Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 96.1%

Time: 21.4s

Alternatives: 25

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: 80.3% 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: 96.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_2 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 -1e-293)
     t_1
     (if (<= t_2 0.0)
       (+ t (* (/ x z) (- y a)))
       (if (<= t_2 0.5)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (if (<= t_2 4e+286) (fma (- y z) (/ (- t x) (- a z)) x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -1e-293) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else if (t_2 <= 0.5) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else if (t_2 <= 4e+286) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-293)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (t_2 <= 0.5)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	elseif (t_2 <= 4e+286)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-293], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.5], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+286], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-293 or 4.00000000000000013e286 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*r/ 76.4%

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

      3. *-commutative 76.4%

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

      4. associate-*r/ 96.2%

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

      5. fma-def 96.3%

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

   3. Simplified 96.3%

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

   if -1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. associate--l+ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. associate-*r/ 81.4%

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

      5. div-sub 81.4%

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

      6. distribute-lft-out-- 81.4%

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

      7. mul-1-neg 81.4%

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

      8. distribute-neg-frac 81.4%

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

      9. unsub-neg 81.4%

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

      10. distribute-rgt-out-- 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. mul-1-neg 81.4%

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

      3. *-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. neg-sub0 81.4%

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

      6. associate--r- 81.4%

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

      7. neg-sub0 81.4%

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

      8. distribute-rgt-out 81.4%

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

      9. +-commutative 81.4%

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

      10. distribute-rgt-out 81.4%

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

      11. sub-neg 81.4%

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

      12. *-commutative 81.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.5

   1. Initial program 77.9%

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

   2. Taylor expanded in x around -inf 99.5%

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

   if 0.5 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.00000000000000013e286

   1. Initial program 97.9%

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

      1. +-commutative 97.9%

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

      2. fma-def 97.9%

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

   3. Simplified 97.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 4 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_2 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- t x) (/ (- y z) (- a z)) x))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 -1e-293)
     t_1
     (if (<= t_2 0.0)
       (+ t (* (/ x z) (- y a)))
       (if (<= t_2 0.5)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         (if (<= t_2 5e+232) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t - x), ((y - z) / (a - z)), x);
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -1e-293) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else if (t_2 <= 0.5) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else if (t_2 <= 5e+232) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-293)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (t_2 <= 0.5)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	elseif (t_2 <= 5e+232)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-293], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.5], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+232], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-293 or 4.99999999999999987e232 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r/ 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-*r/ 96.1%

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

      5. fma-def 96.2%

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

   3. Simplified 96.2%

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

   if -1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. associate--l+ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. associate-*r/ 81.4%

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

      5. div-sub 81.4%

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

      6. distribute-lft-out-- 81.4%

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

      7. mul-1-neg 81.4%

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

      8. distribute-neg-frac 81.4%

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

      9. unsub-neg 81.4%

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

      10. distribute-rgt-out-- 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. mul-1-neg 81.4%

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

      3. *-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. neg-sub0 81.4%

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

      6. associate--r- 81.4%

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

      7. neg-sub0 81.4%

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

      8. distribute-rgt-out 81.4%

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

      9. +-commutative 81.4%

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

      10. distribute-rgt-out 81.4%

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

      11. sub-neg 81.4%

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

      12. *-commutative 81.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.5

   1. Initial program 77.9%

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

   2. Taylor expanded in x around -inf 99.5%

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

   if 0.5 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999987e232

   1. Initial program 98.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-293}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{+232}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternative 3: 93.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;t_1 \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_1 -1e-293)
     t_1
     (if (<= t_1 0.0)
       (+ t (* (/ x z) (- y a)))
       (if (<= t_1 0.5)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- 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-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else if (t_1 <= 0.5) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (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-293)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x / z) * (y - a))
    else if (t_1 <= 0.5d0) then
        tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0d0) - (y / (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-293) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((x / z) * (y - a));
	} else if (t_1 <= 0.5) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (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-293:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + ((x / z) * (y - a))
	elif t_1 <= 0.5:
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (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-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / 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-293)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + ((x / z) * (y - a));
	elseif (t_1 <= 0.5)
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (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-293], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.5], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $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)))) < -1.0000000000000001e-293 or 0.5 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

   if -1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. associate--l+ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. associate-*r/ 81.4%

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

      5. div-sub 81.4%

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

      6. distribute-lft-out-- 81.4%

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

      7. mul-1-neg 81.4%

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

      8. distribute-neg-frac 81.4%

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

      9. unsub-neg 81.4%

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

      10. distribute-rgt-out-- 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. mul-1-neg 81.4%

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

      3. *-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. neg-sub0 81.4%

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

      6. associate--r- 81.4%

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

      7. neg-sub0 81.4%

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

      8. distribute-rgt-out 81.4%

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

      9. +-commutative 81.4%

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

      10. distribute-rgt-out 81.4%

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

      11. sub-neg 81.4%

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

      12. *-commutative 81.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.5

   1. Initial program 77.9%

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

   2. Taylor expanded in x around -inf 99.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z} + -1 \cdot \left(\left(\frac{y}{a - z} - \left(\frac{z}{a - z} + 1\right)\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-293}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0.5:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \end{array} \]

Alternative 4: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-293) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ x 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-293) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / z) * (y - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-293)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((x / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((x / 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-293) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((x / 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-293) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x / 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-293) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((x / 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-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $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)))) < -1.0000000000000001e-293 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.0%

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

   if -1.0000000000000001e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. associate--l+ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. associate-*r/ 81.4%

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

      5. div-sub 81.4%

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

      6. distribute-lft-out-- 81.4%

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

      7. mul-1-neg 81.4%

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

      8. distribute-neg-frac 81.4%

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

      9. unsub-neg 81.4%

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

      10. distribute-rgt-out-- 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. mul-1-neg 81.4%

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

      3. *-commutative 81.4%

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

      4. distribute-rgt-neg-in 81.4%

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

      5. neg-sub0 81.4%

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

      6. associate--r- 81.4%

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

      7. neg-sub0 81.4%

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

      8. distribute-rgt-out 81.4%

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

      9. +-commutative 81.4%

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

      10. distribute-rgt-out 81.4%

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

      11. sub-neg 81.4%

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

      12. *-commutative 81.4%

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

      13. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-293} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 5: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ t (* (/ x z) (- y a)))))
   (if (<= z -1.1e+202)
     t_2
     (if (<= z -2.55e+124)
       t_1
       (if (<= z -7e+61)
         t_2
         (if (<= z -2.05e-129)
           (- x (* y (/ (- x t) a)))
           (if (<= z -7.7e-205)
             (/ y (/ (- a z) (- t x)))
             (if (<= z 1.95e+30)
               (+ x (/ y (/ a (- t x))))
               (if (<= z 2e+71)
                 t_1
                 (if (<= z 9.8e+76) (+ x (/ (* y t) a)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_2;
	} else if (z <= -2.55e+124) {
		tmp = t_1;
	} else if (z <= -7e+61) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = x - (y * ((x - t) / a));
	} else if (z <= -7.7e-205) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.95e+30) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 2e+71) {
		tmp = t_1;
	} else if (z <= 9.8e+76) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t + ((x / z) * (y - a))
    if (z <= (-1.1d+202)) then
        tmp = t_2
    else if (z <= (-2.55d+124)) then
        tmp = t_1
    else if (z <= (-7d+61)) then
        tmp = t_2
    else if (z <= (-2.05d-129)) then
        tmp = x - (y * ((x - t) / a))
    else if (z <= (-7.7d-205)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 1.95d+30) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 2d+71) then
        tmp = t_1
    else if (z <= 9.8d+76) then
        tmp = x + ((y * t) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_2;
	} else if (z <= -2.55e+124) {
		tmp = t_1;
	} else if (z <= -7e+61) {
		tmp = t_2;
	} else if (z <= -2.05e-129) {
		tmp = x - (y * ((x - t) / a));
	} else if (z <= -7.7e-205) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.95e+30) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 2e+71) {
		tmp = t_1;
	} else if (z <= 9.8e+76) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + ((x / z) * (y - a))
	tmp = 0
	if z <= -1.1e+202:
		tmp = t_2
	elif z <= -2.55e+124:
		tmp = t_1
	elif z <= -7e+61:
		tmp = t_2
	elif z <= -2.05e-129:
		tmp = x - (y * ((x - t) / a))
	elif z <= -7.7e-205:
		tmp = y / ((a - z) / (t - x))
	elif z <= 1.95e+30:
		tmp = x + (y / (a / (t - x)))
	elif z <= 2e+71:
		tmp = t_1
	elif z <= 9.8e+76:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(x / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -1.1e+202)
		tmp = t_2;
	elseif (z <= -2.55e+124)
		tmp = t_1;
	elseif (z <= -7e+61)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (z <= -7.7e-205)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 1.95e+30)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 2e+71)
		tmp = t_1;
	elseif (z <= 9.8e+76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t + ((x / z) * (y - a));
	tmp = 0.0;
	if (z <= -1.1e+202)
		tmp = t_2;
	elseif (z <= -2.55e+124)
		tmp = t_1;
	elseif (z <= -7e+61)
		tmp = t_2;
	elseif (z <= -2.05e-129)
		tmp = x - (y * ((x - t) / a));
	elseif (z <= -7.7e-205)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 1.95e+30)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 2e+71)
		tmp = t_1;
	elseif (z <= 9.8e+76)
		tmp = x + ((y * t) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+202], t$95$2, If[LessEqual[z, -2.55e+124], t$95$1, If[LessEqual[z, -7e+61], t$95$2, If[LessEqual[z, -2.05e-129], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.7e-205], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+30], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+71], t$95$1, If[LessEqual[z, 9.8e+76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.09999999999999989e202 or -2.5499999999999999e124 < z < -7.00000000000000036e61 or 9.80000000000000053e76 < z

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate--l+ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. associate-*r/ 62.7%

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

      5. div-sub 62.7%

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

      6. distribute-lft-out-- 62.7%

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

      7. mul-1-neg 62.7%

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

      8. distribute-neg-frac 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in t around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. mul-1-neg 71.1%

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

      3. *-commutative 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. neg-sub0 71.1%

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

      6. associate--r- 71.1%

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

      7. neg-sub0 71.1%

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

      8. distribute-rgt-out 69.8%

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

      9. +-commutative 69.8%

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

      10. distribute-rgt-out 71.1%

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

      11. sub-neg 71.1%

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

      12. *-commutative 71.1%

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

      13. associate-*r/ 79.2%

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

   7. Simplified 79.2%

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

   if -1.09999999999999989e202 < z < -2.5499999999999999e124 or 1.95000000000000005e30 < z < 2.0000000000000001e71

   1. Initial program 84.5%

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

   2. Taylor expanded in t around inf 77.2%

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

      1. div-sub 77.2%

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

   4. Simplified 77.2%

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

   if -7.00000000000000036e61 < z < -2.05e-129

   1. Initial program 99.2%

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

   2. Taylor expanded in a around inf 69.6%

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

      1. +-commutative 69.6%

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

      2. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in y around inf 61.9%

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

      1. associate-*r/ 67.1%

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

   7. Simplified 67.1%

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

   if -2.05e-129 < z < -7.7000000000000001e-205

   1. Initial program 85.3%

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

   2. Taylor expanded in y around inf 81.0%

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

      1. div-sub 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r/ 77.8%

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

      4. associate-/l* 81.1%

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

   4. Simplified 81.1%

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

   if -7.7000000000000001e-205 < z < 1.95000000000000005e30

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 81.1%

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

   4. Simplified 81.1%

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

   if 2.0000000000000001e71 < z < 9.80000000000000053e76

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 6: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\left(--1\right) - \frac{a}{z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- (- -1.0) (/ a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.42e+226)
     t
     (if (<= z -8.2e+198)
       (* x (/ (- y a) z))
       (if (<= z -5e+72)
         t_1
         (if (<= z -9.5e-258)
           t_2
           (if (<= z 1.38e-272)
             (+ x (/ (* y t) a))
             (if (<= z 1.6e-185)
               t_2
               (if (<= z 2.5e-152)
                 (/ t (/ (- a z) y))
                 (if (<= z 1.85e+83) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (-(-1.0) - (a / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.42e+226) {
		tmp = t;
	} else if (z <= -8.2e+198) {
		tmp = x * ((y - a) / z);
	} else if (z <= -5e+72) {
		tmp = t_1;
	} else if (z <= -9.5e-258) {
		tmp = t_2;
	} else if (z <= 1.38e-272) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e-185) {
		tmp = t_2;
	} else if (z <= 2.5e-152) {
		tmp = t / ((a - z) / y);
	} else if (z <= 1.85e+83) {
		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 / (-(-1.0d0) - (a / z))
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.42d+226)) then
        tmp = t
    else if (z <= (-8.2d+198)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-5d+72)) then
        tmp = t_1
    else if (z <= (-9.5d-258)) then
        tmp = t_2
    else if (z <= 1.38d-272) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.6d-185) then
        tmp = t_2
    else if (z <= 2.5d-152) then
        tmp = t / ((a - z) / y)
    else if (z <= 1.85d+83) 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 / (-(-1.0) - (a / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.42e+226) {
		tmp = t;
	} else if (z <= -8.2e+198) {
		tmp = x * ((y - a) / z);
	} else if (z <= -5e+72) {
		tmp = t_1;
	} else if (z <= -9.5e-258) {
		tmp = t_2;
	} else if (z <= 1.38e-272) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e-185) {
		tmp = t_2;
	} else if (z <= 2.5e-152) {
		tmp = t / ((a - z) / y);
	} else if (z <= 1.85e+83) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (-(-1.0) - (a / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.42e+226:
		tmp = t
	elif z <= -8.2e+198:
		tmp = x * ((y - a) / z)
	elif z <= -5e+72:
		tmp = t_1
	elif z <= -9.5e-258:
		tmp = t_2
	elif z <= 1.38e-272:
		tmp = x + ((y * t) / a)
	elif z <= 1.6e-185:
		tmp = t_2
	elif z <= 2.5e-152:
		tmp = t / ((a - z) / y)
	elif z <= 1.85e+83:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(-(-1.0)) - Float64(a / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.42e+226)
		tmp = t;
	elseif (z <= -8.2e+198)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -5e+72)
		tmp = t_1;
	elseif (z <= -9.5e-258)
		tmp = t_2;
	elseif (z <= 1.38e-272)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.6e-185)
		tmp = t_2;
	elseif (z <= 2.5e-152)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	elseif (z <= 1.85e+83)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (-(-1.0) - (a / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.42e+226)
		tmp = t;
	elseif (z <= -8.2e+198)
		tmp = x * ((y - a) / z);
	elseif (z <= -5e+72)
		tmp = t_1;
	elseif (z <= -9.5e-258)
		tmp = t_2;
	elseif (z <= 1.38e-272)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.6e-185)
		tmp = t_2;
	elseif (z <= 2.5e-152)
		tmp = t / ((a - z) / y);
	elseif (z <= 1.85e+83)
		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[((--1.0) - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.42e+226], t, If[LessEqual[z, -8.2e+198], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e+72], t$95$1, If[LessEqual[z, -9.5e-258], t$95$2, If[LessEqual[z, 1.38e-272], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-185], t$95$2, If[LessEqual[z, 2.5e-152], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+83], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.42e226

   1. Initial program 76.1%

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

   2. Taylor expanded in z around inf 76.1%

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

   if -1.42e226 < z < -8.2000000000000003e198

   1. Initial program 51.2%

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

   2. Taylor expanded in x around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. unsub-neg 35.8%

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

   4. Simplified 35.8%

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

   5. Taylor expanded in z around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. sub-neg 77.4%

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

      3. mul-1-neg 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in a around 0 30.0%

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

      1. associate-/l* 44.3%

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

      2. associate-/r/ 45.1%

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

      3. mul-1-neg 45.1%

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

      4. associate-*l/ 77.4%

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

      5. distribute-lft-neg-in 77.4%

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

      6. distribute-rgt-in 77.4%

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

      7. sub-neg 77.4%

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

      8. div-sub 77.4%

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

   10. Simplified 77.4%

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

   if -8.2000000000000003e198 < z < -4.99999999999999992e72 or 1.8500000000000001e83 < z

   1. Initial program 65.5%

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

   2. Taylor expanded in x around 0 33.3%

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

      1. associate-/l* 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in y around 0 49.5%

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

      1. mul-1-neg 49.5%

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

      2. div-sub 49.5%

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

      3. sub-neg 49.5%

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

      4. *-inverses 49.5%

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

      5. metadata-eval 49.5%

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

   7. Simplified 49.5%

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

   if -4.99999999999999992e72 < z < -9.5000000000000009e-258 or 1.37999999999999997e-272 < z < 1.5999999999999999e-185 or 2.4999999999999998e-152 < z < 1.8500000000000001e83

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in z around 0 57.5%

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

   if -9.5000000000000009e-258 < z < 1.37999999999999997e-272

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-/l* 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in t around inf 88.6%

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

   6. Taylor expanded in z around 0 88.4%

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

   if 1.5999999999999999e-185 < z < 2.4999999999999998e-152

   1. Initial program 65.0%

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

   2. Taylor expanded in x around 0 76.4%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{a}{z}}\\ \end{array} \]

Alternative 7: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.05e+226)
     t
     (if (<= z -4.4e+196)
       (* x (/ (- y a) z))
       (if (<= z -8e+75)
         t
         (if (<= z -9e-257)
           t_2
           (if (<= z 9.5e-270)
             t_1
             (if (<= z 4.6e-194)
               t_2
               (if (<= z 5.6e-71) t_1 (if (<= z 2.4e+112) t_2 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t;
	} else if (z <= -4.4e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -8e+75) {
		tmp = t;
	} else if (z <= -9e-257) {
		tmp = t_2;
	} else if (z <= 9.5e-270) {
		tmp = t_1;
	} else if (z <= 4.6e-194) {
		tmp = t_2;
	} else if (z <= 5.6e-71) {
		tmp = t_1;
	} else if (z <= 2.4e+112) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-2.05d+226)) then
        tmp = t
    else if (z <= (-4.4d+196)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-8d+75)) then
        tmp = t
    else if (z <= (-9d-257)) then
        tmp = t_2
    else if (z <= 9.5d-270) then
        tmp = t_1
    else if (z <= 4.6d-194) then
        tmp = t_2
    else if (z <= 5.6d-71) then
        tmp = t_1
    else if (z <= 2.4d+112) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.05e+226) {
		tmp = t;
	} else if (z <= -4.4e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -8e+75) {
		tmp = t;
	} else if (z <= -9e-257) {
		tmp = t_2;
	} else if (z <= 9.5e-270) {
		tmp = t_1;
	} else if (z <= 4.6e-194) {
		tmp = t_2;
	} else if (z <= 5.6e-71) {
		tmp = t_1;
	} else if (z <= 2.4e+112) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.05e+226:
		tmp = t
	elif z <= -4.4e+196:
		tmp = x * ((y - a) / z)
	elif z <= -8e+75:
		tmp = t
	elif z <= -9e-257:
		tmp = t_2
	elif z <= 9.5e-270:
		tmp = t_1
	elif z <= 4.6e-194:
		tmp = t_2
	elif z <= 5.6e-71:
		tmp = t_1
	elif z <= 2.4e+112:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.05e+226)
		tmp = t;
	elseif (z <= -4.4e+196)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -8e+75)
		tmp = t;
	elseif (z <= -9e-257)
		tmp = t_2;
	elseif (z <= 9.5e-270)
		tmp = t_1;
	elseif (z <= 4.6e-194)
		tmp = t_2;
	elseif (z <= 5.6e-71)
		tmp = t_1;
	elseif (z <= 2.4e+112)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.05e+226)
		tmp = t;
	elseif (z <= -4.4e+196)
		tmp = x * ((y - a) / z);
	elseif (z <= -8e+75)
		tmp = t;
	elseif (z <= -9e-257)
		tmp = t_2;
	elseif (z <= 9.5e-270)
		tmp = t_1;
	elseif (z <= 4.6e-194)
		tmp = t_2;
	elseif (z <= 5.6e-71)
		tmp = t_1;
	elseif (z <= 2.4e+112)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+226], t, If[LessEqual[z, -4.4e+196], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e+75], t, If[LessEqual[z, -9e-257], t$95$2, If[LessEqual[z, 9.5e-270], t$95$1, If[LessEqual[z, 4.6e-194], t$95$2, If[LessEqual[z, 5.6e-71], t$95$1, If[LessEqual[z, 2.4e+112], t$95$2, t]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.04999999999999993e226 or -4.39999999999999995e196 < z < -7.99999999999999941e75 or 2.4e112 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in z around inf 46.5%

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

   if -2.04999999999999993e226 < z < -4.39999999999999995e196

   1. Initial program 58.2%

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

   2. Taylor expanded in x around inf 31.4%

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

      1. mul-1-neg 31.4%

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

      2. unsub-neg 31.4%

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

   4. Simplified 31.4%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. sub-neg 66.7%

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

      3. mul-1-neg 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in a around 0 26.0%

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

      1. associate-/l* 38.4%

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

      2. associate-/r/ 39.0%

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

      3. mul-1-neg 39.0%

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

      4. associate-*l/ 66.7%

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

      5. distribute-lft-neg-in 66.7%

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

      6. distribute-rgt-in 66.7%

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

      7. sub-neg 66.7%

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

      8. div-sub 66.7%

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

   10. Simplified 66.7%

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

   if -7.99999999999999941e75 < z < -9.0000000000000005e-257 or 9.5000000000000006e-270 < z < 4.60000000000000005e-194 or 5.60000000000000001e-71 < z < 2.4e112

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. unsub-neg 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in z around 0 55.5%

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

   if -9.0000000000000005e-257 < z < 9.5000000000000006e-270 or 4.60000000000000005e-194 < z < 5.60000000000000001e-71

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in t around inf 80.5%

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

   6. Taylor expanded in z around 0 79.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-270}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -7.1 \cdot 10^{+227}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -7.1e+227)
     t
     (if (<= z -8.8e+196)
       (* x (/ (- y a) z))
       (if (<= z -2.7e+75)
         t
         (if (<= z -6e-256)
           t_1
           (if (<= z 1.05e-274)
             (+ x (/ (* y t) a))
             (if (<= z 1.65e-185)
               t_1
               (if (<= z 5.4e-152)
                 (/ t (/ (- a z) y))
                 (if (<= z 4.15e+111) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7.1e+227) {
		tmp = t;
	} else if (z <= -8.8e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.7e+75) {
		tmp = t;
	} else if (z <= -6e-256) {
		tmp = t_1;
	} else if (z <= 1.05e-274) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 5.4e-152) {
		tmp = t / ((a - z) / y);
	} else if (z <= 4.15e+111) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-7.1d+227)) then
        tmp = t
    else if (z <= (-8.8d+196)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-2.7d+75)) then
        tmp = t
    else if (z <= (-6d-256)) then
        tmp = t_1
    else if (z <= 1.05d-274) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.65d-185) then
        tmp = t_1
    else if (z <= 5.4d-152) then
        tmp = t / ((a - z) / y)
    else if (z <= 4.15d+111) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7.1e+227) {
		tmp = t;
	} else if (z <= -8.8e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.7e+75) {
		tmp = t;
	} else if (z <= -6e-256) {
		tmp = t_1;
	} else if (z <= 1.05e-274) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 5.4e-152) {
		tmp = t / ((a - z) / y);
	} else if (z <= 4.15e+111) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -7.1e+227:
		tmp = t
	elif z <= -8.8e+196:
		tmp = x * ((y - a) / z)
	elif z <= -2.7e+75:
		tmp = t
	elif z <= -6e-256:
		tmp = t_1
	elif z <= 1.05e-274:
		tmp = x + ((y * t) / a)
	elif z <= 1.65e-185:
		tmp = t_1
	elif z <= 5.4e-152:
		tmp = t / ((a - z) / y)
	elif z <= 4.15e+111:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -7.1e+227)
		tmp = t;
	elseif (z <= -8.8e+196)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -2.7e+75)
		tmp = t;
	elseif (z <= -6e-256)
		tmp = t_1;
	elseif (z <= 1.05e-274)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 5.4e-152)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	elseif (z <= 4.15e+111)
		tmp = t_1;
	else
		tmp = t;
	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 (z <= -7.1e+227)
		tmp = t;
	elseif (z <= -8.8e+196)
		tmp = x * ((y - a) / z);
	elseif (z <= -2.7e+75)
		tmp = t;
	elseif (z <= -6e-256)
		tmp = t_1;
	elseif (z <= 1.05e-274)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 5.4e-152)
		tmp = t / ((a - z) / y);
	elseif (z <= 4.15e+111)
		tmp = t_1;
	else
		tmp = t;
	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[z, -7.1e+227], t, If[LessEqual[z, -8.8e+196], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e+75], t, If[LessEqual[z, -6e-256], t$95$1, If[LessEqual[z, 1.05e-274], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-185], t$95$1, If[LessEqual[z, 5.4e-152], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.15e+111], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.1000000000000002e227 or -8.7999999999999999e196 < z < -2.69999999999999998e75 or 4.14999999999999988e111 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in z around inf 46.5%

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

   if -7.1000000000000002e227 < z < -8.7999999999999999e196

   1. Initial program 58.2%

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

   2. Taylor expanded in x around inf 31.4%

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

      1. mul-1-neg 31.4%

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

      2. unsub-neg 31.4%

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

   4. Simplified 31.4%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. sub-neg 66.7%

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

      3. mul-1-neg 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in a around 0 26.0%

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

      1. associate-/l* 38.4%

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

      2. associate-/r/ 39.0%

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

      3. mul-1-neg 39.0%

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

      4. associate-*l/ 66.7%

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

      5. distribute-lft-neg-in 66.7%

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

      6. distribute-rgt-in 66.7%

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

      7. sub-neg 66.7%

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

      8. div-sub 66.7%

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

   10. Simplified 66.7%

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

   if -2.69999999999999998e75 < z < -5.9999999999999996e-256 or 1.04999999999999997e-274 < z < 1.6499999999999999e-185 or 5.39999999999999997e-152 < z < 4.14999999999999988e111

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in z around 0 56.2%

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

   if -5.9999999999999996e-256 < z < 1.04999999999999997e-274

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-/l* 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in t around inf 88.6%

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

   6. Taylor expanded in z around 0 88.4%

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

   if 1.6499999999999999e-185 < z < 5.39999999999999997e-152

   1. Initial program 65.0%

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

   2. Taylor expanded in x around 0 76.4%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+227}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-152}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{z} \cdot \left(y - a\right)\\ t_2 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x z) (- y a)))) (t_2 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= z -1.1e+202)
     t_1
     (if (<= z -9.4e+123)
       (* t (/ (- y z) (- a z)))
       (if (<= z -1.18e+67)
         t_1
         (if (<= z -7.8e-179)
           t_2
           (if (<= z -7.7e-205)
             (/ (* y (- t x)) (- a z))
             (if (<= z 1.85e+78) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x / z) * (y - a));
	double t_2 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_1;
	} else if (z <= -9.4e+123) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.18e+67) {
		tmp = t_1;
	} else if (z <= -7.8e-179) {
		tmp = t_2;
	} else if (z <= -7.7e-205) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.85e+78) {
		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 + ((x / z) * (y - a))
    t_2 = x + ((y - z) / (a / (t - x)))
    if (z <= (-1.1d+202)) then
        tmp = t_1
    else if (z <= (-9.4d+123)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-1.18d+67)) then
        tmp = t_1
    else if (z <= (-7.8d-179)) then
        tmp = t_2
    else if (z <= (-7.7d-205)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 1.85d+78) 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 + ((x / z) * (y - a));
	double t_2 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_1;
	} else if (z <= -9.4e+123) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.18e+67) {
		tmp = t_1;
	} else if (z <= -7.8e-179) {
		tmp = t_2;
	} else if (z <= -7.7e-205) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.85e+78) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x / z) * (y - a))
	t_2 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if z <= -1.1e+202:
		tmp = t_1
	elif z <= -9.4e+123:
		tmp = t * ((y - z) / (a - z))
	elif z <= -1.18e+67:
		tmp = t_1
	elif z <= -7.8e-179:
		tmp = t_2
	elif z <= -7.7e-205:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 1.85e+78:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x / z) * Float64(y - a)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.1e+202)
		tmp = t_1;
	elseif (z <= -9.4e+123)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -1.18e+67)
		tmp = t_1;
	elseif (z <= -7.8e-179)
		tmp = t_2;
	elseif (z <= -7.7e-205)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 1.85e+78)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x / z) * (y - a));
	t_2 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (z <= -1.1e+202)
		tmp = t_1;
	elseif (z <= -9.4e+123)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -1.18e+67)
		tmp = t_1;
	elseif (z <= -7.8e-179)
		tmp = t_2;
	elseif (z <= -7.7e-205)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 1.85e+78)
		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[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+202], t$95$1, If[LessEqual[z, -9.4e+123], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e+67], t$95$1, If[LessEqual[z, -7.8e-179], t$95$2, If[LessEqual[z, -7.7e-205], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+78], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.09999999999999989e202 or -9.39999999999999958e123 < z < -1.17999999999999998e67 or 1.84999999999999992e78 < z

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate--l+ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. associate-*r/ 62.7%

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

      5. div-sub 62.7%

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

      6. distribute-lft-out-- 62.7%

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

      7. mul-1-neg 62.7%

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

      8. distribute-neg-frac 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in t around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. mul-1-neg 71.1%

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

      3. *-commutative 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. neg-sub0 71.1%

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

      6. associate--r- 71.1%

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

      7. neg-sub0 71.1%

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

      8. distribute-rgt-out 69.8%

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

      9. +-commutative 69.8%

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

      10. distribute-rgt-out 71.1%

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

      11. sub-neg 71.1%

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

      12. *-commutative 71.1%

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

      13. associate-*r/ 79.2%

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

   7. Simplified 79.2%

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

   if -1.09999999999999989e202 < z < -9.39999999999999958e123

   1. Initial program 85.9%

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

   2. Taylor expanded in t around inf 76.7%

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

      1. div-sub 76.7%

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

   4. Simplified 76.7%

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

   if -1.17999999999999998e67 < z < -7.8000000000000005e-179 or -7.7000000000000001e-205 < z < 1.84999999999999992e78

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   if -7.8000000000000005e-179 < z < -7.7000000000000001e-205

   1. Initial program 82.1%

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

   2. Taylor expanded in y around inf 82.7%

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

      1. div-sub 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-*r/ 85.3%

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

   4. Simplified 85.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+67}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 10: 57.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -75000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-253}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.5e+106)
     t_2
     (if (<= t -75000000.0)
       t_1
       (if (<= t -8.2e-88)
         t_2
         (if (<= t -1.75e-253)
           (- x (/ (* x y) a))
           (if (<= t 7.8e-305)
             (/ (- x) (/ z (- a y)))
             (if (<= t 1.3e-27) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.5e+106) {
		tmp = t_2;
	} else if (t <= -75000000.0) {
		tmp = t_1;
	} else if (t <= -8.2e-88) {
		tmp = t_2;
	} else if (t <= -1.75e-253) {
		tmp = x - ((x * y) / a);
	} else if (t <= 7.8e-305) {
		tmp = -x / (z / (a - y));
	} else if (t <= 1.3e-27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-3.5d+106)) then
        tmp = t_2
    else if (t <= (-75000000.0d0)) then
        tmp = t_1
    else if (t <= (-8.2d-88)) then
        tmp = t_2
    else if (t <= (-1.75d-253)) then
        tmp = x - ((x * y) / a)
    else if (t <= 7.8d-305) then
        tmp = -x / (z / (a - y))
    else if (t <= 1.3d-27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.5e+106) {
		tmp = t_2;
	} else if (t <= -75000000.0) {
		tmp = t_1;
	} else if (t <= -8.2e-88) {
		tmp = t_2;
	} else if (t <= -1.75e-253) {
		tmp = x - ((x * y) / a);
	} else if (t <= 7.8e-305) {
		tmp = -x / (z / (a - y));
	} else if (t <= 1.3e-27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.5e+106:
		tmp = t_2
	elif t <= -75000000.0:
		tmp = t_1
	elif t <= -8.2e-88:
		tmp = t_2
	elif t <= -1.75e-253:
		tmp = x - ((x * y) / a)
	elif t <= 7.8e-305:
		tmp = -x / (z / (a - y))
	elif t <= 1.3e-27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.5e+106)
		tmp = t_2;
	elseif (t <= -75000000.0)
		tmp = t_1;
	elseif (t <= -8.2e-88)
		tmp = t_2;
	elseif (t <= -1.75e-253)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (t <= 7.8e-305)
		tmp = Float64(Float64(-x) / Float64(z / Float64(a - y)));
	elseif (t <= 1.3e-27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.5e+106)
		tmp = t_2;
	elseif (t <= -75000000.0)
		tmp = t_1;
	elseif (t <= -8.2e-88)
		tmp = t_2;
	elseif (t <= -1.75e-253)
		tmp = x - ((x * y) / a);
	elseif (t <= 7.8e-305)
		tmp = -x / (z / (a - y));
	elseif (t <= 1.3e-27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+106], t$95$2, If[LessEqual[t, -75000000.0], t$95$1, If[LessEqual[t, -8.2e-88], t$95$2, If[LessEqual[t, -1.75e-253], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-305], N[((-x) / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-27], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.49999999999999981e106 or -7.5e7 < t < -8.2000000000000002e-88 or 1.30000000000000009e-27 < t

   1. Initial program 89.7%

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

   2. Taylor expanded in t around inf 75.3%

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

      1. div-sub 75.3%

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

   4. Simplified 75.3%

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

   if -3.49999999999999981e106 < t < -7.5e7 or 7.8000000000000005e-305 < t < 1.30000000000000009e-27

   1. Initial program 80.0%

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

   2. Taylor expanded in x around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in z around 0 62.3%

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

   if -8.2000000000000002e-88 < t < -1.75000000000000011e-253

   1. Initial program 72.9%

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

   2. Taylor expanded in t around 0 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. associate-/l* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around 0 49.6%

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

   if -1.75000000000000011e-253 < t < 7.8000000000000005e-305

   1. Initial program 39.8%

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

   2. Taylor expanded in x around inf 42.6%

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

      1. mul-1-neg 42.6%

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

      2. unsub-neg 42.6%

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

   4. Simplified 42.6%

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

   5. Taylor expanded in z around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. *-commutative 51.8%

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

      3. mul-1-neg 51.8%

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

      4. sub-neg 51.8%

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

      5. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -75000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-253}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 11: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ t (* x (/ (- y a) z)))))
   (if (<= z -4.9e+197)
     t_2
     (if (<= z -1.2e+125)
       t_1
       (if (<= z -5.8e+66)
         t_2
         (if (<= z 6.2e+28)
           (+ x (/ y (/ a (- t x))))
           (if (<= z 5.4e+69)
             t_1
             (if (<= z 2e+77) (+ x (/ (* y t) a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.9e+197) {
		tmp = t_2;
	} else if (z <= -1.2e+125) {
		tmp = t_1;
	} else if (z <= -5.8e+66) {
		tmp = t_2;
	} else if (z <= 6.2e+28) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.4e+69) {
		tmp = t_1;
	} else if (z <= 2e+77) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t + (x * ((y - a) / z))
    if (z <= (-4.9d+197)) then
        tmp = t_2
    else if (z <= (-1.2d+125)) then
        tmp = t_1
    else if (z <= (-5.8d+66)) then
        tmp = t_2
    else if (z <= 6.2d+28) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 5.4d+69) then
        tmp = t_1
    else if (z <= 2d+77) then
        tmp = x + ((y * t) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -4.9e+197) {
		tmp = t_2;
	} else if (z <= -1.2e+125) {
		tmp = t_1;
	} else if (z <= -5.8e+66) {
		tmp = t_2;
	} else if (z <= 6.2e+28) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.4e+69) {
		tmp = t_1;
	} else if (z <= 2e+77) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -4.9e+197:
		tmp = t_2
	elif z <= -1.2e+125:
		tmp = t_1
	elif z <= -5.8e+66:
		tmp = t_2
	elif z <= 6.2e+28:
		tmp = x + (y / (a / (t - x)))
	elif z <= 5.4e+69:
		tmp = t_1
	elif z <= 2e+77:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -4.9e+197)
		tmp = t_2;
	elseif (z <= -1.2e+125)
		tmp = t_1;
	elseif (z <= -5.8e+66)
		tmp = t_2;
	elseif (z <= 6.2e+28)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 5.4e+69)
		tmp = t_1;
	elseif (z <= 2e+77)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -4.9e+197)
		tmp = t_2;
	elseif (z <= -1.2e+125)
		tmp = t_1;
	elseif (z <= -5.8e+66)
		tmp = t_2;
	elseif (z <= 6.2e+28)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 5.4e+69)
		tmp = t_1;
	elseif (z <= 2e+77)
		tmp = x + ((y * t) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+197], t$95$2, If[LessEqual[z, -1.2e+125], t$95$1, If[LessEqual[z, -5.8e+66], t$95$2, If[LessEqual[z, 6.2e+28], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+69], t$95$1, If[LessEqual[z, 2e+77], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.90000000000000026e197 or -1.2e125 < z < -5.79999999999999972e66 or 1.99999999999999997e77 < z

   1. Initial program 62.9%

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

   2. Taylor expanded in z around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. associate--l+ 62.5%

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

      3. associate-*r/ 62.5%

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

      4. associate-*r/ 62.5%

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

      5. div-sub 62.5%

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

      6. distribute-lft-out-- 62.5%

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

      7. mul-1-neg 62.5%

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

      8. distribute-neg-frac 62.5%

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

      9. unsub-neg 62.5%

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

      10. distribute-rgt-out-- 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in y around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. div-sub 71.9%

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

      5. associate-*r/ 62.5%

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

      6. associate-/l* 70.3%

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

      7. associate-/l* 80.3%

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

      8. div-sub 80.2%

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

      9. associate-/l* 63.9%

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

      10. *-commutative 63.9%

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

      11. associate-*r/ 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in t around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. associate-*r* 69.6%

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

      3. neg-mul-1 69.6%

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

      4. neg-sub0 69.6%

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

      5. associate--r- 69.6%

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

      6. neg-sub0 69.6%

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

      7. +-commutative 69.6%

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

      8. sub-neg 69.6%

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

      9. *-commutative 69.6%

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

      10. associate-*r/ 76.5%

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

   10. Simplified 76.5%

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

   if -4.90000000000000026e197 < z < -1.2e125 or 6.2000000000000001e28 < z < 5.3999999999999996e69

   1. Initial program 83.4%

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

   2. Taylor expanded in t around inf 79.2%

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

      1. div-sub 79.2%

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

   4. Simplified 79.2%

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

   if -5.79999999999999972e66 < z < 6.2000000000000001e28

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 73.6%

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

   4. Simplified 73.6%

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

   if 5.3999999999999996e69 < z < 1.99999999999999997e77

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+197}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 12: 69.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ t (* (/ x z) (- y a)))))
   (if (<= z -1.1e+202)
     t_2
     (if (<= z -1.55e+123)
       t_1
       (if (<= z -1.25e+61)
         t_2
         (if (<= z 8.8e+29)
           (+ x (/ y (/ a (- t x))))
           (if (<= z 5.6e+69)
             t_1
             (if (<= z 9.8e+76) (+ x (/ (* y t) a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_2;
	} else if (z <= -1.55e+123) {
		tmp = t_1;
	} else if (z <= -1.25e+61) {
		tmp = t_2;
	} else if (z <= 8.8e+29) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.6e+69) {
		tmp = t_1;
	} else if (z <= 9.8e+76) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t + ((x / z) * (y - a))
    if (z <= (-1.1d+202)) then
        tmp = t_2
    else if (z <= (-1.55d+123)) then
        tmp = t_1
    else if (z <= (-1.25d+61)) then
        tmp = t_2
    else if (z <= 8.8d+29) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 5.6d+69) then
        tmp = t_1
    else if (z <= 9.8d+76) then
        tmp = x + ((y * t) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t + ((x / z) * (y - a));
	double tmp;
	if (z <= -1.1e+202) {
		tmp = t_2;
	} else if (z <= -1.55e+123) {
		tmp = t_1;
	} else if (z <= -1.25e+61) {
		tmp = t_2;
	} else if (z <= 8.8e+29) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 5.6e+69) {
		tmp = t_1;
	} else if (z <= 9.8e+76) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + ((x / z) * (y - a))
	tmp = 0
	if z <= -1.1e+202:
		tmp = t_2
	elif z <= -1.55e+123:
		tmp = t_1
	elif z <= -1.25e+61:
		tmp = t_2
	elif z <= 8.8e+29:
		tmp = x + (y / (a / (t - x)))
	elif z <= 5.6e+69:
		tmp = t_1
	elif z <= 9.8e+76:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(x / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -1.1e+202)
		tmp = t_2;
	elseif (z <= -1.55e+123)
		tmp = t_1;
	elseif (z <= -1.25e+61)
		tmp = t_2;
	elseif (z <= 8.8e+29)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 5.6e+69)
		tmp = t_1;
	elseif (z <= 9.8e+76)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t + ((x / z) * (y - a));
	tmp = 0.0;
	if (z <= -1.1e+202)
		tmp = t_2;
	elseif (z <= -1.55e+123)
		tmp = t_1;
	elseif (z <= -1.25e+61)
		tmp = t_2;
	elseif (z <= 8.8e+29)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 5.6e+69)
		tmp = t_1;
	elseif (z <= 9.8e+76)
		tmp = x + ((y * t) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+202], t$95$2, If[LessEqual[z, -1.55e+123], t$95$1, If[LessEqual[z, -1.25e+61], t$95$2, If[LessEqual[z, 8.8e+29], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+69], t$95$1, If[LessEqual[z, 9.8e+76], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.09999999999999989e202 or -1.55000000000000003e123 < z < -1.25000000000000004e61 or 9.80000000000000053e76 < z

   1. Initial program 62.0%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate--l+ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. associate-*r/ 62.7%

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

      5. div-sub 62.7%

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

      6. distribute-lft-out-- 62.7%

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

      7. mul-1-neg 62.7%

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

      8. distribute-neg-frac 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in t around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. mul-1-neg 71.1%

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

      3. *-commutative 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. neg-sub0 71.1%

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

      6. associate--r- 71.1%

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

      7. neg-sub0 71.1%

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

      8. distribute-rgt-out 69.8%

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

      9. +-commutative 69.8%

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

      10. distribute-rgt-out 71.1%

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

      11. sub-neg 71.1%

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

      12. *-commutative 71.1%

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

      13. associate-*r/ 79.2%

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

   7. Simplified 79.2%

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

   if -1.09999999999999989e202 < z < -1.55000000000000003e123 or 8.8000000000000005e29 < z < 5.59999999999999964e69

   1. Initial program 84.5%

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

   2. Taylor expanded in t around inf 77.2%

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

      1. div-sub 77.2%

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

   4. Simplified 77.2%

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

   if -1.25000000000000004e61 < z < 8.8000000000000005e29

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 73.6%

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

   4. Simplified 73.6%

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

   if 5.59999999999999964e69 < z < 9.80000000000000053e76

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+202}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 13: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.6e+69)
     (/ t (/ (- z) (- y z)))
     (if (<= z -1.25e-255)
       t_1
       (if (<= z 6.5e-274)
         (+ x (/ (* y t) a))
         (if (<= z 1.65e-185)
           t_1
           (if (<= z 5e-153)
             (/ t (/ (- a z) y))
             (if (<= z 8.2e+82) t_1 (/ t (- (- -1.0) (/ a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.6e+69) {
		tmp = t / (-z / (y - z));
	} else if (z <= -1.25e-255) {
		tmp = t_1;
	} else if (z <= 6.5e-274) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 5e-153) {
		tmp = t / ((a - z) / y);
	} else if (z <= 8.2e+82) {
		tmp = t_1;
	} else {
		tmp = t / (-(-1.0) - (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-3.6d+69)) then
        tmp = t / (-z / (y - z))
    else if (z <= (-1.25d-255)) then
        tmp = t_1
    else if (z <= 6.5d-274) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.65d-185) then
        tmp = t_1
    else if (z <= 5d-153) then
        tmp = t / ((a - z) / y)
    else if (z <= 8.2d+82) then
        tmp = t_1
    else
        tmp = t / (-(-1.0d0) - (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.6e+69) {
		tmp = t / (-z / (y - z));
	} else if (z <= -1.25e-255) {
		tmp = t_1;
	} else if (z <= 6.5e-274) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e-185) {
		tmp = t_1;
	} else if (z <= 5e-153) {
		tmp = t / ((a - z) / y);
	} else if (z <= 8.2e+82) {
		tmp = t_1;
	} else {
		tmp = t / (-(-1.0) - (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.6e+69:
		tmp = t / (-z / (y - z))
	elif z <= -1.25e-255:
		tmp = t_1
	elif z <= 6.5e-274:
		tmp = x + ((y * t) / a)
	elif z <= 1.65e-185:
		tmp = t_1
	elif z <= 5e-153:
		tmp = t / ((a - z) / y)
	elif z <= 8.2e+82:
		tmp = t_1
	else:
		tmp = t / (-(-1.0) - (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.6e+69)
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	elseif (z <= -1.25e-255)
		tmp = t_1;
	elseif (z <= 6.5e-274)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 5e-153)
		tmp = Float64(t / Float64(Float64(a - z) / y));
	elseif (z <= 8.2e+82)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(-(-1.0)) - Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.6e+69)
		tmp = t / (-z / (y - z));
	elseif (z <= -1.25e-255)
		tmp = t_1;
	elseif (z <= 6.5e-274)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.65e-185)
		tmp = t_1;
	elseif (z <= 5e-153)
		tmp = t / ((a - z) / y);
	elseif (z <= 8.2e+82)
		tmp = t_1;
	else
		tmp = t / (-(-1.0) - (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+69], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-255], t$95$1, If[LessEqual[z, 6.5e-274], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-185], t$95$1, If[LessEqual[z, 5e-153], N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+82], t$95$1, N[(t / N[((--1.0) - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.6000000000000003e69

   1. Initial program 73.8%

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

   2. Taylor expanded in x around 0 30.2%

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

      1. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   5. Taylor expanded in a around 0 51.4%

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

      1. associate-*r/ 51.4%

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

      2. mul-1-neg 51.4%

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

   7. Simplified 51.4%

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

   if -3.6000000000000003e69 < z < -1.2499999999999999e-255 or 6.49999999999999959e-274 < z < 1.6499999999999999e-185 or 5.00000000000000033e-153 < z < 8.1999999999999999e82

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   4. Simplified 62.7%

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

   5. Taylor expanded in z around 0 57.9%

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

   if -1.2499999999999999e-255 < z < 6.49999999999999959e-274

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-/l* 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in t around inf 88.6%

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

   6. Taylor expanded in z around 0 88.4%

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

   if 1.6499999999999999e-185 < z < 5.00000000000000033e-153

   1. Initial program 65.0%

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

   2. Taylor expanded in x around 0 76.4%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   if 8.1999999999999999e82 < z

   1. Initial program 58.5%

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

   2. Taylor expanded in x around 0 33.2%

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

      1. associate-/l* 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. div-sub 51.0%

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

      3. sub-neg 51.0%

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

      4. *-inverses 51.0%

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

      5. metadata-eval 51.0%

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

   7. Simplified 51.0%

      \[\leadsto \frac{t}{\color{blue}{-\left(\frac{a}{z} + -1\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(--1\right) - \frac{a}{z}}\\ \end{array} \]

Alternative 14: 48.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.35e+226)
     t
     (if (<= z -8.2e+196)
       (* x (/ (- y a) z))
       (if (<= z -6e+74)
         t
         (if (<= z 1.25e-185)
           t_1
           (if (<= z 2.3e-153) (/ t (/ a y)) (if (<= z 6.4e+111) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.35e+226) {
		tmp = t;
	} else if (z <= -8.2e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -6e+74) {
		tmp = t;
	} else if (z <= 1.25e-185) {
		tmp = t_1;
	} else if (z <= 2.3e-153) {
		tmp = t / (a / y);
	} else if (z <= 6.4e+111) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.35d+226)) then
        tmp = t
    else if (z <= (-8.2d+196)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-6d+74)) then
        tmp = t
    else if (z <= 1.25d-185) then
        tmp = t_1
    else if (z <= 2.3d-153) then
        tmp = t / (a / y)
    else if (z <= 6.4d+111) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.35e+226) {
		tmp = t;
	} else if (z <= -8.2e+196) {
		tmp = x * ((y - a) / z);
	} else if (z <= -6e+74) {
		tmp = t;
	} else if (z <= 1.25e-185) {
		tmp = t_1;
	} else if (z <= 2.3e-153) {
		tmp = t / (a / y);
	} else if (z <= 6.4e+111) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.35e+226:
		tmp = t
	elif z <= -8.2e+196:
		tmp = x * ((y - a) / z)
	elif z <= -6e+74:
		tmp = t
	elif z <= 1.25e-185:
		tmp = t_1
	elif z <= 2.3e-153:
		tmp = t / (a / y)
	elif z <= 6.4e+111:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.35e+226)
		tmp = t;
	elseif (z <= -8.2e+196)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -6e+74)
		tmp = t;
	elseif (z <= 1.25e-185)
		tmp = t_1;
	elseif (z <= 2.3e-153)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 6.4e+111)
		tmp = t_1;
	else
		tmp = t;
	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 (z <= -2.35e+226)
		tmp = t;
	elseif (z <= -8.2e+196)
		tmp = x * ((y - a) / z);
	elseif (z <= -6e+74)
		tmp = t;
	elseif (z <= 1.25e-185)
		tmp = t_1;
	elseif (z <= 2.3e-153)
		tmp = t / (a / y);
	elseif (z <= 6.4e+111)
		tmp = t_1;
	else
		tmp = t;
	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[z, -2.35e+226], t, If[LessEqual[z, -8.2e+196], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e+74], t, If[LessEqual[z, 1.25e-185], t$95$1, If[LessEqual[z, 2.3e-153], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+111], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.34999999999999996e226 or -8.1999999999999993e196 < z < -6e74 or 6.4000000000000002e111 < z

   1. Initial program 66.0%

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

   2. Taylor expanded in z around inf 46.5%

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

   if -2.34999999999999996e226 < z < -8.1999999999999993e196

   1. Initial program 58.2%

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

   2. Taylor expanded in x around inf 31.4%

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

      1. mul-1-neg 31.4%

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

      2. unsub-neg 31.4%

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

   4. Simplified 31.4%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. sub-neg 66.7%

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

      3. mul-1-neg 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in a around 0 26.0%

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

      1. associate-/l* 38.4%

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

      2. associate-/r/ 39.0%

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

      3. mul-1-neg 39.0%

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

      4. associate-*l/ 66.7%

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

      5. distribute-lft-neg-in 66.7%

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

      6. distribute-rgt-in 66.7%

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

      7. sub-neg 66.7%

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

      8. div-sub 66.7%

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

   10. Simplified 66.7%

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

   if -6e74 < z < 1.2500000000000001e-185 or 2.29999999999999997e-153 < z < 6.4000000000000002e111

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in z around 0 56.0%

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

   if 1.2500000000000001e-185 < z < 2.29999999999999997e-153

   1. Initial program 65.0%

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

   2. Taylor expanded in x around 0 76.4%

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

      1. associate-/l* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 74.8%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+226}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{t - x}\\ t_2 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y - z}{t_1}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- t x))) (t_2 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= z -9.5e+61)
     t_2
     (if (<= z -3.4e-179)
       (+ x (/ (- y z) t_1))
       (if (<= z -7.7e-205)
         (/ (* y (- t x)) (- a z))
         (if (<= z 4.8e+28) (+ x (/ y t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (t - x);
	double t_2 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -9.5e+61) {
		tmp = t_2;
	} else if (z <= -3.4e-179) {
		tmp = x + ((y - z) / t_1);
	} else if (z <= -7.7e-205) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 4.8e+28) {
		tmp = x + (y / 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 = a / (t - x)
    t_2 = t + (((y - a) / z) * (x - t))
    if (z <= (-9.5d+61)) then
        tmp = t_2
    else if (z <= (-3.4d-179)) then
        tmp = x + ((y - z) / t_1)
    else if (z <= (-7.7d-205)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 4.8d+28) then
        tmp = x + (y / 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 = a / (t - x);
	double t_2 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -9.5e+61) {
		tmp = t_2;
	} else if (z <= -3.4e-179) {
		tmp = x + ((y - z) / t_1);
	} else if (z <= -7.7e-205) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 4.8e+28) {
		tmp = x + (y / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (t - x)
	t_2 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if z <= -9.5e+61:
		tmp = t_2
	elif z <= -3.4e-179:
		tmp = x + ((y - z) / t_1)
	elif z <= -7.7e-205:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 4.8e+28:
		tmp = x + (y / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(t - x))
	t_2 = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -9.5e+61)
		tmp = t_2;
	elseif (z <= -3.4e-179)
		tmp = Float64(x + Float64(Float64(y - z) / t_1));
	elseif (z <= -7.7e-205)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 4.8e+28)
		tmp = Float64(x + Float64(y / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (t - x);
	t_2 = t + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (z <= -9.5e+61)
		tmp = t_2;
	elseif (z <= -3.4e-179)
		tmp = x + ((y - z) / t_1);
	elseif (z <= -7.7e-205)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 4.8e+28)
		tmp = x + (y / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+61], t$95$2, If[LessEqual[z, -3.4e-179], N[(x + N[(N[(y - z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.7e-205], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+28], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.49999999999999959e61 or 4.79999999999999962e28 < z

   1. Initial program 68.4%

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

   2. Taylor expanded in z around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. associate--l+ 57.9%

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

      3. associate-*r/ 57.9%

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

      4. associate-*r/ 57.9%

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

      5. div-sub 57.9%

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

      6. distribute-lft-out-- 57.9%

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

      7. mul-1-neg 57.9%

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

      8. distribute-neg-frac 57.9%

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

      9. unsub-neg 57.9%

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

      10. distribute-rgt-out-- 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in y around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. div-sub 65.7%

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

      5. associate-*r/ 57.9%

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

      6. associate-/l* 64.5%

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

      7. associate-/l* 75.2%

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

      8. div-sub 75.2%

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

      9. associate-/l* 59.0%

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

      10. *-commutative 59.0%

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

      11. associate-*r/ 74.9%

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

   7. Simplified 74.9%

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

   if -9.49999999999999959e61 < z < -3.3999999999999997e-179

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 77.4%

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

   4. Simplified 77.4%

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

   if -3.3999999999999997e-179 < z < -7.7000000000000001e-205

   1. Initial program 82.1%

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

   2. Taylor expanded in y around inf 82.7%

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

      1. div-sub 82.7%

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

      2. *-commutative 82.7%

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

      3. associate-*r/ 85.3%

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

   4. Simplified 85.3%

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

   if -7.7000000000000001e-205 < z < 4.79999999999999962e28

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 81.1%

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

   4. Simplified 81.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -7.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 16: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 520000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= a -4.5e+109)
     (+ x (/ (- x t) (+ -1.0 (/ a z))))
     (if (<= a 4.6e-188)
       t_1
       (if (<= a 2.25e-65)
         (/ (* y (- t x)) (- a z))
         (if (<= a 520000000.0) t_1 (+ x (/ (- y z) (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (a <= -4.5e+109) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else if (a <= 4.6e-188) {
		tmp = t_1;
	} else if (a <= 2.25e-65) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 520000000.0) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((y - a) / z) * (x - t))
    if (a <= (-4.5d+109)) then
        tmp = x + ((x - t) / ((-1.0d0) + (a / z)))
    else if (a <= 4.6d-188) then
        tmp = t_1
    else if (a <= 2.25d-65) then
        tmp = (y * (t - x)) / (a - z)
    else if (a <= 520000000.0d0) then
        tmp = t_1
    else
        tmp = x + ((y - z) / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (a <= -4.5e+109) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else if (a <= 4.6e-188) {
		tmp = t_1;
	} else if (a <= 2.25e-65) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 520000000.0) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if a <= -4.5e+109:
		tmp = x + ((x - t) / (-1.0 + (a / z)))
	elif a <= 4.6e-188:
		tmp = t_1
	elif a <= 2.25e-65:
		tmp = (y * (t - x)) / (a - z)
	elif a <= 520000000.0:
		tmp = t_1
	else:
		tmp = x + ((y - z) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (a <= -4.5e+109)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(-1.0 + Float64(a / z))));
	elseif (a <= 4.6e-188)
		tmp = t_1;
	elseif (a <= 2.25e-65)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (a <= 520000000.0)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (a <= -4.5e+109)
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	elseif (a <= 4.6e-188)
		tmp = t_1;
	elseif (a <= 2.25e-65)
		tmp = (y * (t - x)) / (a - z);
	elseif (a <= 520000000.0)
		tmp = t_1;
	else
		tmp = x + ((y - z) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+109], N[(x + N[(N[(x - t), $MachinePrecision] / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e-188], t$95$1, If[LessEqual[a, 2.25e-65], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 520000000.0], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.4999999999999996e109

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

      3. *-commutative 58.4%

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

      4. associate-/l* 82.1%

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

      5. div-sub 82.1%

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

      6. *-inverses 82.1%

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

   4. Simplified 82.1%

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

   if -4.4999999999999996e109 < a < 4.6e-188 or 2.2499999999999999e-65 < a < 5.2e8

   1. Initial program 71.7%

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

   2. Taylor expanded in z around inf 69.4%

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

      1. +-commutative 69.4%

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

      2. associate--l+ 69.4%

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

      3. associate-*r/ 69.4%

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

      4. associate-*r/ 69.4%

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

      5. div-sub 71.2%

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

      6. distribute-lft-out-- 71.2%

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

      7. mul-1-neg 71.2%

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

      8. distribute-neg-frac 71.2%

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

      9. unsub-neg 71.2%

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

      10. distribute-rgt-out-- 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in y around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. div-sub 73.8%

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

      5. associate-*r/ 69.4%

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

      6. associate-/l* 74.1%

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

      7. associate-/l* 72.3%

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

      8. div-sub 77.7%

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

      9. associate-/l* 72.1%

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

      10. *-commutative 72.1%

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

      11. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

   if 4.6e-188 < a < 2.2499999999999999e-65

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf 67.3%

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

      1. div-sub 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r/ 70.7%

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

   4. Simplified 70.7%

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

   if 5.2e8 < a

   1. Initial program 93.0%

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

   2. Taylor expanded in a around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-188}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 520000000:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-188}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 5200000000000:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.3e+74)
   (+ x (/ (- y z) (/ a t)))
   (if (<= a 4.4e-188)
     (+ t (* (/ y z) (- x t)))
     (if (<= a 1.8e-65)
       (/ (* y (- t x)) (- a z))
       (if (<= a 5200000000000.0)
         (+ t (* x (/ (- y a) z)))
         (- x (* y (/ (- x t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e+74) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 4.4e-188) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 1.8e-65) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 5200000000000.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.3d+74)) then
        tmp = x + ((y - z) / (a / t))
    else if (a <= 4.4d-188) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 1.8d-65) then
        tmp = (y * (t - x)) / (a - z)
    else if (a <= 5200000000000.0d0) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = x - (y * ((x - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.3e+74) {
		tmp = x + ((y - z) / (a / t));
	} else if (a <= 4.4e-188) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 1.8e-65) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 5200000000000.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x - (y * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.3e+74:
		tmp = x + ((y - z) / (a / t))
	elif a <= 4.4e-188:
		tmp = t + ((y / z) * (x - t))
	elif a <= 1.8e-65:
		tmp = (y * (t - x)) / (a - z)
	elif a <= 5200000000000.0:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = x - (y * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.3e+74)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	elseif (a <= 4.4e-188)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 1.8e-65)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (a <= 5200000000000.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.3e+74)
		tmp = x + ((y - z) / (a / t));
	elseif (a <= 4.4e-188)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 1.8e-65)
		tmp = (y * (t - x)) / (a - z);
	elseif (a <= 5200000000000.0)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = x - (y * ((x - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.3e+74], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-188], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-65], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5200000000000.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.3000000000000002e74

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around inf 65.7%

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

   if -3.3000000000000002e74 < a < 4.3999999999999999e-188

   1. Initial program 72.8%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. associate--l+ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. associate-*r/ 74.2%

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

      5. div-sub 75.3%

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

      6. distribute-lft-out-- 75.3%

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

      7. mul-1-neg 75.3%

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

      8. distribute-neg-frac 75.3%

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

      9. unsub-neg 75.3%

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

      10. distribute-rgt-out-- 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

      4. div-sub 77.7%

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

      5. associate-*r/ 74.2%

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

      6. associate-/l* 78.1%

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

      7. associate-/l* 73.6%

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

      8. div-sub 79.4%

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

      9. associate-/l* 75.3%

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

      10. *-commutative 75.3%

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

      11. associate-*r/ 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in y around inf 73.5%

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

   if 4.3999999999999999e-188 < a < 1.7999999999999999e-65

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf 67.3%

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

      1. div-sub 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r/ 70.7%

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

   4. Simplified 70.7%

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

   if 1.7999999999999999e-65 < a < 5.2e12

   1. Initial program 66.0%

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

   2. Taylor expanded in z around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. associate--l+ 65.9%

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

      3. associate-*r/ 65.9%

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

      4. associate-*r/ 65.9%

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

      5. div-sub 71.8%

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

      6. distribute-lft-out-- 71.8%

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

      7. mul-1-neg 71.8%

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

      8. distribute-neg-frac 71.8%

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

      9. unsub-neg 71.8%

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

      10. distribute-rgt-out-- 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in y around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. div-sub 76.8%

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

      5. associate-*r/ 65.9%

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

      6. associate-/l* 76.8%

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

      7. associate-/l* 76.8%

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

      8. div-sub 82.6%

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

      9. associate-/l* 71.8%

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

      10. *-commutative 71.8%

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

      11. associate-*r/ 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in t around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. associate-*r* 65.5%

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

      3. neg-mul-1 65.5%

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

      4. neg-sub0 65.5%

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

      5. associate--r- 65.5%

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

      6. neg-sub0 65.5%

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

      7. +-commutative 65.5%

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

      8. sub-neg 65.5%

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

      9. *-commutative 65.5%

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

      10. associate-*r/ 65.6%

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

   10. Simplified 65.6%

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

   if 5.2e12 < a

   1. Initial program 93.0%

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

   2. Taylor expanded in a around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in y around inf 63.3%

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

      1. associate-*r/ 80.2%

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

   7. Simplified 80.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-188}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 5200000000000:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \end{array} \]

Alternative 18: 36.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+46)
   x
   (if (<= a -2.6e-54)
     (* x (/ y z))
     (if (<= a 2.8e-188) t (if (<= a 7.8e+27) (* t (/ (- y z) a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+46) {
		tmp = x;
	} else if (a <= -2.6e-54) {
		tmp = x * (y / z);
	} else if (a <= 2.8e-188) {
		tmp = t;
	} else if (a <= 7.8e+27) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.6d+46)) then
        tmp = x
    else if (a <= (-2.6d-54)) then
        tmp = x * (y / z)
    else if (a <= 2.8d-188) then
        tmp = t
    else if (a <= 7.8d+27) then
        tmp = t * ((y - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+46) {
		tmp = x;
	} else if (a <= -2.6e-54) {
		tmp = x * (y / z);
	} else if (a <= 2.8e-188) {
		tmp = t;
	} else if (a <= 7.8e+27) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+46:
		tmp = x
	elif a <= -2.6e-54:
		tmp = x * (y / z)
	elif a <= 2.8e-188:
		tmp = t
	elif a <= 7.8e+27:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+46)
		tmp = x;
	elseif (a <= -2.6e-54)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.8e-188)
		tmp = t;
	elseif (a <= 7.8e+27)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e+46)
		tmp = x;
	elseif (a <= -2.6e-54)
		tmp = x * (y / z);
	elseif (a <= 2.8e-188)
		tmp = t;
	elseif (a <= 7.8e+27)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+46], x, If[LessEqual[a, -2.6e-54], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-188], t, If[LessEqual[a, 7.8e+27], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.60000000000000013e46 or 7.7999999999999997e27 < a

   1. Initial program 90.7%

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

   2. Taylor expanded in a around inf 44.2%

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

   if -2.60000000000000013e46 < a < -2.60000000000000002e-54

   1. Initial program 84.4%

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

   2. Taylor expanded in x around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in a around 0 40.4%

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

   if -2.60000000000000002e-54 < a < 2.8000000000000001e-188

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf 43.4%

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

   if 2.8000000000000001e-188 < a < 7.7999999999999997e27

   1. Initial program 74.8%

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

   2. Taylor expanded in x around 0 45.5%

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

      1. associate-/l* 53.5%

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

   4. Simplified 53.5%

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

   5. Taylor expanded in a around inf 29.8%

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

      1. div-inv 29.8%

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

      2. clear-num 29.8%

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

   7. Applied egg-rr 29.8%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-240}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1150:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= a -4.6e+109)
     x
     (if (<= a -5.4e-54)
       t_1
       (if (<= a 2.2e-240) t (if (<= a 1150.0) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -4.6e+109) {
		tmp = x;
	} else if (a <= -5.4e-54) {
		tmp = t_1;
	} else if (a <= 2.2e-240) {
		tmp = t;
	} else if (a <= 1150.0) {
		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 = x * ((y - a) / z)
    if (a <= (-4.6d+109)) then
        tmp = x
    else if (a <= (-5.4d-54)) then
        tmp = t_1
    else if (a <= 2.2d-240) then
        tmp = t
    else if (a <= 1150.0d0) 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 = x * ((y - a) / z);
	double tmp;
	if (a <= -4.6e+109) {
		tmp = x;
	} else if (a <= -5.4e-54) {
		tmp = t_1;
	} else if (a <= 2.2e-240) {
		tmp = t;
	} else if (a <= 1150.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if a <= -4.6e+109:
		tmp = x
	elif a <= -5.4e-54:
		tmp = t_1
	elif a <= 2.2e-240:
		tmp = t
	elif a <= 1150.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (a <= -4.6e+109)
		tmp = x;
	elseif (a <= -5.4e-54)
		tmp = t_1;
	elseif (a <= 2.2e-240)
		tmp = t;
	elseif (a <= 1150.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (a <= -4.6e+109)
		tmp = x;
	elseif (a <= -5.4e-54)
		tmp = t_1;
	elseif (a <= 2.2e-240)
		tmp = t;
	elseif (a <= 1150.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+109], x, If[LessEqual[a, -5.4e-54], t$95$1, If[LessEqual[a, 2.2e-240], t, If[LessEqual[a, 1150.0], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.60000000000000021e109 or 1150 < a

   1. Initial program 91.6%

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

   2. Taylor expanded in a around inf 44.4%

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

   if -4.60000000000000021e109 < a < -5.40000000000000051e-54 or 2.1999999999999999e-240 < a < 1150

   1. Initial program 76.5%

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

   2. Taylor expanded in x around inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

   4. Simplified 44.5%

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

   5. Taylor expanded in z around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. sub-neg 39.8%

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

      3. mul-1-neg 39.8%

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

   7. Simplified 39.8%

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

   8. Taylor expanded in a around 0 32.5%

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

      1. associate-/l* 33.5%

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

      2. associate-/r/ 36.9%

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

      3. mul-1-neg 36.9%

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

      4. associate-*l/ 37.4%

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

      5. distribute-lft-neg-in 37.4%

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

      6. distribute-rgt-in 39.8%

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

      7. sub-neg 39.8%

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

      8. div-sub 39.8%

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

   10. Simplified 39.8%

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

   if -5.40000000000000051e-54 < a < 2.1999999999999999e-240

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 43.8%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-240}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1150:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 340:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -2.3e+46)
     x
     (if (<= a -9.5e-55)
       t_1
       (if (<= a 3.7e-120) t (if (<= a 340.0) t_1 (if (<= a 4e+57) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2.3e+46) {
		tmp = x;
	} else if (a <= -9.5e-55) {
		tmp = t_1;
	} else if (a <= 3.7e-120) {
		tmp = t;
	} else if (a <= 340.0) {
		tmp = t_1;
	} else if (a <= 4e+57) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-2.3d+46)) then
        tmp = x
    else if (a <= (-9.5d-55)) then
        tmp = t_1
    else if (a <= 3.7d-120) then
        tmp = t
    else if (a <= 340.0d0) then
        tmp = t_1
    else if (a <= 4d+57) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2.3e+46) {
		tmp = x;
	} else if (a <= -9.5e-55) {
		tmp = t_1;
	} else if (a <= 3.7e-120) {
		tmp = t;
	} else if (a <= 340.0) {
		tmp = t_1;
	} else if (a <= 4e+57) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -2.3e+46:
		tmp = x
	elif a <= -9.5e-55:
		tmp = t_1
	elif a <= 3.7e-120:
		tmp = t
	elif a <= 340.0:
		tmp = t_1
	elif a <= 4e+57:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -2.3e+46)
		tmp = x;
	elseif (a <= -9.5e-55)
		tmp = t_1;
	elseif (a <= 3.7e-120)
		tmp = t;
	elseif (a <= 340.0)
		tmp = t_1;
	elseif (a <= 4e+57)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -2.3e+46)
		tmp = x;
	elseif (a <= -9.5e-55)
		tmp = t_1;
	elseif (a <= 3.7e-120)
		tmp = t;
	elseif (a <= 340.0)
		tmp = t_1;
	elseif (a <= 4e+57)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+46], x, If[LessEqual[a, -9.5e-55], t$95$1, If[LessEqual[a, 3.7e-120], t, If[LessEqual[a, 340.0], t$95$1, If[LessEqual[a, 4e+57], t, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3000000000000001e46 or 4.00000000000000019e57 < a

   1. Initial program 90.7%

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

   2. Taylor expanded in a around inf 45.3%

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

   if -2.3000000000000001e46 < a < -9.5000000000000006e-55 or 3.70000000000000001e-120 < a < 340

   1. Initial program 76.9%

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

   2. Taylor expanded in x around inf 40.9%

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

      1. mul-1-neg 40.9%

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

      2. unsub-neg 40.9%

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

   4. Simplified 40.9%

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

   5. Taylor expanded in a around 0 34.1%

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

   if -9.5000000000000006e-55 < a < 3.70000000000000001e-120 or 340 < a < 4.00000000000000019e57

   1. Initial program 73.2%

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

   2. Taylor expanded in z around inf 40.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-120}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 340:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120} \lor \neg \left(x \leq 8 \cdot 10^{+76}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.6e-120) (not (<= x 8e+76)))
   (- x (* y (/ (- x t) a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.6e-120) || !(x <= 8e+76)) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.6d-120)) .or. (.not. (x <= 8d+76))) then
        tmp = x - (y * ((x - t) / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.6e-120) || !(x <= 8e+76)) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.6e-120) or not (x <= 8e+76):
		tmp = x - (y * ((x - t) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.6e-120) || !(x <= 8e+76))
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.6e-120) || ~((x <= 8e+76)))
		tmp = x - (y * ((x - t) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.6e-120], N[Not[LessEqual[x, 8e+76]], $MachinePrecision]], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999973e-120 or 8.0000000000000004e76 < x

   1. Initial program 76.6%

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

   2. Taylor expanded in a around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. associate-/l* 58.6%

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

   4. Simplified 58.6%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. associate-*r/ 58.8%

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

   7. Simplified 58.8%

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

   if -4.59999999999999973e-120 < x < 8.0000000000000004e76

   1. Initial program 88.0%

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

   2. Taylor expanded in t around inf 74.2%

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

      1. div-sub 74.2%

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

   4. Simplified 74.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120} \lor \neg \left(x \leq 8 \cdot 10^{+76}\right):\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 22: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.6e-120)
   (- x (* y (/ (- x t) a)))
   (if (<= x 3e+77) (* t (/ (- y z) (- a z))) (+ x (/ y (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.6e-120) {
		tmp = x - (y * ((x - t) / a));
	} else if (x <= 3e+77) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - 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 (x <= (-4.6d-120)) then
        tmp = x - (y * ((x - t) / a))
    else if (x <= 3d+77) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - 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 (x <= -4.6e-120) {
		tmp = x - (y * ((x - t) / a));
	} else if (x <= 3e+77) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.6e-120:
		tmp = x - (y * ((x - t) / a))
	elif x <= 3e+77:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.6e-120)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (x <= 3e+77)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.6e-120)
		tmp = x - (y * ((x - t) / a));
	elseif (x <= 3e+77)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.6e-120], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+77], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999973e-120

   1. Initial program 77.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in a around inf 46.0%

      \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a} + x} \]
   3. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto \color{blue}{x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 57.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a}{t - x}}} \]

   4. Simplified 57.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a}{t - x}}} \]

   5. Taylor expanded in y around inf 49.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 57.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 57.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   if -4.59999999999999973e-120 < x < 2.9999999999999998e77

   1. Initial program 88.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in t around inf 74.2%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   3. Step-by-step derivation

      1. div-sub 74.2%

         \[\leadsto t \cdot \color{blue}{\frac{y - z}{a - z}} \]

   4. Simplified 74.2%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]

   if 2.9999999999999998e77 < x

   1. Initial program 75.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around 0 51.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a} + x} \]
   3. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

      2. associate-/l* 61.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{t - x}}} \]

   4. Simplified 61.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-120}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 23: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-49)
   x
   (if (<= a 3.6e-188)
     t
     (if (<= a 8.2e-22) (* y (/ t a)) (if (<= a 9e+57) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-49) {
		tmp = x;
	} else if (a <= 3.6e-188) {
		tmp = t;
	} else if (a <= 8.2e-22) {
		tmp = y * (t / a);
	} else if (a <= 9e+57) {
		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 <= (-3.1d-49)) then
        tmp = x
    else if (a <= 3.6d-188) then
        tmp = t
    else if (a <= 8.2d-22) then
        tmp = y * (t / a)
    else if (a <= 9d+57) 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 <= -3.1e-49) {
		tmp = x;
	} else if (a <= 3.6e-188) {
		tmp = t;
	} else if (a <= 8.2e-22) {
		tmp = y * (t / a);
	} else if (a <= 9e+57) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-49:
		tmp = x
	elif a <= 3.6e-188:
		tmp = t
	elif a <= 8.2e-22:
		tmp = y * (t / a)
	elif a <= 9e+57:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-49)
		tmp = x;
	elseif (a <= 3.6e-188)
		tmp = t;
	elseif (a <= 8.2e-22)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= 9e+57)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e-49)
		tmp = x;
	elseif (a <= 3.6e-188)
		tmp = t;
	elseif (a <= 8.2e-22)
		tmp = y * (t / a);
	elseif (a <= 9e+57)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-49], x, If[LessEqual[a, 3.6e-188], t, If[LessEqual[a, 8.2e-22], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+57], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1e-49 or 8.99999999999999991e57 < a

   1. Initial program 89.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{x} \]

   if -3.1e-49 < a < 3.5999999999999997e-188 or 8.1999999999999999e-22 < a < 8.99999999999999991e57

   1. Initial program 71.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf 41.3%

      \[\leadsto \color{blue}{t} \]

   if 3.5999999999999997e-188 < a < 8.1999999999999999e-22

   1. Initial program 76.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0 40.2%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   3. Step-by-step derivation

      1. associate-/l* 47.5%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   4. Simplified 47.5%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   5. Taylor expanded in a around inf 28.6%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y - z}}} \]

   6. Taylor expanded in y around inf 27.1%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 24.6%

         \[\leadsto \color{blue}{y \cdot \frac{t}{a}} \]

      2. *-commutative 24.6%

         \[\leadsto \color{blue}{\frac{t}{a} \cdot y} \]

   8. Simplified 24.6%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-188}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 38.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-49) x (if (<= a 1.15e+58) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-49) {
		tmp = x;
	} else if (a <= 1.15e+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 <= (-3.1d-49)) then
        tmp = x
    else if (a <= 1.15d+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 <= -3.1e-49) {
		tmp = x;
	} else if (a <= 1.15e+58) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-49:
		tmp = x
	elif a <= 1.15e+58:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-49)
		tmp = x;
	elseif (a <= 1.15e+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 <= -3.1e-49)
		tmp = x;
	elseif (a <= 1.15e+58)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-49], x, If[LessEqual[a, 1.15e+58], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1e-49 or 1.15000000000000001e58 < a

   1. Initial program 89.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in a around inf 40.7%

      \[\leadsto \color{blue}{x} \]

   if -3.1e-49 < a < 1.15000000000000001e58

   1. Initial program 73.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf 32.8%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 82.1%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf 21.8%

   \[\leadsto \color{blue}{t} \]

3. Final simplification 21.8%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023171 
(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)))))