x)), -1.0);
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-244)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t - (Float64(Float64(z / Float64(y - a)) / Float64(t - x)) ^ -1.0));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-244], 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[(t - N[Power[N[(N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245

   1. Initial program 90.6%

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

      1. associate-*r/ 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. div-sub 71.7%

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

      5. distribute-lft-out-- 71.7%

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

      6. associate-*r/ 71.7%

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

      7. mul-1-neg 71.7%

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

      8. unsub-neg 71.7%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 95.1%

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

   4. Simplified 95.1%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

   6. Applied egg-rr 95.2%

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

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

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. remove-double-neg 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-*r/ 80.1%

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

      5. associate-/l* 91.3%

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

      6. associate-/r/ 97.7%

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

      7. fma-neg 97.7%

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

      8. remove-double-neg 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t - {\left(\frac{\frac{z}{y - a}}{t - x}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]

Alternative 3: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-244)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (/ (- y z) (- a z)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-244) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-244)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-244], 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[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245

   1. Initial program 90.6%

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

      1. associate-*r/ 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. div-sub 71.7%

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

      5. distribute-lft-out-- 71.7%

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

      6. associate-*r/ 71.7%

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

      7. mul-1-neg 71.7%

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

      8. unsub-neg 71.7%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 95.1%

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

   4. Simplified 95.1%

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

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

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. remove-double-neg 92.1%

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

      3. unsub-neg 92.1%

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

      4. associate-*r/ 80.1%

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

      5. associate-/l* 91.3%

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

      6. associate-/r/ 97.7%

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

      7. fma-neg 97.7%

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

      8. remove-double-neg 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]

Alternative 4: 92.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-244)
     t_1
     (if (<= t_1 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= t_1 2e-22) (+ x (/ (* (- y z) (- t x)) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-244) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_1 <= 2e-22) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    if (t_1 <= (-1d-244)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if (t_1 <= 2d-22) then
        tmp = x + (((y - z) * (t - x)) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -1e-244) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (t_1 <= 2e-22) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if t_1 <= -1e-244:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + ((x - t) / (z / (y - a)))
	elif t_1 <= 2e-22:
		tmp = x + (((y - z) * (t - x)) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-244)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (t_1 <= 2e-22)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-244)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif (t_1 <= 2e-22)
		tmp = x + (((y - z) * (t - x)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-244], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-22], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245 or 2.0000000000000001e-22 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.3%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. div-sub 71.7%

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

      5. distribute-lft-out-- 71.7%

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

      6. associate-*r/ 71.7%

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

      7. mul-1-neg 71.7%

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

      8. unsub-neg 71.7%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 95.1%

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

   4. Simplified 95.1%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.0000000000000001e-22

   1. Initial program 80.1%

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

      1. associate-*r/ 98.7%

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

   3. Simplified 98.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]

Alternative 5: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244} \lor \neg \left(t_1 \leq 10^{-262}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-244) (not (<= t_1 1e-262)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-244) || !(t_1 <= 1e-262)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-244)) .or. (.not. (t_1 <= 1d-262))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-244) || !(t_1 <= 1e-262)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-244) or not (t_1 <= 1e-262):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-244) || !(t_1 <= 1e-262))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-244) || ~((t_1 <= 1e-262)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-244], N[Not[LessEqual[t$95$1, 1e-262]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245 or 1.00000000000000001e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.8%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000001e-262

   1. Initial program 8.9%

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

   2. Taylor expanded in z around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. associate-*r/ 68.7%

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

      3. associate-*r/ 68.7%

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

      4. div-sub 68.7%

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

      5. distribute-lft-out-- 68.7%

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

      6. associate-*r/ 68.7%

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

      7. mul-1-neg 68.7%

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

      8. unsub-neg 68.7%

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

      9. distribute-rgt-out-- 68.9%

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

      10. associate-/l* 88.4%

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

   4. Simplified 88.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{-262}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 6: 94.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-244} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-244) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-244) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-244)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-244) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-244) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-244) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-244) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-244], 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[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999993e-245 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.3%

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

      1. associate-*r/ 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-/l* 96.0%

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

   3. Applied egg-rr 96.0%

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

   if -9.9999999999999993e-245 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 71.7%

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

      1. associate--l+ 71.7%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 71.7%

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

      4. div-sub 71.7%

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

      5. distribute-lft-out-- 71.7%

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

      6. associate-*r/ 71.7%

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

      7. mul-1-neg 71.7%

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

      8. unsub-neg 71.7%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 95.1%

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

   4. Simplified 95.1%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-244} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 7: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= t -5.6e+42)
     t_1
     (if (<= t -4.2e-150)
       (+ t (* y (/ x z)))
       (if (<= t -1.12e-206)
         t_2
         (if (<= t -2.9e-255)
           (/ (* x (- y a)) z)
           (if (<= t 1.22e-91) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (t <= -5.6e+42) {
		tmp = t_1;
	} else if (t <= -4.2e-150) {
		tmp = t + (y * (x / z));
	} else if (t <= -1.12e-206) {
		tmp = t_2;
	} else if (t <= -2.9e-255) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 1.22e-91) {
		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 - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (t <= (-5.6d+42)) then
        tmp = t_1
    else if (t <= (-4.2d-150)) then
        tmp = t + (y * (x / z))
    else if (t <= (-1.12d-206)) then
        tmp = t_2
    else if (t <= (-2.9d-255)) then
        tmp = (x * (y - a)) / z
    else if (t <= 1.22d-91) 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 - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (t <= -5.6e+42) {
		tmp = t_1;
	} else if (t <= -4.2e-150) {
		tmp = t + (y * (x / z));
	} else if (t <= -1.12e-206) {
		tmp = t_2;
	} else if (t <= -2.9e-255) {
		tmp = (x * (y - a)) / z;
	} else if (t <= 1.22e-91) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if t <= -5.6e+42:
		tmp = t_1
	elif t <= -4.2e-150:
		tmp = t + (y * (x / z))
	elif t <= -1.12e-206:
		tmp = t_2
	elif t <= -2.9e-255:
		tmp = (x * (y - a)) / z
	elif t <= 1.22e-91:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (t <= -5.6e+42)
		tmp = t_1;
	elseif (t <= -4.2e-150)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (t <= -1.12e-206)
		tmp = t_2;
	elseif (t <= -2.9e-255)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (t <= 1.22e-91)
		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 - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (t <= -5.6e+42)
		tmp = t_1;
	elseif (t <= -4.2e-150)
		tmp = t + (y * (x / z));
	elseif (t <= -1.12e-206)
		tmp = t_2;
	elseif (t <= -2.9e-255)
		tmp = (x * (y - a)) / z;
	elseif (t <= 1.22e-91)
		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[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+42], t$95$1, If[LessEqual[t, -4.2e-150], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e-206], t$95$2, If[LessEqual[t, -2.9e-255], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.22e-91], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5999999999999999e42 or 1.21999999999999998e-91 < t

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 75.9%

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

   4. Simplified 75.9%

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

   if -5.5999999999999999e42 < t < -4.2000000000000002e-150

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. associate-*r/ 62.5%

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

      3. associate-*r/ 62.5%

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

      4. div-sub 62.6%

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

      5. distribute-lft-out-- 62.6%

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

      6. associate-*r/ 62.6%

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

      7. mul-1-neg 62.6%

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

      8. unsub-neg 62.6%

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

      9. distribute-rgt-out-- 62.9%

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

      10. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in y around inf 63.4%

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

   6. Taylor expanded in t around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-/l* 56.9%

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

      3. associate-/r/ 57.8%

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

      4. distribute-rgt-neg-in 57.8%

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

   8. Simplified 57.8%

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

   if -4.2000000000000002e-150 < t < -1.11999999999999997e-206 or -2.90000000000000007e-255 < t < 1.21999999999999998e-91

   1. Initial program 72.4%

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

      1. associate-*r/ 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-/l* 75.0%

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

   3. Applied egg-rr 75.0%

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

   4. Taylor expanded in z around 0 61.0%

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

   5. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   7. Simplified 59.2%

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

   if -1.11999999999999997e-206 < t < -2.90000000000000007e-255

   1. Initial program 17.1%

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

   2. Taylor expanded in z around inf 88.2%

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

      1. associate--l+ 88.2%

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

      2. associate-*r/ 88.2%

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

      3. associate-*r/ 88.2%

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

      4. div-sub 88.2%

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

      5. distribute-lft-out-- 88.2%

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

      6. associate-*r/ 88.2%

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

      7. mul-1-neg 88.2%

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

      8. unsub-neg 88.2%

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

      9. distribute-rgt-out-- 88.2%

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

      10. associate-/l* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in t around 0 65.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 8: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-148}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-255}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= t -1.95e+43)
     t_1
     (if (<= t -2.55e-148)
       (+ t (* y (/ x z)))
       (if (<= t -3.6e-223)
         t_2
         (if (<= t -4.8e-255)
           (+ t (/ a (/ z (- t x))))
           (if (<= t 6e-89) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (t <= -1.95e+43) {
		tmp = t_1;
	} else if (t <= -2.55e-148) {
		tmp = t + (y * (x / z));
	} else if (t <= -3.6e-223) {
		tmp = t_2;
	} else if (t <= -4.8e-255) {
		tmp = t + (a / (z / (t - x)));
	} else if (t <= 6e-89) {
		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 - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (t <= (-1.95d+43)) then
        tmp = t_1
    else if (t <= (-2.55d-148)) then
        tmp = t + (y * (x / z))
    else if (t <= (-3.6d-223)) then
        tmp = t_2
    else if (t <= (-4.8d-255)) then
        tmp = t + (a / (z / (t - x)))
    else if (t <= 6d-89) 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 - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (t <= -1.95e+43) {
		tmp = t_1;
	} else if (t <= -2.55e-148) {
		tmp = t + (y * (x / z));
	} else if (t <= -3.6e-223) {
		tmp = t_2;
	} else if (t <= -4.8e-255) {
		tmp = t + (a / (z / (t - x)));
	} else if (t <= 6e-89) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if t <= -1.95e+43:
		tmp = t_1
	elif t <= -2.55e-148:
		tmp = t + (y * (x / z))
	elif t <= -3.6e-223:
		tmp = t_2
	elif t <= -4.8e-255:
		tmp = t + (a / (z / (t - x)))
	elif t <= 6e-89:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (t <= -1.95e+43)
		tmp = t_1;
	elseif (t <= -2.55e-148)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (t <= -3.6e-223)
		tmp = t_2;
	elseif (t <= -4.8e-255)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (t <= 6e-89)
		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 - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (t <= -1.95e+43)
		tmp = t_1;
	elseif (t <= -2.55e-148)
		tmp = t + (y * (x / z));
	elseif (t <= -3.6e-223)
		tmp = t_2;
	elseif (t <= -4.8e-255)
		tmp = t + (a / (z / (t - x)));
	elseif (t <= 6e-89)
		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[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+43], t$95$1, If[LessEqual[t, -2.55e-148], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.6e-223], t$95$2, If[LessEqual[t, -4.8e-255], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-89], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.95e43 or 5.9999999999999999e-89 < t

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 75.9%

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

   4. Simplified 75.9%

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

   if -1.95e43 < t < -2.55e-148

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. associate-*r/ 62.5%

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

      3. associate-*r/ 62.5%

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

      4. div-sub 62.6%

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

      5. distribute-lft-out-- 62.6%

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

      6. associate-*r/ 62.6%

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

      7. mul-1-neg 62.6%

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

      8. unsub-neg 62.6%

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

      9. distribute-rgt-out-- 62.9%

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

      10. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in y around inf 63.4%

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

   6. Taylor expanded in t around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-/l* 56.9%

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

      3. associate-/r/ 57.8%

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

      4. distribute-rgt-neg-in 57.8%

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

   8. Simplified 57.8%

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

   if -2.55e-148 < t < -3.6000000000000004e-223 or -4.7999999999999997e-255 < t < 5.9999999999999999e-89

   1. Initial program 71.9%

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

      1. associate-*r/ 74.4%

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

      2. *-commutative 74.4%

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

      3. associate-/l* 75.7%

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

   3. Applied egg-rr 75.7%

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

   4. Taylor expanded in z around 0 60.7%

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

   5. Taylor expanded in x around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   7. Simplified 59.0%

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

   if -3.6000000000000004e-223 < t < -4.7999999999999997e-255

   1. Initial program 4.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. div-sub 100.0%

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

      5. distribute-lft-out-- 100.0%

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

      6. associate-*r/ 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. associate-/l* 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in y around 0 83.4%

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

      1. sub-neg 83.4%

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

      2. mul-1-neg 83.4%

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

      3. remove-double-neg 83.4%

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

      4. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-148}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-255}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ y (/ a (- t x))))))
   (if (<= z -1.9e+182)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -2.65e-79)
       t_1
       (if (<= z -2.6e-126)
         t_2
         (if (<= z -4.2e-153)
           t_1
           (if (<= z 1.25e-21) t_2 (+ t (* y (/ x z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -1.9e+182) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.65e-79) {
		tmp = t_1;
	} else if (z <= -2.6e-126) {
		tmp = t_2;
	} else if (z <= -4.2e-153) {
		tmp = t_1;
	} else if (z <= 1.25e-21) {
		tmp = t_2;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y / (a / (t - x)))
    if (z <= (-1.9d+182)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-2.65d-79)) then
        tmp = t_1
    else if (z <= (-2.6d-126)) then
        tmp = t_2
    else if (z <= (-4.2d-153)) then
        tmp = t_1
    else if (z <= 1.25d-21) then
        tmp = t_2
    else
        tmp = t + (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / (t - x)));
	double tmp;
	if (z <= -1.9e+182) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.65e-79) {
		tmp = t_1;
	} else if (z <= -2.6e-126) {
		tmp = t_2;
	} else if (z <= -4.2e-153) {
		tmp = t_1;
	} else if (z <= 1.25e-21) {
		tmp = t_2;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y / (a / (t - x)))
	tmp = 0
	if z <= -1.9e+182:
		tmp = t + (a / (z / (t - x)))
	elif z <= -2.65e-79:
		tmp = t_1
	elif z <= -2.6e-126:
		tmp = t_2
	elif z <= -4.2e-153:
		tmp = t_1
	elif z <= 1.25e-21:
		tmp = t_2
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.9e+182)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -2.65e-79)
		tmp = t_1;
	elseif (z <= -2.6e-126)
		tmp = t_2;
	elseif (z <= -4.2e-153)
		tmp = t_1;
	elseif (z <= 1.25e-21)
		tmp = t_2;
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (z <= -1.9e+182)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -2.65e-79)
		tmp = t_1;
	elseif (z <= -2.6e-126)
		tmp = t_2;
	elseif (z <= -4.2e-153)
		tmp = t_1;
	elseif (z <= 1.25e-21)
		tmp = t_2;
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+182], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.65e-79], t$95$1, If[LessEqual[z, -2.6e-126], t$95$2, If[LessEqual[z, -4.2e-153], t$95$1, If[LessEqual[z, 1.25e-21], t$95$2, N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.90000000000000006e182

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. associate-*r/ 73.8%

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

      3. associate-*r/ 73.8%

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

      4. div-sub 73.8%

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

      5. distribute-lft-out-- 73.8%

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

      6. associate-*r/ 73.8%

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

      7. mul-1-neg 73.8%

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

      8. unsub-neg 73.8%

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

      9. distribute-rgt-out-- 73.8%

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

      10. associate-/l* 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. sub-neg 69.0%

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

      2. mul-1-neg 69.0%

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

      3. remove-double-neg 69.0%

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

      4. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   if -1.90000000000000006e182 < z < -2.6499999999999999e-79 or -2.59999999999999999e-126 < z < -4.20000000000000008e-153

   1. Initial program 82.6%

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

   2. Taylor expanded in x around 0 54.5%

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

      1. associate-*r/ 67.6%

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

   4. Simplified 67.6%

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

   if -2.6499999999999999e-79 < z < -2.59999999999999999e-126 or -4.20000000000000008e-153 < z < 1.24999999999999993e-21

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 74.0%

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

      1. associate-/l* 84.1%

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

   4. Simplified 84.1%

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

   if 1.24999999999999993e-21 < z

   1. Initial program 71.3%

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

   2. Taylor expanded in z around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. associate-*r/ 58.1%

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

      3. associate-*r/ 58.1%

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

      4. div-sub 58.1%

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

      5. distribute-lft-out-- 58.1%

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

      6. associate-*r/ 58.1%

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

      7. mul-1-neg 58.1%

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

      8. unsub-neg 58.1%

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

      9. distribute-rgt-out-- 58.3%

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

      10. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in y around inf 70.7%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-/l* 63.1%

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

      3. associate-/r/ 62.2%

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

      4. distribute-rgt-neg-in 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-126}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+182}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3e+182)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -5.6e-71)
       t_1
       (if (<= z -8.5e-122)
         (+ x (/ (- t x) (/ a y)))
         (if (<= z -4.2e-153)
           t_1
           (if (<= z 7.5e-21)
             (+ x (/ y (/ a (- t x))))
             (+ t (* y (/ x z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3e+182) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.6e-71) {
		tmp = t_1;
	} else if (z <= -8.5e-122) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= -4.2e-153) {
		tmp = t_1;
	} else if (z <= 7.5e-21) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-3d+182)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-5.6d-71)) then
        tmp = t_1
    else if (z <= (-8.5d-122)) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= (-4.2d-153)) then
        tmp = t_1
    else if (z <= 7.5d-21) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3e+182) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.6e-71) {
		tmp = t_1;
	} else if (z <= -8.5e-122) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= -4.2e-153) {
		tmp = t_1;
	} else if (z <= 7.5e-21) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3e+182:
		tmp = t + (a / (z / (t - x)))
	elif z <= -5.6e-71:
		tmp = t_1
	elif z <= -8.5e-122:
		tmp = x + ((t - x) / (a / y))
	elif z <= -4.2e-153:
		tmp = t_1
	elif z <= 7.5e-21:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -3e+182)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -5.6e-71)
		tmp = t_1;
	elseif (z <= -8.5e-122)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= -4.2e-153)
		tmp = t_1;
	elseif (z <= 7.5e-21)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -3e+182)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -5.6e-71)
		tmp = t_1;
	elseif (z <= -8.5e-122)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= -4.2e-153)
		tmp = t_1;
	elseif (z <= 7.5e-21)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+182], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-71], t$95$1, If[LessEqual[z, -8.5e-122], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-153], t$95$1, If[LessEqual[z, 7.5e-21], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.0000000000000002e182

   1. Initial program 30.2%

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

   2. Taylor expanded in z around inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. associate-*r/ 73.8%

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

      3. associate-*r/ 73.8%

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

      4. div-sub 73.8%

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

      5. distribute-lft-out-- 73.8%

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

      6. associate-*r/ 73.8%

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

      7. mul-1-neg 73.8%

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

      8. unsub-neg 73.8%

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

      9. distribute-rgt-out-- 73.8%

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

      10. associate-/l* 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. sub-neg 69.0%

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

      2. mul-1-neg 69.0%

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

      3. remove-double-neg 69.0%

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

      4. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   if -3.0000000000000002e182 < z < -5.60000000000000001e-71 or -8.50000000000000003e-122 < z < -4.20000000000000008e-153

   1. Initial program 82.6%

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

   2. Taylor expanded in x around 0 54.5%

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

      1. associate-*r/ 67.6%

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

   4. Simplified 67.6%

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

   if -5.60000000000000001e-71 < z < -8.50000000000000003e-122

   1. Initial program 100.0%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/l* 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   if -4.20000000000000008e-153 < z < 7.50000000000000072e-21

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 72.6%

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

      1. associate-/l* 83.3%

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

   4. Simplified 83.3%

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

   if 7.50000000000000072e-21 < z

   1. Initial program 71.3%

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

   2. Taylor expanded in z around inf 58.1%

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

      1. associate--l+ 58.1%

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

      2. associate-*r/ 58.1%

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

      3. associate-*r/ 58.1%

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

      4. div-sub 58.1%

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

      5. distribute-lft-out-- 58.1%

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

      6. associate-*r/ 58.1%

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

      7. mul-1-neg 58.1%

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

      8. unsub-neg 58.1%

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

      9. distribute-rgt-out-- 58.3%

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

      10. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in y around inf 70.7%

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

   6. Taylor expanded in t around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-/l* 63.1%

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

      3. associate-/r/ 62.2%

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

      4. distribute-rgt-neg-in 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+182}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 53.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-40}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -3e+165)
     t_2
     (if (<= a -2e-43)
       (* x (- 1.0 (/ y a)))
       (if (<= a 3.3e-107)
         t_1
         (if (<= a 6.6e-40) (* (- y a) (/ x z)) (if (<= a 6e+57) 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 tmp;
	if (a <= -3e+165) {
		tmp = t_2;
	} else if (a <= -2e-43) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.3e-107) {
		tmp = t_1;
	} else if (a <= 6.6e-40) {
		tmp = (y - a) * (x / z);
	} else if (a <= 6e+57) {
		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 = t * (1.0d0 - (y / z))
    t_2 = x + (t * (y / a))
    if (a <= (-3d+165)) then
        tmp = t_2
    else if (a <= (-2d-43)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 3.3d-107) then
        tmp = t_1
    else if (a <= 6.6d-40) then
        tmp = (y - a) * (x / z)
    else if (a <= 6d+57) 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 tmp;
	if (a <= -3e+165) {
		tmp = t_2;
	} else if (a <= -2e-43) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.3e-107) {
		tmp = t_1;
	} else if (a <= 6.6e-40) {
		tmp = (y - a) * (x / z);
	} else if (a <= 6e+57) {
		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))
	tmp = 0
	if a <= -3e+165:
		tmp = t_2
	elif a <= -2e-43:
		tmp = x * (1.0 - (y / a))
	elif a <= 3.3e-107:
		tmp = t_1
	elif a <= 6.6e-40:
		tmp = (y - a) * (x / z)
	elif a <= 6e+57:
		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)))
	tmp = 0.0
	if (a <= -3e+165)
		tmp = t_2;
	elseif (a <= -2e-43)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 3.3e-107)
		tmp = t_1;
	elseif (a <= 6.6e-40)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 6e+57)
		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));
	tmp = 0.0;
	if (a <= -3e+165)
		tmp = t_2;
	elseif (a <= -2e-43)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 3.3e-107)
		tmp = t_1;
	elseif (a <= 6.6e-40)
		tmp = (y - a) * (x / z);
	elseif (a <= 6e+57)
		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]}, If[LessEqual[a, -3e+165], t$95$2, If[LessEqual[a, -2e-43], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-107], t$95$1, If[LessEqual[a, 6.6e-40], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+57], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9999999999999999e165 or 5.9999999999999999e57 < a

   1. Initial program 93.2%

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

      1. associate-*r/ 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-/l* 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in z around 0 79.8%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. associate-*r/ 72.8%

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

   7. Simplified 72.8%

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

   if -2.9999999999999999e165 < a < -2.00000000000000015e-43

   1. Initial program 79.3%

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

      1. associate-*r/ 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-/l* 83.3%

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

   3. Applied egg-rr 83.3%

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

   4. Taylor expanded in z around 0 55.6%

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

   5. Taylor expanded in x around inf 46.5%

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

      1. mul-1-neg 46.5%

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

      2. unsub-neg 46.5%

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

   7. Simplified 46.5%

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

   if -2.00000000000000015e-43 < a < 3.30000000000000004e-107 or 6.59999999999999986e-40 < a < 5.9999999999999999e57

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. associate-*r/ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. div-sub 76.9%

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

      5. distribute-lft-out-- 76.9%

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

      6. associate-*r/ 76.9%

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

      7. mul-1-neg 76.9%

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

      8. unsub-neg 76.9%

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

      9. distribute-rgt-out-- 76.9%

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

      10. associate-/l* 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in y around inf 77.2%

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

   6. Taylor expanded in t around inf 60.8%

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

   if 3.30000000000000004e-107 < a < 6.59999999999999986e-40

   1. Initial program 82.3%

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

   2. Taylor expanded in z around inf 49.8%

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

      1. associate--l+ 49.8%

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

      2. associate-*r/ 49.8%

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

      3. associate-*r/ 49.8%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 58.9%

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

      10. associate-/l* 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in t around 0 56.5%

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

      1. associate-/l* 64.7%

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

      2. associate-/r/ 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+165}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-40}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.25e+78)
     x
     (if (<= a 7e-103)
       t_1
       (if (<= a 5.8e-40) (/ y (/ z x)) (if (<= a 2.1e+59) t_1 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 <= -1.25e+78) {
		tmp = x;
	} else if (a <= 7e-103) {
		tmp = t_1;
	} else if (a <= 5.8e-40) {
		tmp = y / (z / x);
	} else if (a <= 2.1e+59) {
		tmp = t_1;
	} 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 <= (-1.25d+78)) then
        tmp = x
    else if (a <= 7d-103) then
        tmp = t_1
    else if (a <= 5.8d-40) then
        tmp = y / (z / x)
    else if (a <= 2.1d+59) then
        tmp = t_1
    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 <= -1.25e+78) {
		tmp = x;
	} else if (a <= 7e-103) {
		tmp = t_1;
	} else if (a <= 5.8e-40) {
		tmp = y / (z / x);
	} else if (a <= 2.1e+59) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.25e+78:
		tmp = x
	elif a <= 7e-103:
		tmp = t_1
	elif a <= 5.8e-40:
		tmp = y / (z / x)
	elif a <= 2.1e+59:
		tmp = t_1
	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 <= -1.25e+78)
		tmp = x;
	elseif (a <= 7e-103)
		tmp = t_1;
	elseif (a <= 5.8e-40)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 2.1e+59)
		tmp = t_1;
	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 <= -1.25e+78)
		tmp = x;
	elseif (a <= 7e-103)
		tmp = t_1;
	elseif (a <= 5.8e-40)
		tmp = y / (z / x);
	elseif (a <= 2.1e+59)
		tmp = t_1;
	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, -1.25e+78], x, If[LessEqual[a, 7e-103], t$95$1, If[LessEqual[a, 5.8e-40], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+59], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.24999999999999996e78 or 2.09999999999999984e59 < a

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 48.2%

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

   if -1.24999999999999996e78 < a < 7.00000000000000032e-103 or 5.7999999999999998e-40 < a < 2.09999999999999984e59

   1. Initial program 73.8%

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

   2. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. associate-*r/ 68.0%

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

      3. associate-*r/ 68.0%

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

      4. div-sub 69.4%

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

      5. distribute-lft-out-- 69.4%

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

      6. associate-*r/ 69.4%

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

      7. mul-1-neg 69.4%

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

      8. unsub-neg 69.4%

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

      9. distribute-rgt-out-- 69.4%

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

      10. associate-/l* 74.9%

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

   4. Simplified 74.9%

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

   5. Taylor expanded in y around inf 70.0%

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

   6. Taylor expanded in t around inf 54.3%

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

   if 7.00000000000000032e-103 < a < 5.7999999999999998e-40

   1. Initial program 82.3%

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

   2. Taylor expanded in z around inf 49.8%

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

      1. associate--l+ 49.8%

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

      2. associate-*r/ 49.8%

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

      3. associate-*r/ 49.8%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 58.9%

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

      10. associate-/l* 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in y around -inf 50.3%

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

      1. associate-*r/ 50.3%

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

      2. associate-*r* 50.3%

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

      3. mul-1-neg 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 56.5%

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

      2. associate-/r/ 56.5%

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

   10. Simplified 56.5%

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

       1. *-commutative 56.5%

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

       2. clear-num 56.6%

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

       3. un-div-inv 56.6%

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

   12. Applied egg-rr 56.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.55e-42)
     t_2
     (if (<= a 4.4e-103)
       t_1
       (if (<= a 1.8e-41) (/ y (/ z x)) (if (<= a 6.8e+59) 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -1.55e-42) {
		tmp = t_2;
	} else if (a <= 4.4e-103) {
		tmp = t_1;
	} else if (a <= 1.8e-41) {
		tmp = y / (z / x);
	} else if (a <= 6.8e+59) {
		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 = t * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.55d-42)) then
        tmp = t_2
    else if (a <= 4.4d-103) then
        tmp = t_1
    else if (a <= 1.8d-41) then
        tmp = y / (z / x)
    else if (a <= 6.8d+59) 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 * (1.0 - (y / a));
	double tmp;
	if (a <= -1.55e-42) {
		tmp = t_2;
	} else if (a <= 4.4e-103) {
		tmp = t_1;
	} else if (a <= 1.8e-41) {
		tmp = y / (z / x);
	} else if (a <= 6.8e+59) {
		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 * (1.0 - (y / a))
	tmp = 0
	if a <= -1.55e-42:
		tmp = t_2
	elif a <= 4.4e-103:
		tmp = t_1
	elif a <= 1.8e-41:
		tmp = y / (z / x)
	elif a <= 6.8e+59:
		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(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.55e-42)
		tmp = t_2;
	elseif (a <= 4.4e-103)
		tmp = t_1;
	elseif (a <= 1.8e-41)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 6.8e+59)
		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 * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.55e-42)
		tmp = t_2;
	elseif (a <= 4.4e-103)
		tmp = t_1;
	elseif (a <= 1.8e-41)
		tmp = y / (z / x);
	elseif (a <= 6.8e+59)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-42], t$95$2, If[LessEqual[a, 4.4e-103], t$95$1, If[LessEqual[a, 1.8e-41], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5500000000000001e-42 or 6.80000000000000012e59 < a

   1. Initial program 88.1%

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

      1. associate-*r/ 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-/l* 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in z around 0 70.9%

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

   5. Taylor expanded in x around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

   7. Simplified 54.7%

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

   if -1.5500000000000001e-42 < a < 4.3999999999999999e-103 or 1.8e-41 < a < 6.80000000000000012e59

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. associate-*r/ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. div-sub 76.9%

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

      5. distribute-lft-out-- 76.9%

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

      6. associate-*r/ 76.9%

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

      7. mul-1-neg 76.9%

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

      8. unsub-neg 76.9%

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

      9. distribute-rgt-out-- 76.9%

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

      10. associate-/l* 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in y around inf 77.2%

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

   6. Taylor expanded in t around inf 60.8%

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

   if 4.3999999999999999e-103 < a < 1.8e-41

   1. Initial program 82.3%

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

   2. Taylor expanded in z around inf 49.8%

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

      1. associate--l+ 49.8%

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

      2. associate-*r/ 49.8%

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

      3. associate-*r/ 49.8%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 58.9%

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

      10. associate-/l* 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in y around -inf 50.3%

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

      1. associate-*r/ 50.3%

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

      2. associate-*r* 50.3%

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

      3. mul-1-neg 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 56.5%

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

      2. associate-/r/ 56.5%

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

   10. Simplified 56.5%

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

       1. *-commutative 56.5%

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

       2. clear-num 56.6%

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

       3. un-div-inv 56.6%

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

   12. Applied egg-rr 56.6%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 14: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-25} \lor \neg \left(a \leq 102\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.1e-25) (not (<= a 102.0)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.1e-25) || !(a <= 102.0)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (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) :: tmp
    if ((a <= (-6.1d-25)) .or. (.not. (a <= 102.0d0))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.1e-25) || !(a <= 102.0)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.1e-25) or not (a <= 102.0):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.1e-25) || !(a <= 102.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.1e-25) || ~((a <= 102.0)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.1e-25], N[Not[LessEqual[a, 102.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.10000000000000018e-25 or 102 < a

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf 79.9%

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

   if -6.10000000000000018e-25 < a < 102

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 78.6%

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

      5. distribute-lft-out-- 78.6%

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

      6. associate-*r/ 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

      9. distribute-rgt-out-- 78.6%

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

      10. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in y around inf 77.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-25} \lor \neg \left(a \leq 102\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 15: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.58 \cdot 10^{-24}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 400:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.58e-24)
   (+ x (* (- y z) (/ (- t x) a)))
   (if (<= a 400.0)
     (+ t (/ (- x t) (/ z y)))
     (+ x (/ (- t x) (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.58e-24) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 400.0) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.58d-24)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 400.0d0) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.58e-24) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 400.0) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.58e-24:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 400.0:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.58e-24)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 400.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.58e-24)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 400.0)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.58e-24], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 400.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5799999999999999e-24

   1. Initial program 87.4%

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

   2. Taylor expanded in a around inf 76.1%

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

   if -1.5799999999999999e-24 < a < 400

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 78.6%

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

      5. distribute-lft-out-- 78.6%

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

      6. associate-*r/ 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

      9. distribute-rgt-out-- 78.6%

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

      10. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in y around inf 77.8%

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

   if 400 < a

   1. Initial program 94.2%

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

   2. Taylor expanded in a around inf 69.1%

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

      1. associate-/l* 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.58 \cdot 10^{-24}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 400:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 16: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 440:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e-23)
   (+ x (* (- y z) (/ (- t x) a)))
   (if (<= a 440.0)
     (+ t (/ (- x t) (/ z (- y a))))
     (+ x (/ (- t x) (/ a (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e-23) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 440.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.2d-23)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 440.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e-23) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 440.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e-23:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 440.0:
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e-23)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 440.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.2e-23)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 440.0)
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e-23], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 440.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2e-23

   1. Initial program 87.4%

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

   2. Taylor expanded in a around inf 76.1%

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

   if -5.2e-23 < a < 440

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 78.6%

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

      5. distribute-lft-out-- 78.6%

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

      6. associate-*r/ 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

      9. distribute-rgt-out-- 78.6%

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

      10. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   if 440 < a

   1. Initial program 94.2%

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

   2. Taylor expanded in a around inf 69.1%

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

      1. associate-/l* 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 440:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 17: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 140:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -2.3e-45)
     t_1
     (if (<= a 3.2e-107)
       (* t (- 1.0 (/ y z)))
       (if (<= a 140.0) (* (- y a) (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.3e-45) {
		tmp = t_1;
	} else if (a <= 3.2e-107) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 140.0) {
		tmp = (y - a) * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-2.3d-45)) then
        tmp = t_1
    else if (a <= 3.2d-107) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 140.0d0) then
        tmp = (y - a) * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.3e-45) {
		tmp = t_1;
	} else if (a <= 3.2e-107) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 140.0) {
		tmp = (y - a) * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -2.3e-45:
		tmp = t_1
	elif a <= 3.2e-107:
		tmp = t * (1.0 - (y / z))
	elif a <= 140.0:
		tmp = (y - a) * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -2.3e-45)
		tmp = t_1;
	elseif (a <= 3.2e-107)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 140.0)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -2.3e-45)
		tmp = t_1;
	elseif (a <= 3.2e-107)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 140.0)
		tmp = (y - a) * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-45], t$95$1, If[LessEqual[a, 3.2e-107], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 140.0], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.29999999999999992e-45 or 140 < a

   1. Initial program 88.4%

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

      1. associate-*r/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-/l* 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in z around 0 69.8%

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

   5. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   7. Simplified 53.5%

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

   if -2.29999999999999992e-45 < a < 3.20000000000000013e-107

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 80.1%

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

      1. associate--l+ 80.1%

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

      2. associate-*r/ 80.1%

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

      3. associate-*r/ 80.1%

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

      4. div-sub 82.1%

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

      5. distribute-lft-out-- 82.1%

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

      6. associate-*r/ 82.1%

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

      7. mul-1-neg 82.1%

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

      8. unsub-neg 82.1%

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

      9. distribute-rgt-out-- 82.1%

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

      10. associate-/l* 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in y around inf 79.9%

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

   6. Taylor expanded in t around inf 63.6%

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

   if 3.20000000000000013e-107 < a < 140

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 54.4%

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

      1. associate--l+ 54.4%

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

      2. associate-*r/ 54.4%

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

      3. associate-*r/ 54.4%

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

      4. div-sub 60.3%

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

      5. distribute-lft-out-- 60.3%

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

      6. associate-*r/ 60.3%

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

      7. mul-1-neg 60.3%

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

      8. unsub-neg 60.3%

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

      9. distribute-rgt-out-- 60.3%

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

      10. associate-/l* 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in t around 0 44.6%

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

      1. associate-/l* 55.4%

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

      2. associate-/r/ 55.3%

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

   7. Simplified 55.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 140:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 18: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -4.4e-35)
     t_1
     (if (<= z -1.1e-165)
       (* x (- 1.0 (/ y a)))
       (if (<= z 5.1e-21) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -4.4e-35) {
		tmp = t_1;
	} else if (z <= -1.1e-165) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.1e-21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-4.4d-35)) then
        tmp = t_1
    else if (z <= (-1.1d-165)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.1d-21) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -4.4e-35) {
		tmp = t_1;
	} else if (z <= -1.1e-165) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.1e-21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -4.4e-35:
		tmp = t_1
	elif z <= -1.1e-165:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.1e-21:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -4.4e-35)
		tmp = t_1;
	elseif (z <= -1.1e-165)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.1e-21)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	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 <= -4.4e-35)
		tmp = t_1;
	elseif (z <= -1.1e-165)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.1e-21)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e-35], t$95$1, If[LessEqual[z, -1.1e-165], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-21], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999987e-35 or 5.10000000000000004e-21 < z

   1. Initial program 67.8%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. associate--l+ 62.7%

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

      2. associate-*r/ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. div-sub 62.7%

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

      5. distribute-lft-out-- 62.7%

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

      6. associate-*r/ 62.7%

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

      7. mul-1-neg 62.7%

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

      8. unsub-neg 62.7%

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

      9. distribute-rgt-out-- 62.9%

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

      10. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in y around inf 69.9%

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

   6. Taylor expanded in t around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-/l* 60.8%

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

      3. associate-/r/ 59.8%

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

      4. distribute-rgt-neg-in 59.8%

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

   8. Simplified 59.8%

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

   if -4.39999999999999987e-35 < z < -1.0999999999999999e-165

   1. Initial program 87.5%

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

      1. associate-*r/ 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-/l* 93.4%

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

   3. Applied egg-rr 93.4%

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

   4. Taylor expanded in z around 0 58.5%

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

   5. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   7. Simplified 53.4%

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

   if -1.0999999999999999e-165 < z < 5.10000000000000004e-21

   1. Initial program 93.4%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in z around 0 80.6%

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

   5. Taylor expanded in t around inf 57.2%

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

      1. associate-*r/ 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 19: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 19000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.1e-24)
   (+ x (/ y (/ a (- t x))))
   (if (<= a 19000.0) (- t (/ y (/ z (- t x)))) (+ x (/ (- t x) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.1e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 19000.0) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) / (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) :: tmp
    if (a <= (-6.1d-24)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= 19000.0d0) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.1e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 19000.0) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.1e-24:
		tmp = x + (y / (a / (t - x)))
	elif a <= 19000.0:
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.1e-24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= 19000.0)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.1e-24)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= 19000.0)
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.1e-24], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 19000.0], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.10000000000000036e-24

   1. Initial program 87.4%

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

   2. Taylor expanded in z around 0 52.8%

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

      1. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -6.10000000000000036e-24 < a < 19000

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 78.6%

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

      5. distribute-lft-out-- 78.6%

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

      6. associate-*r/ 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

      9. distribute-rgt-out-- 78.6%

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

      10. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in y around inf 72.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   if 19000 < a

   1. Initial program 94.2%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-/l* 96.6%

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

   3. Applied egg-rr 96.6%

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

   4. Taylor expanded in z around 0 76.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 19000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 20: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 110:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e-24)
   (+ x (/ y (/ a (- t x))))
   (if (<= a 110.0) (+ t (/ (- x t) (/ z y))) (+ x (/ (- t x) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 110.0) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + ((t - x) / (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) :: tmp
    if (a <= (-3.6d-24)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= 110.0d0) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 110.0) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e-24:
		tmp = x + (y / (a / (t - x)))
	elif a <= 110.0:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e-24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= 110.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e-24)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= 110.0)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e-24], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 110.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6000000000000001e-24

   1. Initial program 87.4%

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

   2. Taylor expanded in z around 0 52.8%

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

      1. associate-/l* 67.5%

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

   4. Simplified 67.5%

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

   if -3.6000000000000001e-24 < a < 110

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 78.6%

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

      5. distribute-lft-out-- 78.6%

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

      6. associate-*r/ 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

      9. distribute-rgt-out-- 78.6%

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

      10. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in y around inf 77.8%

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

   if 110 < a

   1. Initial program 94.2%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-/l* 96.6%

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

   3. Applied egg-rr 96.6%

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

   4. Taylor expanded in z around 0 76.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 110:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 21: 37.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7800:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e-54)
   x
   (if (<= a 7.2e-104) t (if (<= a 7800.0) (* y (/ x z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-54) {
		tmp = x;
	} else if (a <= 7.2e-104) {
		tmp = t;
	} else if (a <= 7800.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d-54)) then
        tmp = x
    else if (a <= 7.2d-104) then
        tmp = t
    else if (a <= 7800.0d0) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e-54) {
		tmp = x;
	} else if (a <= 7.2e-104) {
		tmp = t;
	} else if (a <= 7800.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e-54:
		tmp = x
	elif a <= 7.2e-104:
		tmp = t
	elif a <= 7800.0:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e-54)
		tmp = x;
	elseif (a <= 7.2e-104)
		tmp = t;
	elseif (a <= 7800.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e-54)
		tmp = x;
	elseif (a <= 7.2e-104)
		tmp = t;
	elseif (a <= 7800.0)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e-54], x, If[LessEqual[a, 7.2e-104], t, If[LessEqual[a, 7800.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5e-54 or 7800 < a

   1. Initial program 87.9%

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

   2. Taylor expanded in a around inf 39.4%

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

   if -8.5e-54 < a < 7.1999999999999996e-104

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 41.2%

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

   if 7.1999999999999996e-104 < a < 7800

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 54.4%

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

      1. associate--l+ 54.4%

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

      2. associate-*r/ 54.4%

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

      3. associate-*r/ 54.4%

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

      4. div-sub 60.3%

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

      5. distribute-lft-out-- 60.3%

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

      6. associate-*r/ 60.3%

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

      7. mul-1-neg 60.3%

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

      8. unsub-neg 60.3%

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

      9. distribute-rgt-out-- 60.3%

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

      10. associate-/l* 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in y around -inf 45.1%

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

      1. associate-*r/ 45.1%

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

      2. associate-*r* 45.1%

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

      3. mul-1-neg 45.1%

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

   7. Simplified 45.1%

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

   8. Taylor expanded in t around 0 37.8%

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

      1. associate-/l* 49.0%

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

      2. associate-/r/ 48.9%

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

   10. Simplified 48.9%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7800:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 580:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-54)
   x
   (if (<= a 1.9e-100) t (if (<= a 580.0) (/ y (/ z x)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-54) {
		tmp = x;
	} else if (a <= 1.9e-100) {
		tmp = t;
	} else if (a <= 580.0) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-54)) then
        tmp = x
    else if (a <= 1.9d-100) then
        tmp = t
    else if (a <= 580.0d0) then
        tmp = y / (z / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-54) {
		tmp = x;
	} else if (a <= 1.9e-100) {
		tmp = t;
	} else if (a <= 580.0) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-54:
		tmp = x
	elif a <= 1.9e-100:
		tmp = t
	elif a <= 580.0:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-54)
		tmp = x;
	elseif (a <= 1.9e-100)
		tmp = t;
	elseif (a <= 580.0)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-54)
		tmp = x;
	elseif (a <= 1.9e-100)
		tmp = t;
	elseif (a <= 580.0)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-54], x, If[LessEqual[a, 1.9e-100], t, If[LessEqual[a, 580.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.50000000000000046e-54 or 580 < a

   1. Initial program 87.9%

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

   2. Taylor expanded in a around inf 39.4%

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

   if -5.50000000000000046e-54 < a < 1.89999999999999999e-100

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 41.2%

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

   if 1.89999999999999999e-100 < a < 580

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 54.4%

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

      1. associate--l+ 54.4%

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

      2. associate-*r/ 54.4%

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

      3. associate-*r/ 54.4%

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

      4. div-sub 60.3%

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

      5. distribute-lft-out-- 60.3%

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

      6. associate-*r/ 60.3%

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

      7. mul-1-neg 60.3%

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

      8. unsub-neg 60.3%

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

      9. distribute-rgt-out-- 60.3%

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

      10. associate-/l* 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in y around -inf 45.1%

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

      1. associate-*r/ 45.1%

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

      2. associate-*r* 45.1%

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

      3. mul-1-neg 45.1%

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

   7. Simplified 45.1%

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

   8. Taylor expanded in t around 0 37.8%

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

      1. associate-/l* 49.0%

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

      2. associate-/r/ 48.9%

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

   10. Simplified 48.9%

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

       1. *-commutative 48.9%

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

       2. clear-num 49.1%

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

       3. un-div-inv 49.1%

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

   12. Applied egg-rr 49.1%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 580:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 37.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e-54) x (if (<= a 4e+58) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-54) {
		tmp = x;
	} else if (a <= 4e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d-54)) then
        tmp = x
    else if (a <= 4d+58) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-54) {
		tmp = x;
	} else if (a <= 4e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e-54:
		tmp = x
	elif a <= 4e+58:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e-54)
		tmp = x;
	elseif (a <= 4e+58)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e-54)
		tmp = x;
	elseif (a <= 4e+58)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e-54], x, If[LessEqual[a, 4e+58], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.20000000000000008e-54 or 3.99999999999999978e58 < a

   1. Initial program 87.6%

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

   2. Taylor expanded in a around inf 41.6%

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

   if -6.20000000000000008e-54 < a < 3.99999999999999978e58

   1. Initial program 73.3%

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

   2. Taylor expanded in z around inf 36.0%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 24.7% 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 80.7%

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

2. Taylor expanded in z around inf 22.6%

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

3. Final simplification 22.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))