Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 91.4%

Time: 19.6s

Alternatives: 21

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: 80.4% 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: 91.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -5e-246)
     (fma (- y z) t_1 x)
     (if (<= t_2 2e-264)
       (+ t (* (- y a) (/ (- x t) z)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -5e-246) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= 2e-264) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -5e-246)
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= 2e-264)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-246], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 2e-264], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999997e-246

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 93.5%

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

   3. Simplified 93.5%

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

   if -4.9999999999999997e-246 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-264

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. associate-*r/ 78.8%

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

      3. associate-*r/ 78.8%

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

      4. div-sub 78.8%

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

      5. distribute-lft-out-- 78.8%

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

      6. sub-neg 78.8%

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

      7. mul-1-neg 78.8%

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

      8. +-commutative 78.8%

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

      9. associate-*r/ 78.8%

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

      10. mul-1-neg 78.8%

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

      11. +-commutative 78.8%

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

      12. mul-1-neg 78.8%

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

      13. sub-neg 78.8%

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

      14. distribute-rgt-out-- 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. sub-neg 79.0%

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

      3. associate-*l/ 97.9%

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

   7. Simplified 97.9%

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

   if 2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

      1. associate-*r/ 82.1%

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

      2. associate-/l* 93.5%

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

   3. Applied egg-rr 93.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246} \lor \neg \left(t_1 \leq 2 \cdot 10^{-264}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-246) (not (<= t_1 2e-264)))
     t_1
     (+ t (* (- y a) (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-246) || !(t_1 <= 2e-264)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-246)) .or. (.not. (t_1 <= 2d-264))) then
        tmp = t_1
    else
        tmp = t + ((y - a) * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-246) || !(t_1 <= 2e-264)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-246) or not (t_1 <= 2e-264):
		tmp = t_1
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-246) || !(t_1 <= 2e-264))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-246) || ~((t_1 <= 2e-264)))
		tmp = t_1;
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-246], N[Not[LessEqual[t$95$1, 2e-264]], $MachinePrecision]], t$95$1, N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $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)))) < -4.9999999999999997e-246 or 2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

   if -4.9999999999999997e-246 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-264

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. associate-*r/ 78.8%

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

      3. associate-*r/ 78.8%

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

      4. div-sub 78.8%

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

      5. distribute-lft-out-- 78.8%

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

      6. sub-neg 78.8%

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

      7. mul-1-neg 78.8%

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

      8. +-commutative 78.8%

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

      9. associate-*r/ 78.8%

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

      10. mul-1-neg 78.8%

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

      11. +-commutative 78.8%

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

      12. mul-1-neg 78.8%

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

      13. sub-neg 78.8%

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

      14. distribute-rgt-out-- 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. sub-neg 79.0%

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

      3. associate-*l/ 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-246} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-264}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 3: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-246)
     t_1
     (if (<= t_1 2e-264)
       (+ t (* (- y a) (/ (- x t) z)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = t_1;
	} else if (t_1 <= 2e-264) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-246)) then
        tmp = t_1
    else if (t_1 <= 2d-264) then
        tmp = t + ((y - a) * ((x - t) / z))
    else
        tmp = x + ((y - z) / ((a - z) / (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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = t_1;
	} else if (t_1 <= 2e-264) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-246:
		tmp = t_1
	elif t_1 <= 2e-264:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-246)
		tmp = t_1;
	elseif (t_1 <= 2e-264)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-246)
		tmp = t_1;
	elseif (t_1 <= 2e-264)
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-246], t$95$1, If[LessEqual[t$95$1, 2e-264], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999997e-246

   1. Initial program 93.5%

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

   if -4.9999999999999997e-246 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-264

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. associate-*r/ 78.8%

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

      3. associate-*r/ 78.8%

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

      4. div-sub 78.8%

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

      5. distribute-lft-out-- 78.8%

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

      6. sub-neg 78.8%

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

      7. mul-1-neg 78.8%

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

      8. +-commutative 78.8%

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

      9. associate-*r/ 78.8%

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

      10. mul-1-neg 78.8%

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

      11. +-commutative 78.8%

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

      12. mul-1-neg 78.8%

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

      13. sub-neg 78.8%

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

      14. distribute-rgt-out-- 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. sub-neg 79.0%

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

      3. associate-*l/ 97.9%

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

   7. Simplified 97.9%

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

   if 2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

      1. associate-*r/ 82.1%

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

      2. associate-/l* 93.5%

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

   3. Applied egg-rr 93.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 4: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-246)
     (+ x (* (- y z) (* (- t x) (/ 1.0 (- a z)))))
     (if (<= t_1 2e-264)
       (+ t (* (- y a) (/ (- x t) z)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = x + ((y - z) * ((t - x) * (1.0 / (a - z))));
	} else if (t_1 <= 2e-264) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-246)) then
        tmp = x + ((y - z) * ((t - x) * (1.0d0 / (a - z))))
    else if (t_1 <= 2d-264) then
        tmp = t + ((y - a) * ((x - t) / z))
    else
        tmp = x + ((y - z) / ((a - z) / (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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-246) {
		tmp = x + ((y - z) * ((t - x) * (1.0 / (a - z))));
	} else if (t_1 <= 2e-264) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -5e-246:
		tmp = x + ((y - z) * ((t - x) * (1.0 / (a - z))))
	elif t_1 <= 2e-264:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-246)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) * Float64(1.0 / Float64(a - z)))));
	elseif (t_1 <= 2e-264)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-246)
		tmp = x + ((y - z) * ((t - x) * (1.0 / (a - z))));
	elseif (t_1 <= 2e-264)
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-246], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-264], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999997e-246

   1. Initial program 93.5%

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

      1. div-inv 93.5%

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

      2. *-commutative 93.5%

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

   3. Applied egg-rr 93.5%

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

   if -4.9999999999999997e-246 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-264

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. associate-*r/ 78.8%

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

      3. associate-*r/ 78.8%

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

      4. div-sub 78.8%

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

      5. distribute-lft-out-- 78.8%

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

      6. sub-neg 78.8%

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

      7. mul-1-neg 78.8%

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

      8. +-commutative 78.8%

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

      9. associate-*r/ 78.8%

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

      10. mul-1-neg 78.8%

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

      11. +-commutative 78.8%

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

      12. mul-1-neg 78.8%

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

      13. sub-neg 78.8%

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

      14. distribute-rgt-out-- 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. sub-neg 79.0%

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

      3. associate-*l/ 97.9%

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

   7. Simplified 97.9%

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

   if 2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.5%

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

      1. associate-*r/ 82.1%

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

      2. associate-/l* 93.5%

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

   3. Applied egg-rr 93.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-264}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]

Alternative 5: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -4e+40)
     t_2
     (if (<= a 7.9e-50)
       t_1
       (if (<= a 2.9e+40)
         (+ x (/ y (/ (- a) x)))
         (if (<= a 8.8e+179) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -4e+40) {
		tmp = t_2;
	} else if (a <= 7.9e-50) {
		tmp = t_1;
	} else if (a <= 2.9e+40) {
		tmp = x + (y / (-a / x));
	} else if (a <= 8.8e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y / (a / t))
    if (a <= (-4d+40)) then
        tmp = t_2
    else if (a <= 7.9d-50) then
        tmp = t_1
    else if (a <= 2.9d+40) then
        tmp = x + (y / (-a / x))
    else if (a <= 8.8d+179) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -4e+40) {
		tmp = t_2;
	} else if (a <= 7.9e-50) {
		tmp = t_1;
	} else if (a <= 2.9e+40) {
		tmp = x + (y / (-a / x));
	} else if (a <= 8.8e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -4e+40:
		tmp = t_2
	elif a <= 7.9e-50:
		tmp = t_1
	elif a <= 2.9e+40:
		tmp = x + (y / (-a / x))
	elif a <= 8.8e+179:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -4e+40)
		tmp = t_2;
	elseif (a <= 7.9e-50)
		tmp = t_1;
	elseif (a <= 2.9e+40)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (a <= 8.8e+179)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -4e+40)
		tmp = t_2;
	elseif (a <= 7.9e-50)
		tmp = t_1;
	elseif (a <= 2.9e+40)
		tmp = x + (y / (-a / x));
	elseif (a <= 8.8e+179)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+40], t$95$2, If[LessEqual[a, 7.9e-50], t$95$1, If[LessEqual[a, 2.9e+40], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+179], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000012e40 or 8.8000000000000002e179 < a

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 62.7%

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

      1. associate-/l* 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in t around inf 67.5%

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

   if -4.00000000000000012e40 < a < 7.9000000000000002e-50 or 2.90000000000000017e40 < a < 8.8000000000000002e179

   1. Initial program 75.2%

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

   2. Taylor expanded in t around inf 66.4%

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

      1. div-sub 66.4%

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

   4. Simplified 66.4%

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

   if 7.9000000000000002e-50 < a < 2.90000000000000017e40

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 72.7%

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

      1. associate-/l* 72.7%

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

   4. Simplified 72.7%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+179}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 54.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := \frac{-t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (/ (- t) (+ (/ a z) -1.0))))
   (if (<= z -1.05e+25)
     t_2
     (if (<= z 3.2e-223)
       t_1
       (if (<= z 2.1e-98)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 4.9e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -1.05e+25) {
		tmp = t_2;
	} else if (z <= 3.2e-223) {
		tmp = t_1;
	} else if (z <= 2.1e-98) {
		tmp = x + (y / (-a / x));
	} else if (z <= 4.9e+63) {
		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 + (y / (a / t))
    t_2 = -t / ((a / z) + (-1.0d0))
    if (z <= (-1.05d+25)) then
        tmp = t_2
    else if (z <= 3.2d-223) then
        tmp = t_1
    else if (z <= 2.1d-98) then
        tmp = x + (y / (-a / x))
    else if (z <= 4.9d+63) 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 + (y / (a / t));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -1.05e+25) {
		tmp = t_2;
	} else if (z <= 3.2e-223) {
		tmp = t_1;
	} else if (z <= 2.1e-98) {
		tmp = x + (y / (-a / x));
	} else if (z <= 4.9e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = -t / ((a / z) + -1.0)
	tmp = 0
	if z <= -1.05e+25:
		tmp = t_2
	elif z <= 3.2e-223:
		tmp = t_1
	elif z <= 2.1e-98:
		tmp = x + (y / (-a / x))
	elif z <= 4.9e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0))
	tmp = 0.0
	if (z <= -1.05e+25)
		tmp = t_2;
	elseif (z <= 3.2e-223)
		tmp = t_1;
	elseif (z <= 2.1e-98)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 4.9e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = -t / ((a / z) + -1.0);
	tmp = 0.0;
	if (z <= -1.05e+25)
		tmp = t_2;
	elseif (z <= 3.2e-223)
		tmp = t_1;
	elseif (z <= 2.1e-98)
		tmp = x + (y / (-a / x));
	elseif (z <= 4.9e+63)
		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[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+25], t$95$2, If[LessEqual[z, 3.2e-223], t$95$1, If[LessEqual[z, 2.1e-98], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e25 or 4.8999999999999997e63 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf 67.4%

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

      1. div-sub 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in y around 0 37.3%

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

      1. associate-/l* 58.7%

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

      2. associate-*r/ 58.7%

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

      3. neg-mul-1 58.7%

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

      4. div-sub 58.7%

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

      5. *-inverses 58.7%

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

   7. Simplified 58.7%

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

   if -1.05e25 < z < 3.2000000000000001e-223 or 2.09999999999999992e-98 < z < 4.8999999999999997e63

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 67.2%

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

      1. associate-/l* 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around inf 63.2%

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

   if 3.2000000000000001e-223 < z < 2.09999999999999992e-98

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 7: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := \frac{-t}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (/ (- t) (/ z (- y z)))))
   (if (<= z -3.1e+25)
     t_2
     (if (<= z 3.4e-223)
       t_1
       (if (<= z 9e-99)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 2.7e+51) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = -t / (z / (y - z));
	double tmp;
	if (z <= -3.1e+25) {
		tmp = t_2;
	} else if (z <= 3.4e-223) {
		tmp = t_1;
	} else if (z <= 9e-99) {
		tmp = x + (y / (-a / x));
	} else if (z <= 2.7e+51) {
		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 + (y / (a / t))
    t_2 = -t / (z / (y - z))
    if (z <= (-3.1d+25)) then
        tmp = t_2
    else if (z <= 3.4d-223) then
        tmp = t_1
    else if (z <= 9d-99) then
        tmp = x + (y / (-a / x))
    else if (z <= 2.7d+51) 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 + (y / (a / t));
	double t_2 = -t / (z / (y - z));
	double tmp;
	if (z <= -3.1e+25) {
		tmp = t_2;
	} else if (z <= 3.4e-223) {
		tmp = t_1;
	} else if (z <= 9e-99) {
		tmp = x + (y / (-a / x));
	} else if (z <= 2.7e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = -t / (z / (y - z))
	tmp = 0
	if z <= -3.1e+25:
		tmp = t_2
	elif z <= 3.4e-223:
		tmp = t_1
	elif z <= 9e-99:
		tmp = x + (y / (-a / x))
	elif z <= 2.7e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (z <= -3.1e+25)
		tmp = t_2;
	elseif (z <= 3.4e-223)
		tmp = t_1;
	elseif (z <= 9e-99)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 2.7e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = -t / (z / (y - z));
	tmp = 0.0;
	if (z <= -3.1e+25)
		tmp = t_2;
	elseif (z <= 3.4e-223)
		tmp = t_1;
	elseif (z <= 9e-99)
		tmp = x + (y / (-a / x));
	elseif (z <= 2.7e+51)
		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[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+25], t$95$2, If[LessEqual[z, 3.4e-223], t$95$1, If[LessEqual[z, 9e-99], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0999999999999998e25 or 2.69999999999999992e51 < z

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 66.9%

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

      1. div-sub 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in a around 0 39.4%

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

      1. associate-/l* 59.3%

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

      2. associate-*r/ 59.3%

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

      3. neg-mul-1 59.3%

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

   7. Simplified 59.3%

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

   if -3.0999999999999998e25 < z < 3.3999999999999998e-223 or 9.0000000000000006e-99 < z < 2.69999999999999992e51

   1. Initial program 92.3%

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

   2. Taylor expanded in z around 0 67.7%

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

      1. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in t around inf 63.6%

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

   if 3.3999999999999998e-223 < z < 9.0000000000000006e-99

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 8: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -4.2e+26)
     t
     (if (<= z 1.05e-226)
       t_1
       (if (<= z 5.6e-99)
         (+ x (/ y (/ (- a) x)))
         (if (<= z 1.1e+59) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -4.2e+26) {
		tmp = t;
	} else if (z <= 1.05e-226) {
		tmp = t_1;
	} else if (z <= 5.6e-99) {
		tmp = x + (y / (-a / x));
	} else if (z <= 1.1e+59) {
		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 + (y / (a / t))
    if (z <= (-4.2d+26)) then
        tmp = t
    else if (z <= 1.05d-226) then
        tmp = t_1
    else if (z <= 5.6d-99) then
        tmp = x + (y / (-a / x))
    else if (z <= 1.1d+59) 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 + (y / (a / t));
	double tmp;
	if (z <= -4.2e+26) {
		tmp = t;
	} else if (z <= 1.05e-226) {
		tmp = t_1;
	} else if (z <= 5.6e-99) {
		tmp = x + (y / (-a / x));
	} else if (z <= 1.1e+59) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -4.2e+26:
		tmp = t
	elif z <= 1.05e-226:
		tmp = t_1
	elif z <= 5.6e-99:
		tmp = x + (y / (-a / x))
	elif z <= 1.1e+59:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 1.05e-226)
		tmp = t_1;
	elseif (z <= 5.6e-99)
		tmp = Float64(x + Float64(y / Float64(Float64(-a) / x)));
	elseif (z <= 1.1e+59)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 1.05e-226)
		tmp = t_1;
	elseif (z <= 5.6e-99)
		tmp = x + (y / (-a / x));
	elseif (z <= 1.1e+59)
		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[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+26], t, If[LessEqual[z, 1.05e-226], t$95$1, If[LessEqual[z, 5.6e-99], N[(x + N[(y / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+59], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000002e26 or 1.1e59 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -4.2000000000000002e26 < z < 1.0500000000000001e-226 or 5.6000000000000001e-99 < z < 1.1e59

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 68.0%

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

      1. associate-/l* 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in t around inf 64.0%

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

   if 1.0500000000000001e-226 < z < 5.6000000000000001e-99

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.2%

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

      1. associate-/l* 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+24} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+24) (not (<= z 8e+36)))
   (+ t (* (- y a) (/ (- x t) z)))
   (+ x (/ (- y z) (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+24) || !(z <= 8e+36)) {
		tmp = t + ((y - a) * ((x - t) / z));
	} 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) :: tmp
    if ((z <= (-7.2d+24)) .or. (.not. (z <= 8d+36))) then
        tmp = t + ((y - a) * ((x - t) / z))
    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 tmp;
	if ((z <= -7.2e+24) || !(z <= 8e+36)) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+24) or not (z <= 8e+36):
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = x + ((y - z) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+24) || !(z <= 8e+36))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	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)
	tmp = 0.0;
	if ((z <= -7.2e+24) || ~((z <= 8e+36)))
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = x + ((y - z) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+24], N[Not[LessEqual[z, 8e+36]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999966e24 or 8.00000000000000034e36 < z

   1. Initial program 67.7%

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

   2. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. div-sub 61.4%

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

      5. distribute-lft-out-- 61.4%

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

      6. sub-neg 61.4%

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

      7. mul-1-neg 61.4%

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

      8. +-commutative 61.4%

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

      9. associate-*r/ 61.4%

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

      10. mul-1-neg 61.4%

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

      11. +-commutative 61.4%

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

      12. mul-1-neg 61.4%

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

      13. sub-neg 61.4%

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

      14. distribute-rgt-out-- 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in z around 0 62.3%

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

      1. mul-1-neg 62.3%

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

      2. sub-neg 62.3%

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

      3. associate-*l/ 79.6%

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

   7. Simplified 79.6%

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

   if -7.19999999999999966e24 < z < 8.00000000000000034e36

   1. Initial program 94.4%

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

      1. associate-*r/ 89.9%

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

      2. associate-/l* 94.3%

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

   3. Applied egg-rr 94.3%

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

   4. Taylor expanded in a around inf 79.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+24} \lor \neg \left(z \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+26)
   (+ t (/ x (/ z (- y a))))
   (if (<= z 1.3e+37)
     (+ x (/ (- t x) (/ a (- y z))))
     (- t (/ y (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 1.3e+37) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - (y / (z / (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 (z <= (-1.9d+26)) then
        tmp = t + (x / (z / (y - a)))
    else if (z <= 1.3d+37) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t - (y / (z / (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 (z <= -1.9e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 1.3e+37) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+26:
		tmp = t + (x / (z / (y - a)))
	elif z <= 1.3e+37:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+26)
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	elseif (z <= 1.3e+37)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+26)
		tmp = t + (x / (z / (y - a)));
	elseif (z <= 1.3e+37)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+26], N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+37], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9000000000000001e26

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-*r/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. div-sub 68.9%

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

      5. distribute-lft-out-- 68.9%

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

      6. sub-neg 68.9%

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

      7. mul-1-neg 68.9%

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

      8. +-commutative 68.9%

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

      9. associate-*r/ 68.9%

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

      10. mul-1-neg 68.9%

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

      11. +-commutative 68.9%

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

      12. mul-1-neg 68.9%

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

      13. sub-neg 68.9%

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

      14. distribute-rgt-out-- 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. sub-neg 70.8%

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

      3. associate-*l/ 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 70.1%

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

      1. associate-/l* 76.4%

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

      2. associate-*r/ 76.4%

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

      3. neg-mul-1 76.4%

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

   10. Simplified 76.4%

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

   if -1.9000000000000001e26 < z < 1.3e37

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 74.0%

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

      1. associate-/l* 79.2%

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

   4. Simplified 79.2%

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

   if 1.3e37 < z

   1. Initial program 67.0%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-*r/ 55.0%

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

      3. associate-*r/ 55.0%

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

      4. div-sub 55.0%

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

      5. distribute-lft-out-- 55.0%

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

      6. sub-neg 55.0%

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

      7. mul-1-neg 55.0%

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

      8. +-commutative 55.0%

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

      9. associate-*r/ 55.0%

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

      10. mul-1-neg 55.0%

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

      11. +-commutative 55.0%

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

      12. mul-1-neg 55.0%

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

      13. sub-neg 55.0%

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

      14. distribute-rgt-out-- 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in a around 0 52.6%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 11: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 10^{+37}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+26)
   (+ t (/ x (/ z (- y a))))
   (if (<= z 1e+37)
     (+ x (/ (- y z) (/ a (- t x))))
     (- t (/ y (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 1e+37) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t - (y / (z / (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 (z <= (-1.7d+26)) then
        tmp = t + (x / (z / (y - a)))
    else if (z <= 1d+37) then
        tmp = x + ((y - z) / (a / (t - x)))
    else
        tmp = t - (y / (z / (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 (z <= -1.7e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 1e+37) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+26:
		tmp = t + (x / (z / (y - a)))
	elif z <= 1e+37:
		tmp = x + ((y - z) / (a / (t - x)))
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+26)
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	elseif (z <= 1e+37)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+26)
		tmp = t + (x / (z / (y - a)));
	elseif (z <= 1e+37)
		tmp = x + ((y - z) / (a / (t - x)));
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+26], N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+37], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e26

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-*r/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. div-sub 68.9%

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

      5. distribute-lft-out-- 68.9%

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

      6. sub-neg 68.9%

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

      7. mul-1-neg 68.9%

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

      8. +-commutative 68.9%

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

      9. associate-*r/ 68.9%

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

      10. mul-1-neg 68.9%

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

      11. +-commutative 68.9%

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

      12. mul-1-neg 68.9%

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

      13. sub-neg 68.9%

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

      14. distribute-rgt-out-- 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. sub-neg 70.8%

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

      3. associate-*l/ 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 70.1%

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

      1. associate-/l* 76.4%

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

      2. associate-*r/ 76.4%

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

      3. neg-mul-1 76.4%

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

   10. Simplified 76.4%

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

   if -1.7000000000000001e26 < z < 9.99999999999999954e36

   1. Initial program 94.4%

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

      1. associate-*r/ 89.9%

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

      2. associate-/l* 94.3%

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

   3. Applied egg-rr 94.3%

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

   4. Taylor expanded in a around inf 79.9%

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

   if 9.99999999999999954e36 < z

   1. Initial program 67.0%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-*r/ 55.0%

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

      3. associate-*r/ 55.0%

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

      4. div-sub 55.0%

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

      5. distribute-lft-out-- 55.0%

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

      6. sub-neg 55.0%

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

      7. mul-1-neg 55.0%

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

      8. +-commutative 55.0%

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

      9. associate-*r/ 55.0%

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

      10. mul-1-neg 55.0%

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

      11. +-commutative 55.0%

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

      12. mul-1-neg 55.0%

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

      13. sub-neg 55.0%

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

      14. distribute-rgt-out-- 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in a around 0 52.6%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 10^{+37}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 12: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+25)
   t
   (if (<= z -1.25e-92)
     x
     (if (<= z 2.6e-218) (* t (/ (- y z) a)) (if (<= z 2.6e+58) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t;
	} else if (z <= -1.25e-92) {
		tmp = x;
	} else if (z <= 2.6e-218) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.6e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d+25)) then
        tmp = t
    else if (z <= (-1.25d-92)) then
        tmp = x
    else if (z <= 2.6d-218) then
        tmp = t * ((y - z) / a)
    else if (z <= 2.6d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t;
	} else if (z <= -1.25e-92) {
		tmp = x;
	} else if (z <= 2.6e-218) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.6e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+25:
		tmp = t
	elif z <= -1.25e-92:
		tmp = x
	elif z <= 2.6e-218:
		tmp = t * ((y - z) / a)
	elif z <= 2.6e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+25)
		tmp = t;
	elseif (z <= -1.25e-92)
		tmp = x;
	elseif (z <= 2.6e-218)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 2.6e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+25)
		tmp = t;
	elseif (z <= -1.25e-92)
		tmp = x;
	elseif (z <= 2.6e-218)
		tmp = t * ((y - z) / a);
	elseif (z <= 2.6e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+25], t, If[LessEqual[z, -1.25e-92], x, If[LessEqual[z, 2.6e-218], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+58], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e25 or 2.59999999999999988e58 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -2.2000000000000001e25 < z < -1.25000000000000003e-92 or 2.59999999999999983e-218 < z < 2.59999999999999988e58

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 42.2%

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

   if -1.25000000000000003e-92 < z < 2.59999999999999983e-218

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 51.0%

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

      1. div-sub 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in a around inf 47.3%

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

      1. associate-*r/ 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-218}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 43.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-147}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+26)
   t
   (if (<= z -5.8e-30)
     x
     (if (<= z 4.4e-147) (* (- t x) (/ y a)) (if (<= z 3e+58) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+26) {
		tmp = t;
	} else if (z <= -5.8e-30) {
		tmp = x;
	} else if (z <= 4.4e-147) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d+26)) then
        tmp = t
    else if (z <= (-5.8d-30)) then
        tmp = x
    else if (z <= 4.4d-147) then
        tmp = (t - x) * (y / a)
    else if (z <= 3d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+26) {
		tmp = t;
	} else if (z <= -5.8e-30) {
		tmp = x;
	} else if (z <= 4.4e-147) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+26:
		tmp = t
	elif z <= -5.8e-30:
		tmp = x
	elif z <= 4.4e-147:
		tmp = (t - x) * (y / a)
	elif z <= 3e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+26)
		tmp = t;
	elseif (z <= -5.8e-30)
		tmp = x;
	elseif (z <= 4.4e-147)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 3e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+26)
		tmp = t;
	elseif (z <= -5.8e-30)
		tmp = x;
	elseif (z <= 4.4e-147)
		tmp = (t - x) * (y / a);
	elseif (z <= 3e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+26], t, If[LessEqual[z, -5.8e-30], x, If[LessEqual[z, 4.4e-147], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+58], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e26 or 3.0000000000000002e58 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -1.25e26 < z < -5.79999999999999978e-30 or 4.4000000000000002e-147 < z < 3.0000000000000002e58

   1. Initial program 88.8%

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

   2. Taylor expanded in a around inf 42.9%

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

   if -5.79999999999999978e-30 < z < 4.4000000000000002e-147

   1. Initial program 97.4%

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

   2. Taylor expanded in y around -inf 62.8%

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

      1. associate-*l/ 62.9%

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

   4. Simplified 62.9%

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

   5. Taylor expanded in a around inf 54.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-147}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+37} \lor \neg \left(z \leq 3.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+37) (not (<= z 3.3e-13)))
   (* 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 ((z <= -3.2e+37) || !(z <= 3.3e-13)) {
		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 ((z <= (-3.2d+37)) .or. (.not. (z <= 3.3d-13))) 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 ((z <= -3.2e+37) || !(z <= 3.3e-13)) {
		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 (z <= -3.2e+37) or not (z <= 3.3e-13):
		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 ((z <= -3.2e+37) || !(z <= 3.3e-13))
		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 ((z <= -3.2e+37) || ~((z <= 3.3e-13)))
		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[Or[LessEqual[z, -3.2e+37], N[Not[LessEqual[z, 3.3e-13]], $MachinePrecision]], 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 2 regimes

2. if z < -3.20000000000000014e37 or 3.3000000000000001e-13 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in t around inf 66.1%

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

      1. div-sub 66.1%

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

   4. Simplified 66.1%

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

   if -3.20000000000000014e37 < z < 3.3000000000000001e-13

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 72.6%

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

      1. associate-/l* 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+37} \lor \neg \left(z \leq 3.3 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 15: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+25} \lor \neg \left(z \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+25) (not (<= z 9.2e+36)))
   (- t (/ y (/ z (- t x))))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+25) || !(z <= 9.2e+36)) {
		tmp = t - (y / (z / (t - x)));
	} 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 ((z <= (-6.8d+25)) .or. (.not. (z <= 9.2d+36))) then
        tmp = t - (y / (z / (t - x)))
    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 ((z <= -6.8e+25) || !(z <= 9.2e+36)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+25) or not (z <= 9.2e+36):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+25) || !(z <= 9.2e+36))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	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 ((z <= -6.8e+25) || ~((z <= 9.2e+36)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+25], N[Not[LessEqual[z, 9.2e+36]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.79999999999999967e25 or 9.19999999999999986e36 < z

   1. Initial program 67.7%

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

   2. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. div-sub 61.4%

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

      5. distribute-lft-out-- 61.4%

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

      6. sub-neg 61.4%

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

      7. mul-1-neg 61.4%

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

      8. +-commutative 61.4%

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

      9. associate-*r/ 61.4%

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

      10. mul-1-neg 61.4%

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

      11. +-commutative 61.4%

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

      12. mul-1-neg 61.4%

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

      13. sub-neg 61.4%

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

      14. distribute-rgt-out-- 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

   if -6.79999999999999967e25 < z < 9.19999999999999986e36

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 76.3%

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

   4. Simplified 76.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+25} \lor \neg \left(z \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.85e+26)
   (+ t (/ x (/ z (- y a))))
   (if (<= z 9.2e+36) (+ x (/ y (/ a (- t x)))) (- t (/ y (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.85e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 9.2e+36) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - (y / (z / (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 (z <= (-2.85d+26)) then
        tmp = t + (x / (z / (y - a)))
    else if (z <= 9.2d+36) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t - (y / (z / (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 (z <= -2.85e+26) {
		tmp = t + (x / (z / (y - a)));
	} else if (z <= 9.2e+36) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.85e+26:
		tmp = t + (x / (z / (y - a)))
	elif z <= 9.2e+36:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.85e+26)
		tmp = Float64(t + Float64(x / Float64(z / Float64(y - a))));
	elseif (z <= 9.2e+36)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.85e+26)
		tmp = t + (x / (z / (y - a)));
	elseif (z <= 9.2e+36)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.85e+26], N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+36], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8500000000000002e26

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-*r/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. div-sub 68.9%

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

      5. distribute-lft-out-- 68.9%

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

      6. sub-neg 68.9%

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

      7. mul-1-neg 68.9%

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

      8. +-commutative 68.9%

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

      9. associate-*r/ 68.9%

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

      10. mul-1-neg 68.9%

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

      11. +-commutative 68.9%

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

      12. mul-1-neg 68.9%

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

      13. sub-neg 68.9%

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

      14. distribute-rgt-out-- 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. sub-neg 70.8%

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

      3. associate-*l/ 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in t around 0 70.1%

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

      1. associate-/l* 76.4%

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

      2. associate-*r/ 76.4%

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

      3. neg-mul-1 76.4%

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

   10. Simplified 76.4%

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

   if -2.8500000000000002e26 < z < 9.19999999999999986e36

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 76.3%

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

   4. Simplified 76.3%

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

   if 9.19999999999999986e36 < z

   1. Initial program 67.0%

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

   2. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-*r/ 55.0%

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

      3. associate-*r/ 55.0%

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

      4. div-sub 55.0%

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

      5. distribute-lft-out-- 55.0%

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

      6. sub-neg 55.0%

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

      7. mul-1-neg 55.0%

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

      8. +-commutative 55.0%

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

      9. associate-*r/ 55.0%

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

      10. mul-1-neg 55.0%

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

      11. +-commutative 55.0%

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

      12. mul-1-neg 55.0%

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

      13. sub-neg 55.0%

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

      14. distribute-rgt-out-- 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in a around 0 52.6%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+26}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 17: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+25)
   t
   (if (<= z -1.15e-93)
     x
     (if (<= z 8e-233) (* t (/ y a)) (if (<= z 1.3e+59) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+25) {
		tmp = t;
	} else if (z <= -1.15e-93) {
		tmp = x;
	} else if (z <= 8e-233) {
		tmp = t * (y / a);
	} else if (z <= 1.3e+59) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+25)) then
        tmp = t
    else if (z <= (-1.15d-93)) then
        tmp = x
    else if (z <= 8d-233) then
        tmp = t * (y / a)
    else if (z <= 1.3d+59) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+25) {
		tmp = t;
	} else if (z <= -1.15e-93) {
		tmp = x;
	} else if (z <= 8e-233) {
		tmp = t * (y / a);
	} else if (z <= 1.3e+59) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+25:
		tmp = t
	elif z <= -1.15e-93:
		tmp = x
	elif z <= 8e-233:
		tmp = t * (y / a)
	elif z <= 1.3e+59:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+25)
		tmp = t;
	elseif (z <= -1.15e-93)
		tmp = x;
	elseif (z <= 8e-233)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.3e+59)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+25)
		tmp = t;
	elseif (z <= -1.15e-93)
		tmp = x;
	elseif (z <= 8e-233)
		tmp = t * (y / a);
	elseif (z <= 1.3e+59)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+25], t, If[LessEqual[z, -1.15e-93], x, If[LessEqual[z, 8e-233], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+59], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e25 or 1.3e59 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -1.35e25 < z < -1.1499999999999999e-93 or 7.99999999999999966e-233 < z < 1.3e59

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 42.2%

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

   if -1.1499999999999999e-93 < z < 7.99999999999999966e-233

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 51.0%

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

      1. div-sub 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in z around 0 43.7%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+26)
   t
   (if (<= z -7.5e-94)
     x
     (if (<= z 4.5e-234) (/ (* y t) a) (if (<= z 9.5e+58) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+26) {
		tmp = t;
	} else if (z <= -7.5e-94) {
		tmp = x;
	} else if (z <= 4.5e-234) {
		tmp = (y * t) / a;
	} else if (z <= 9.5e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+26)) then
        tmp = t
    else if (z <= (-7.5d-94)) then
        tmp = x
    else if (z <= 4.5d-234) then
        tmp = (y * t) / a
    else if (z <= 9.5d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+26) {
		tmp = t;
	} else if (z <= -7.5e-94) {
		tmp = x;
	} else if (z <= 4.5e-234) {
		tmp = (y * t) / a;
	} else if (z <= 9.5e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+26:
		tmp = t
	elif z <= -7.5e-94:
		tmp = x
	elif z <= 4.5e-234:
		tmp = (y * t) / a
	elif z <= 9.5e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+26)
		tmp = t;
	elseif (z <= -7.5e-94)
		tmp = x;
	elseif (z <= 4.5e-234)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 9.5e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+26)
		tmp = t;
	elseif (z <= -7.5e-94)
		tmp = x;
	elseif (z <= 4.5e-234)
		tmp = (y * t) / a;
	elseif (z <= 9.5e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+26], t, If[LessEqual[z, -7.5e-94], x, If[LessEqual[z, 4.5e-234], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 9.5e+58], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000002e26 or 9.5000000000000002e58 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -2.60000000000000002e26 < z < -7.5000000000000003e-94 or 4.50000000000000009e-234 < z < 9.5000000000000002e58

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 42.2%

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

   if -7.5000000000000003e-94 < z < 4.50000000000000009e-234

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 51.0%

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

      1. div-sub 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in z around 0 43.7%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 53.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+26) t (if (<= z 5.8e+58) (+ x (/ y (/ a t))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+26) {
		tmp = t;
	} else if (z <= 5.8e+58) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+26)) then
        tmp = t
    else if (z <= 5.8d+58) then
        tmp = x + (y / (a / t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+26) {
		tmp = t;
	} else if (z <= 5.8e+58) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+26:
		tmp = t
	elif z <= 5.8e+58:
		tmp = x + (y / (a / t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 5.8e+58)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 5.8e+58)
		tmp = x + (y / (a / t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+26], t, If[LessEqual[z, 5.8e+58], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e26 or 5.80000000000000004e58 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -4.2000000000000002e26 < z < 5.80000000000000004e58

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 70.6%

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

      1. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in t around inf 62.7%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 39.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+25) t (if (<= z 2.3e+58) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+25) {
		tmp = t;
	} else if (z <= 2.3e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+25)) then
        tmp = t
    else if (z <= 2.3d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+25) {
		tmp = t;
	} else if (z <= 2.3e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+25:
		tmp = t
	elif z <= 2.3e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+25)
		tmp = t;
	elseif (z <= 2.3e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+25)
		tmp = t;
	elseif (z <= 2.3e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+25], t, If[LessEqual[z, 2.3e+58], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000005e25 or 2.30000000000000002e58 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -6.50000000000000005e25 < z < 2.30000000000000002e58

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 37.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 25.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 80.8%

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

2. Taylor expanded in z around inf 30.5%

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

3. Final simplification 30.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023297 
(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)))))