Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.0%

Time: 23.1s

Alternatives: 27

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: 94.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-209) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (+ t (/ (- x t) (* z (/ 1.0 (- y a))))))))

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-209) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	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-209) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	end
	return 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-209], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. remove-double-neg 90.3%

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

      3. unsub-neg 90.3%

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

      4. associate-*r/ 73.1%

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

      5. associate-/l* 90.8%

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

      6. associate-/r/ 93.7%

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

      7. fma-neg 93.7%

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

      8. remove-double-neg 93.7%

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

   3. Simplified 93.7%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 2.9%

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

   2. Taylor expanded in z around inf 77.3%

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

      1. associate--l+ 77.3%

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

      2. associate-*r/ 77.3%

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

      3. associate-*r/ 77.3%

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

      4. div-sub 77.3%

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

      5. distribute-lft-out-- 77.3%

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

      6. associate-*r/ 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

      9. distribute-rgt-out-- 77.3%

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

      10. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{z \cdot \frac{1}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \]

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (* (- y z) (- t x)) (- a z)))
     (if (or (<= t_1 -5e-209) (not (<= t_1 5e-293)))
       t_1
       (+ t (/ (- x t) (/ z (- y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else if ((t_1 <= -5e-209) || !(t_1 <= 5e-293)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else if ((t_1 <= -5e-209) || !(t_1 <= 5e-293)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (((y - z) * (t - x)) / (a - z))
	elif (t_1 <= -5e-209) or not (t_1 <= 5e-293):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)));
	elseif ((t_1 <= -5e-209) || !(t_1 <= 5e-293))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (((y - z) * (t - x)) / (a - z));
	elseif ((t_1 <= -5e-209) || ~((t_1 <= 5e-293)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-209], N[Not[LessEqual[t$95$1, 5e-293]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 77.4%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 5.0000000000000003e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.6%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000003e-293

   1. Initial program 3.1%

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

   2. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. div-sub 75.8%

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

      5. distribute-lft-out-- 75.8%

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

      6. associate-*r/ 75.8%

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

      7. mul-1-neg 75.8%

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

      8. unsub-neg 75.8%

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

      9. distribute-rgt-out-- 75.9%

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

      10. associate-/l* 97.0%

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

   4. Simplified 97.0%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - z}{y - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{t - x}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a z) (- y z))) (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -5e-209)
     (+ x (/ (- t x) t_1))
     (if (<= t_2 0.0)
       (+ t (/ (- x t) (* z (/ 1.0 (- y a)))))
       (+ x (/ 1.0 (/ t_1 (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / (y - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-209) {
		tmp = x + ((t - x) / t_1);
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	} else {
		tmp = x + (1.0 / (t_1 / (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) :: t_2
    real(8) :: tmp
    t_1 = (a - z) / (y - z)
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-5d-209)) then
        tmp = x + ((t - x) / t_1)
    else if (t_2 <= 0.0d0) then
        tmp = t + ((x - t) / (z * (1.0d0 / (y - a))))
    else
        tmp = x + (1.0d0 / (t_1 / (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 = (a - z) / (y - z);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -5e-209) {
		tmp = x + ((t - x) / t_1);
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	} else {
		tmp = x + (1.0 / (t_1 / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a - z) / (y - z)
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -5e-209:
		tmp = x + ((t - x) / t_1)
	elif t_2 <= 0.0:
		tmp = t + ((x - t) / (z * (1.0 / (y - a))))
	else:
		tmp = x + (1.0 / (t_1 / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - z) / Float64(y - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-209)
		tmp = Float64(x + Float64(Float64(t - x) / t_1));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - z) / (y - z);
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -5e-209)
		tmp = x + ((t - x) / t_1);
	elseif (t_2 <= 0.0)
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	else
		tmp = x + (1.0 / (t_1 / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-209], N[(x + N[(N[(t - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(t$95$1 / 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)))) < -5.0000000000000005e-209

   1. Initial program 91.3%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-/l* 94.8%

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

   3. Applied egg-rr 94.8%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 2.9%

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

   2. Taylor expanded in z around inf 77.3%

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

      1. associate--l+ 77.3%

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

      2. associate-*r/ 77.3%

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

      3. associate-*r/ 77.3%

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

      4. div-sub 77.3%

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

      5. distribute-lft-out-- 77.3%

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

      6. associate-*r/ 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

      9. distribute-rgt-out-- 77.3%

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

      10. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

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

   1. Initial program 89.4%

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

      1. associate-*r/ 70.6%

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

      2. clear-num 70.8%

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

      3. associate-/r* 92.5%

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

   3. Applied egg-rr 92.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - z}{y - z}}{t - x}}\\ \end{array} \]

Alternative 4: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-209) (not (<= t_1 5e-293)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 5e-293)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-209)) .or. (.not. (t_1 <= 5d-293))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 5e-293)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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-209) or not (t_1 <= 5e-293):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-209) || !(t_1 <= 5e-293))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-209) || ~((t_1 <= 5e-293)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-209], N[Not[LessEqual[t$95$1, 5e-293]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 5.0000000000000003e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.1%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000003e-293

   1. Initial program 3.1%

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

   2. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. div-sub 75.8%

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

      5. distribute-lft-out-- 75.8%

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

      6. associate-*r/ 75.8%

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

      7. mul-1-neg 75.8%

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

      8. unsub-neg 75.8%

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

      9. distribute-rgt-out-- 75.9%

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

      10. associate-/l* 97.0%

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

   4. Simplified 97.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-293}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 5: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-209) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-209)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-209) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-209) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-209], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

      1. associate-*r/ 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-/l* 93.7%

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

   3. Applied egg-rr 93.7%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 2.9%

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

   2. Taylor expanded in z around inf 77.3%

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

      1. associate--l+ 77.3%

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

      2. associate-*r/ 77.3%

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

      3. associate-*r/ 77.3%

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

      4. div-sub 77.3%

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

      5. distribute-lft-out-- 77.3%

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

      6. associate-*r/ 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

      9. distribute-rgt-out-- 77.3%

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

      10. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 6: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-209} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-209) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (- x t) (* z (/ 1.0 (- y a))))))))

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-209) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-209)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((x - t) / (z * (1.0d0 / (y - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-209) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	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-209) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((x - t) / (z * (1.0 / (y - a))))
	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-209) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	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-209) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	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-209], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

      1. associate-*r/ 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-/l* 93.7%

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

   3. Applied egg-rr 93.7%

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 2.9%

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

   2. Taylor expanded in z around inf 77.3%

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

      1. associate--l+ 77.3%

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

      2. associate-*r/ 77.3%

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

      3. associate-*r/ 77.3%

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

      4. div-sub 77.3%

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

      5. distribute-lft-out-- 77.3%

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

      6. associate-*r/ 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

      9. distribute-rgt-out-- 77.3%

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

      10. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto t - \frac{t - x}{\color{blue}{z \cdot \frac{1}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \]

Alternative 7: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := \frac{z}{a - z} \cdot \left(-t\right)\\ t_3 := \frac{t}{\frac{a - z}{y}}\\ \mathbf{if}\;z \leq -36000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a))))
        (t_2 (* (/ z (- a z)) (- t)))
        (t_3 (/ t (/ (- a z) y))))
   (if (<= z -36000.0)
     t_2
     (if (<= z -1.7e-31)
       t_1
       (if (<= z -2.8e-119)
         t_3
         (if (<= z 1.45e-91)
           (+ x (/ (* y t) a))
           (if (<= z 1.56e+49) t_1 (if (<= z 3.8e+72) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = (z / (a - z)) * -t;
	double t_3 = t / ((a - z) / y);
	double tmp;
	if (z <= -36000.0) {
		tmp = t_2;
	} else if (z <= -1.7e-31) {
		tmp = t_1;
	} else if (z <= -2.8e-119) {
		tmp = t_3;
	} else if (z <= 1.45e-91) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.56e+49) {
		tmp = t_1;
	} else if (z <= 3.8e+72) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = (z / (a - z)) * -t
    t_3 = t / ((a - z) / y)
    if (z <= (-36000.0d0)) then
        tmp = t_2
    else if (z <= (-1.7d-31)) then
        tmp = t_1
    else if (z <= (-2.8d-119)) then
        tmp = t_3
    else if (z <= 1.45d-91) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.56d+49) then
        tmp = t_1
    else if (z <= 3.8d+72) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = (z / (a - z)) * -t;
	double t_3 = t / ((a - z) / y);
	double tmp;
	if (z <= -36000.0) {
		tmp = t_2;
	} else if (z <= -1.7e-31) {
		tmp = t_1;
	} else if (z <= -2.8e-119) {
		tmp = t_3;
	} else if (z <= 1.45e-91) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.56e+49) {
		tmp = t_1;
	} else if (z <= 3.8e+72) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = (z / (a - z)) * -t
	t_3 = t / ((a - z) / y)
	tmp = 0
	if z <= -36000.0:
		tmp = t_2
	elif z <= -1.7e-31:
		tmp = t_1
	elif z <= -2.8e-119:
		tmp = t_3
	elif z <= 1.45e-91:
		tmp = x + ((y * t) / a)
	elif z <= 1.56e+49:
		tmp = t_1
	elif z <= 3.8e+72:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(Float64(z / Float64(a - z)) * Float64(-t))
	t_3 = Float64(t / Float64(Float64(a - z) / y))
	tmp = 0.0
	if (z <= -36000.0)
		tmp = t_2;
	elseif (z <= -1.7e-31)
		tmp = t_1;
	elseif (z <= -2.8e-119)
		tmp = t_3;
	elseif (z <= 1.45e-91)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.56e+49)
		tmp = t_1;
	elseif (z <= 3.8e+72)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = (z / (a - z)) * -t;
	t_3 = t / ((a - z) / y);
	tmp = 0.0;
	if (z <= -36000.0)
		tmp = t_2;
	elseif (z <= -1.7e-31)
		tmp = t_1;
	elseif (z <= -2.8e-119)
		tmp = t_3;
	elseif (z <= 1.45e-91)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.56e+49)
		tmp = t_1;
	elseif (z <= 3.8e+72)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision]}, Block[{t$95$3 = N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -36000.0], t$95$2, If[LessEqual[z, -1.7e-31], t$95$1, If[LessEqual[z, -2.8e-119], t$95$3, If[LessEqual[z, 1.45e-91], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e+49], t$95$1, If[LessEqual[z, 3.8e+72], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -36000 or 3.80000000000000006e72 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0 37.6%

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

      1. associate-*r/ 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in y around 0 50.8%

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

      1. neg-mul-1 50.8%

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

      2. distribute-neg-frac 50.8%

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

   7. Simplified 50.8%

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

   if -36000 < z < -1.7000000000000001e-31 or 1.45e-91 < z < 1.56e49

   1. Initial program 84.7%

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

      1. associate-*r/ 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-/l* 84.7%

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

   3. Applied egg-rr 84.7%

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

   4. Taylor expanded in x around inf 62.3%

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

      1. distribute-lft-in 62.3%

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

      2. *-rgt-identity 62.3%

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

      3. mul-1-neg 62.3%

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

      4. distribute-rgt-neg-in 62.3%

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

      5. unsub-neg 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in z around 0 57.6%

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

   if -1.7000000000000001e-31 < z < -2.8e-119 or 1.56e49 < z < 3.80000000000000006e72

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 46.1%

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

   3. Taylor expanded in y around inf 35.6%

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

      1. associate-/l* 47.8%

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

   5. Simplified 47.8%

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

   if -2.8e-119 < z < 1.45e-91

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf 68.6%

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

   3. Taylor expanded in z around 0 62.5%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-31}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+49}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \end{array} \]

Alternative 8: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.1e+74)
     t_2
     (if (<= t -1.95e+24)
       t_1
       (if (<= t -1.35e-98)
         t_2
         (if (<= t 6.5e-131)
           (/ (- y a) (/ z x))
           (if (<= t 1.35e-64) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.1e+74) {
		tmp = t_2;
	} else if (t <= -1.95e+24) {
		tmp = t_1;
	} else if (t <= -1.35e-98) {
		tmp = t_2;
	} else if (t <= 6.5e-131) {
		tmp = (y - a) / (z / x);
	} else if (t <= 1.35e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-2.1d+74)) then
        tmp = t_2
    else if (t <= (-1.95d+24)) then
        tmp = t_1
    else if (t <= (-1.35d-98)) then
        tmp = t_2
    else if (t <= 6.5d-131) then
        tmp = (y - a) / (z / x)
    else if (t <= 1.35d-64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.1e+74) {
		tmp = t_2;
	} else if (t <= -1.95e+24) {
		tmp = t_1;
	} else if (t <= -1.35e-98) {
		tmp = t_2;
	} else if (t <= 6.5e-131) {
		tmp = (y - a) / (z / x);
	} else if (t <= 1.35e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.1e+74:
		tmp = t_2
	elif t <= -1.95e+24:
		tmp = t_1
	elif t <= -1.35e-98:
		tmp = t_2
	elif t <= 6.5e-131:
		tmp = (y - a) / (z / x)
	elif t <= 1.35e-64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -2.1e+74)
		tmp = t_2;
	elseif (t <= -1.95e+24)
		tmp = t_1;
	elseif (t <= -1.35e-98)
		tmp = t_2;
	elseif (t <= 6.5e-131)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (t <= 1.35e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -2.1e+74)
		tmp = t_2;
	elseif (t <= -1.95e+24)
		tmp = t_1;
	elseif (t <= -1.35e-98)
		tmp = t_2;
	elseif (t <= 6.5e-131)
		tmp = (y - a) / (z / x);
	elseif (t <= 1.35e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+74], t$95$2, If[LessEqual[t, -1.95e+24], t$95$1, If[LessEqual[t, -1.35e-98], t$95$2, If[LessEqual[t, 6.5e-131], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-64], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e74 or -1.9499999999999999e24 < t < -1.3499999999999999e-98 or 1.34999999999999993e-64 < t

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 49.8%

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

      1. associate-*r/ 70.9%

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

   4. Simplified 70.9%

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

   if -2.0999999999999999e74 < t < -1.9499999999999999e24 or 6.5000000000000002e-131 < t < 1.34999999999999993e-64

   1. Initial program 80.7%

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

      1. associate-*r/ 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-/l* 85.1%

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

   3. Applied egg-rr 85.1%

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

   4. Taylor expanded in x around inf 67.4%

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

      1. distribute-lft-in 67.4%

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

      2. *-rgt-identity 67.4%

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

      3. mul-1-neg 67.4%

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

      4. distribute-rgt-neg-in 67.4%

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

      5. unsub-neg 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in z around 0 64.6%

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

   if -1.3499999999999999e-98 < t < 6.5000000000000002e-131

   1. Initial program 62.7%

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

   2. Taylor expanded in z around inf 56.2%

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

      1. associate--l+ 56.2%

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

      2. associate-*r/ 56.2%

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

      3. associate-*r/ 56.2%

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

      4. div-sub 56.3%

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

      5. distribute-lft-out-- 56.3%

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

      6. associate-*r/ 56.3%

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

      7. mul-1-neg 56.3%

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

      8. unsub-neg 56.3%

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

      9. distribute-rgt-out-- 56.4%

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

      10. associate-/l* 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. *-un-lft-identity 42.9%

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

      2. *-commutative 42.9%

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

      3. associate-/l* 52.1%

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

   7. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{1 \cdot \frac{y - a}{\frac{z}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+24}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-164}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -3.6e+120)
     t_2
     (if (<= y -1.75e-94)
       t_1
       (if (<= y -9e-164)
         (- x (/ (* x y) a))
         (if (<= y 1.02e+117) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -3.6e+120) {
		tmp = t_2;
	} else if (y <= -1.75e-94) {
		tmp = t_1;
	} else if (y <= -9e-164) {
		tmp = x - ((x * y) / a);
	} else if (y <= 1.02e+117) {
		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 = y * ((t - x) / (a - z))
    if (y <= (-3.6d+120)) then
        tmp = t_2
    else if (y <= (-1.75d-94)) then
        tmp = t_1
    else if (y <= (-9d-164)) then
        tmp = x - ((x * y) / a)
    else if (y <= 1.02d+117) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -3.6e+120) {
		tmp = t_2;
	} else if (y <= -1.75e-94) {
		tmp = t_1;
	} else if (y <= -9e-164) {
		tmp = x - ((x * y) / a);
	} else if (y <= 1.02e+117) {
		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 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -3.6e+120:
		tmp = t_2
	elif y <= -1.75e-94:
		tmp = t_1
	elif y <= -9e-164:
		tmp = x - ((x * y) / a)
	elif y <= 1.02e+117:
		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(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.6e+120)
		tmp = t_2;
	elseif (y <= -1.75e-94)
		tmp = t_1;
	elseif (y <= -9e-164)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	elseif (y <= 1.02e+117)
		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 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -3.6e+120)
		tmp = t_2;
	elseif (y <= -1.75e-94)
		tmp = t_1;
	elseif (y <= -9e-164)
		tmp = x - ((x * y) / a);
	elseif (y <= 1.02e+117)
		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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+120], t$95$2, If[LessEqual[y, -1.75e-94], t$95$1, If[LessEqual[y, -9e-164], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+117], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000016e120 or 1.02e117 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. div-sub 86.1%

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

   4. Simplified 86.1%

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

   if -3.60000000000000016e120 < y < -1.74999999999999999e-94 or -8.9999999999999995e-164 < y < 1.02e117

   1. Initial program 70.9%

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

   2. Taylor expanded in x around 0 45.0%

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

      1. associate-*r/ 57.9%

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

   4. Simplified 57.9%

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

   if -1.74999999999999999e-94 < y < -8.9999999999999995e-164

   1. Initial program 87.1%

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

      1. associate-*r/ 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-/l* 87.1%

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

   3. Applied egg-rr 87.1%

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

   4. Taylor expanded in x around inf 80.8%

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

      1. distribute-lft-in 80.8%

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

      2. *-rgt-identity 80.8%

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

      3. mul-1-neg 80.8%

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

      4. distribute-rgt-neg-in 80.8%

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

      5. unsub-neg 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in z around 0 80.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-164}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 10: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-163}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* y (/ (- t x) (- a z)))))
   (if (<= y -9.8e+120)
     t_2
     (if (<= y -5.6e-95)
       t_1
       (if (<= y -8.6e-163)
         (+ x (* (- y z) (/ t a)))
         (if (<= y 1e+117) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -9.8e+120) {
		tmp = t_2;
	} else if (y <= -5.6e-95) {
		tmp = t_1;
	} else if (y <= -8.6e-163) {
		tmp = x + ((y - z) * (t / a));
	} else if (y <= 1e+117) {
		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 = y * ((t - x) / (a - z))
    if (y <= (-9.8d+120)) then
        tmp = t_2
    else if (y <= (-5.6d-95)) then
        tmp = t_1
    else if (y <= (-8.6d-163)) then
        tmp = x + ((y - z) * (t / a))
    else if (y <= 1d+117) 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -9.8e+120) {
		tmp = t_2;
	} else if (y <= -5.6e-95) {
		tmp = t_1;
	} else if (y <= -8.6e-163) {
		tmp = x + ((y - z) * (t / a));
	} else if (y <= 1e+117) {
		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 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -9.8e+120:
		tmp = t_2
	elif y <= -5.6e-95:
		tmp = t_1
	elif y <= -8.6e-163:
		tmp = x + ((y - z) * (t / a))
	elif y <= 1e+117:
		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(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -9.8e+120)
		tmp = t_2;
	elseif (y <= -5.6e-95)
		tmp = t_1;
	elseif (y <= -8.6e-163)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	elseif (y <= 1e+117)
		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 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -9.8e+120)
		tmp = t_2;
	elseif (y <= -5.6e-95)
		tmp = t_1;
	elseif (y <= -8.6e-163)
		tmp = x + ((y - z) * (t / a));
	elseif (y <= 1e+117)
		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[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+120], t$95$2, If[LessEqual[y, -5.6e-95], t$95$1, If[LessEqual[y, -8.6e-163], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+117], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.80000000000000021e120 or 1.00000000000000005e117 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. div-sub 86.1%

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

   4. Simplified 86.1%

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

   if -9.80000000000000021e120 < y < -5.5999999999999998e-95 or -8.60000000000000017e-163 < y < 1.00000000000000005e117

   1. Initial program 70.9%

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

   2. Taylor expanded in x around 0 45.0%

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

      1. associate-*r/ 57.9%

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

   4. Simplified 57.9%

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

   if -5.5999999999999998e-95 < y < -8.60000000000000017e-163

   1. Initial program 87.1%

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

   2. Taylor expanded in t around inf 86.8%

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

   3. Taylor expanded in a around inf 86.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-163}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 10^{+117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 11: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= y -4.5e+115)
     t_1
     (if (<= y -8.4e-94)
       t
       (if (<= y -2.7e-169)
         x
         (if (<= y 1.45e-168) t (if (<= y 5e+217) t_1 (* y (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (y <= -4.5e+115) {
		tmp = t_1;
	} else if (y <= -8.4e-94) {
		tmp = t;
	} else if (y <= -2.7e-169) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 5e+217) {
		tmp = t_1;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / y)
    if (y <= (-4.5d+115)) then
        tmp = t_1
    else if (y <= (-8.4d-94)) then
        tmp = t
    else if (y <= (-2.7d-169)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else if (y <= 5d+217) then
        tmp = t_1
    else
        tmp = y * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (y <= -4.5e+115) {
		tmp = t_1;
	} else if (y <= -8.4e-94) {
		tmp = t;
	} else if (y <= -2.7e-169) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 5e+217) {
		tmp = t_1;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z / y)
	tmp = 0
	if y <= -4.5e+115:
		tmp = t_1
	elif y <= -8.4e-94:
		tmp = t
	elif y <= -2.7e-169:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	elif y <= 5e+217:
		tmp = t_1
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (y <= -4.5e+115)
		tmp = t_1;
	elseif (y <= -8.4e-94)
		tmp = t;
	elseif (y <= -2.7e-169)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 5e+217)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (y <= -4.5e+115)
		tmp = t_1;
	elseif (y <= -8.4e-94)
		tmp = t;
	elseif (y <= -2.7e-169)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 5e+217)
		tmp = t_1;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+115], t$95$1, If[LessEqual[y, -8.4e-94], t, If[LessEqual[y, -2.7e-169], x, If[LessEqual[y, 1.45e-168], t, If[LessEqual[y, 5e+217], t$95$1, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.49999999999999963e115 or 1.4499999999999999e-168 < y < 5.00000000000000041e217

   1. Initial program 83.3%

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

   2. Taylor expanded in z around inf 44.3%

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

      1. associate--l+ 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*r/ 44.3%

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

      4. div-sub 44.3%

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

      5. distribute-lft-out-- 44.3%

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

      6. associate-*r/ 44.3%

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

      7. mul-1-neg 44.3%

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

      8. unsub-neg 44.3%

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

      9. distribute-rgt-out-- 45.4%

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

      10. associate-/l* 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in t around 0 28.8%

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

   6. Taylor expanded in y around inf 28.8%

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

      1. associate-/l* 36.0%

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

   8. Simplified 36.0%

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

   if -4.49999999999999963e115 < y < -8.4000000000000004e-94 or -2.7000000000000002e-169 < y < 1.4499999999999999e-168

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 44.9%

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

   if -8.4000000000000004e-94 < y < -2.7000000000000002e-169

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 80.5%

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

   if 5.00000000000000041e217 < y

   1. Initial program 91.1%

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

   2. Taylor expanded in x around 0 46.0%

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

   3. Taylor expanded in z around 0 37.7%

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

      1. associate-/l* 49.7%

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

   5. Simplified 49.7%

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

      1. associate-/r/ 49.8%

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

   7. Applied egg-rr 49.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+217}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ z y))))
   (if (<= y -4.3e+114)
     t_1
     (if (<= y -5.5e-94)
       t
       (if (<= y -9.6e-173)
         x
         (if (<= y 1.45e-168) t (if (<= y 6.2e+216) t_1 (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z / y);
	double tmp;
	if (y <= -4.3e+114) {
		tmp = t_1;
	} else if (y <= -5.5e-94) {
		tmp = t;
	} else if (y <= -9.6e-173) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 6.2e+216) {
		tmp = t_1;
	} else {
		tmp = y / (a / 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 / (z / y)
    if (y <= (-4.3d+114)) then
        tmp = t_1
    else if (y <= (-5.5d-94)) then
        tmp = t
    else if (y <= (-9.6d-173)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else if (y <= 6.2d+216) then
        tmp = t_1
    else
        tmp = y / (a / 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 / (z / y);
	double tmp;
	if (y <= -4.3e+114) {
		tmp = t_1;
	} else if (y <= -5.5e-94) {
		tmp = t;
	} else if (y <= -9.6e-173) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 6.2e+216) {
		tmp = t_1;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z / y)
	tmp = 0
	if y <= -4.3e+114:
		tmp = t_1
	elif y <= -5.5e-94:
		tmp = t
	elif y <= -9.6e-173:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	elif y <= 6.2e+216:
		tmp = t_1
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (y <= -4.3e+114)
		tmp = t_1;
	elseif (y <= -5.5e-94)
		tmp = t;
	elseif (y <= -9.6e-173)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 6.2e+216)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (z / y);
	tmp = 0.0;
	if (y <= -4.3e+114)
		tmp = t_1;
	elseif (y <= -5.5e-94)
		tmp = t;
	elseif (y <= -9.6e-173)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 6.2e+216)
		tmp = t_1;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+114], t$95$1, If[LessEqual[y, -5.5e-94], t, If[LessEqual[y, -9.6e-173], x, If[LessEqual[y, 1.45e-168], t, If[LessEqual[y, 6.2e+216], t$95$1, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3000000000000001e114 or 1.4499999999999999e-168 < y < 6.20000000000000007e216

   1. Initial program 83.3%

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

   2. Taylor expanded in z around inf 44.3%

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

      1. associate--l+ 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*r/ 44.3%

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

      4. div-sub 44.3%

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

      5. distribute-lft-out-- 44.3%

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

      6. associate-*r/ 44.3%

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

      7. mul-1-neg 44.3%

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

      8. unsub-neg 44.3%

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

      9. distribute-rgt-out-- 45.4%

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

      10. associate-/l* 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in t around 0 28.8%

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

   6. Taylor expanded in y around inf 28.8%

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

      1. associate-/l* 36.0%

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

   8. Simplified 36.0%

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

   if -4.3000000000000001e114 < y < -5.49999999999999989e-94 or -9.60000000000000068e-173 < y < 1.4499999999999999e-168

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 44.9%

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

   if -5.49999999999999989e-94 < y < -9.60000000000000068e-173

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 80.5%

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

   if 6.20000000000000007e216 < y

   1. Initial program 91.1%

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

   2. Taylor expanded in x around 0 46.0%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

      1. clear-num 58.0%

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

      2. un-div-inv 58.0%

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

   6. Applied egg-rr 58.0%

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

   7. Taylor expanded in z around 0 37.7%

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

      1. *-commutative 37.7%

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

      2. associate-/l* 49.9%

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

   9. Simplified 49.9%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 13: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ z x))))
   (if (<= y -6.2e+116)
     t_1
     (if (<= y -2.05e-94)
       t
       (if (<= y -3.1e-165)
         x
         (if (<= y 1.45e-168) t (if (<= y 4.8e+217) t_1 (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z / x);
	double tmp;
	if (y <= -6.2e+116) {
		tmp = t_1;
	} else if (y <= -2.05e-94) {
		tmp = t;
	} else if (y <= -3.1e-165) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 4.8e+217) {
		tmp = t_1;
	} else {
		tmp = y / (a / 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 = y / (z / x)
    if (y <= (-6.2d+116)) then
        tmp = t_1
    else if (y <= (-2.05d-94)) then
        tmp = t
    else if (y <= (-3.1d-165)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t
    else if (y <= 4.8d+217) then
        tmp = t_1
    else
        tmp = y / (a / 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 = y / (z / x);
	double tmp;
	if (y <= -6.2e+116) {
		tmp = t_1;
	} else if (y <= -2.05e-94) {
		tmp = t;
	} else if (y <= -3.1e-165) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t;
	} else if (y <= 4.8e+217) {
		tmp = t_1;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (z / x)
	tmp = 0
	if y <= -6.2e+116:
		tmp = t_1
	elif y <= -2.05e-94:
		tmp = t
	elif y <= -3.1e-165:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t
	elif y <= 4.8e+217:
		tmp = t_1
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (y <= -6.2e+116)
		tmp = t_1;
	elseif (y <= -2.05e-94)
		tmp = t;
	elseif (y <= -3.1e-165)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 4.8e+217)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (z / x);
	tmp = 0.0;
	if (y <= -6.2e+116)
		tmp = t_1;
	elseif (y <= -2.05e-94)
		tmp = t;
	elseif (y <= -3.1e-165)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t;
	elseif (y <= 4.8e+217)
		tmp = t_1;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+116], t$95$1, If[LessEqual[y, -2.05e-94], t, If[LessEqual[y, -3.1e-165], x, If[LessEqual[y, 1.45e-168], t, If[LessEqual[y, 4.8e+217], t$95$1, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.19999999999999992e116 or 1.4499999999999999e-168 < y < 4.7999999999999996e217

   1. Initial program 83.3%

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

   2. Taylor expanded in z around inf 44.3%

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

      1. associate--l+ 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*r/ 44.3%

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

      4. div-sub 44.3%

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

      5. distribute-lft-out-- 44.3%

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

      6. associate-*r/ 44.3%

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

      7. mul-1-neg 44.3%

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

      8. unsub-neg 44.3%

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

      9. distribute-rgt-out-- 45.4%

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

      10. associate-/l* 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in t around 0 28.8%

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

   6. Taylor expanded in y around inf 28.8%

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

      1. *-commutative 28.8%

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

      2. associate-/l* 36.0%

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

   8. Simplified 36.0%

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

   if -6.19999999999999992e116 < y < -2.05e-94 or -3.09999999999999996e-165 < y < 1.4499999999999999e-168

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 44.9%

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

   if -2.05e-94 < y < -3.09999999999999996e-165

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 80.5%

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

   if 4.7999999999999996e217 < y

   1. Initial program 91.1%

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

   2. Taylor expanded in x around 0 46.0%

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

      1. associate-*r/ 58.1%

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

   4. Simplified 58.1%

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

      1. clear-num 58.0%

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

      2. un-div-inv 58.0%

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

   6. Applied egg-rr 58.0%

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

   7. Taylor expanded in z around 0 37.7%

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

      1. *-commutative 37.7%

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

      2. associate-/l* 49.9%

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

   9. Simplified 49.9%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+217}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 14: 36.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+152}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -1e+152)
     t
     (if (<= z -6.2e-173)
       t_1
       (if (<= z 3.7e-241)
         x
         (if (<= z 2.5e-91) t_1 (if (<= z 8.5e+72) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -1e+152) {
		tmp = t;
	} else if (z <= -6.2e-173) {
		tmp = t_1;
	} else if (z <= 3.7e-241) {
		tmp = x;
	} else if (z <= 2.5e-91) {
		tmp = t_1;
	} else if (z <= 8.5e+72) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (z <= (-1d+152)) then
        tmp = t
    else if (z <= (-6.2d-173)) then
        tmp = t_1
    else if (z <= 3.7d-241) then
        tmp = x
    else if (z <= 2.5d-91) then
        tmp = t_1
    else if (z <= 8.5d+72) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -1e+152) {
		tmp = t;
	} else if (z <= -6.2e-173) {
		tmp = t_1;
	} else if (z <= 3.7e-241) {
		tmp = x;
	} else if (z <= 2.5e-91) {
		tmp = t_1;
	} else if (z <= 8.5e+72) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -1e+152:
		tmp = t
	elif z <= -6.2e-173:
		tmp = t_1
	elif z <= 3.7e-241:
		tmp = x
	elif z <= 2.5e-91:
		tmp = t_1
	elif z <= 8.5e+72:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -1e+152)
		tmp = t;
	elseif (z <= -6.2e-173)
		tmp = t_1;
	elseif (z <= 3.7e-241)
		tmp = x;
	elseif (z <= 2.5e-91)
		tmp = t_1;
	elseif (z <= 8.5e+72)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -1e+152)
		tmp = t;
	elseif (z <= -6.2e-173)
		tmp = t_1;
	elseif (z <= 3.7e-241)
		tmp = x;
	elseif (z <= 2.5e-91)
		tmp = t_1;
	elseif (z <= 8.5e+72)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+152], t, If[LessEqual[z, -6.2e-173], t$95$1, If[LessEqual[z, 3.7e-241], x, If[LessEqual[z, 2.5e-91], t$95$1, If[LessEqual[z, 8.5e+72], x, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e152 or 8.5000000000000004e72 < z

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 52.0%

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

   if -1e152 < z < -6.20000000000000011e-173 or 3.6999999999999999e-241 < z < 2.49999999999999999e-91

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 41.4%

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

      1. associate-*r/ 53.2%

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

   4. Simplified 53.2%

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

   5. Taylor expanded in a around inf 38.3%

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

   if -6.20000000000000011e-173 < z < 3.6999999999999999e-241 or 2.49999999999999999e-91 < z < 8.5000000000000004e72

   1. Initial program 87.6%

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

   2. Taylor expanded in a around inf 41.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+152}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 33.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -2.4e+49)
     (* x (/ (- y a) z))
     (if (<= z -1.15e-170)
       t_1
       (if (<= z 2.05e-240)
         x
         (if (<= z 8.8e-88) t_1 (if (<= z 3e+74) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.4e+49) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.15e-170) {
		tmp = t_1;
	} else if (z <= 2.05e-240) {
		tmp = x;
	} else if (z <= 8.8e-88) {
		tmp = t_1;
	} else if (z <= 3e+74) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (z <= (-2.4d+49)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.15d-170)) then
        tmp = t_1
    else if (z <= 2.05d-240) then
        tmp = x
    else if (z <= 8.8d-88) then
        tmp = t_1
    else if (z <= 3d+74) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -2.4e+49) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.15e-170) {
		tmp = t_1;
	} else if (z <= 2.05e-240) {
		tmp = x;
	} else if (z <= 8.8e-88) {
		tmp = t_1;
	} else if (z <= 3e+74) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -2.4e+49:
		tmp = x * ((y - a) / z)
	elif z <= -1.15e-170:
		tmp = t_1
	elif z <= 2.05e-240:
		tmp = x
	elif z <= 8.8e-88:
		tmp = t_1
	elif z <= 3e+74:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -2.4e+49)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.15e-170)
		tmp = t_1;
	elseif (z <= 2.05e-240)
		tmp = x;
	elseif (z <= 8.8e-88)
		tmp = t_1;
	elseif (z <= 3e+74)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -2.4e+49)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.15e-170)
		tmp = t_1;
	elseif (z <= 2.05e-240)
		tmp = x;
	elseif (z <= 8.8e-88)
		tmp = t_1;
	elseif (z <= 3e+74)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+49], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-170], t$95$1, If[LessEqual[z, 2.05e-240], x, If[LessEqual[z, 8.8e-88], t$95$1, If[LessEqual[z, 3e+74], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e49

   1. Initial program 65.7%

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

   2. Taylor expanded in z around inf 62.0%

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

      1. associate--l+ 62.0%

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

      2. associate-*r/ 62.0%

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

      3. associate-*r/ 62.0%

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

      4. div-sub 62.0%

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

      5. distribute-lft-out-- 62.0%

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

      6. associate-*r/ 62.0%

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

      7. mul-1-neg 62.0%

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

      8. unsub-neg 62.0%

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

      9. distribute-rgt-out-- 62.0%

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

      10. associate-/l* 80.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in t around 0 29.1%

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

      1. associate-*r/ 42.2%

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

   7. Simplified 42.2%

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

   if -2.4e49 < z < -1.14999999999999993e-170 or 2.0500000000000001e-240 < z < 8.8000000000000002e-88

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 46.0%

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

      1. associate-*r/ 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in a around inf 41.2%

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

   if -1.14999999999999993e-170 < z < 2.0500000000000001e-240 or 8.8000000000000002e-88 < z < 3e74

   1. Initial program 87.6%

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

   2. Taylor expanded in a around inf 41.5%

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

   if 3e74 < z

   1. Initial program 64.0%

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

   2. Taylor expanded in z around inf 53.4%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -265000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -265000000000.0)
     (+ x (/ (* y t) a))
     (if (<= a 5.3e-219)
       t_1
       (if (<= a 5.2e-201)
         (/ x (/ z y))
         (if (<= a 2.7e-48) t_1 (- x (/ x (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -265000000000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.3e-219) {
		tmp = t_1;
	} else if (a <= 5.2e-201) {
		tmp = x / (z / y);
	} else if (a <= 2.7e-48) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-265000000000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= 5.3d-219) then
        tmp = t_1
    else if (a <= 5.2d-201) then
        tmp = x / (z / y)
    else if (a <= 2.7d-48) then
        tmp = t_1
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -265000000000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.3e-219) {
		tmp = t_1;
	} else if (a <= 5.2e-201) {
		tmp = x / (z / y);
	} else if (a <= 2.7e-48) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -265000000000.0:
		tmp = x + ((y * t) / a)
	elif a <= 5.3e-219:
		tmp = t_1
	elif a <= 5.2e-201:
		tmp = x / (z / y)
	elif a <= 2.7e-48:
		tmp = t_1
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -265000000000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 5.3e-219)
		tmp = t_1;
	elseif (a <= 5.2e-201)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.7e-48)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -265000000000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= 5.3e-219)
		tmp = t_1;
	elseif (a <= 5.2e-201)
		tmp = x / (z / y);
	elseif (a <= 2.7e-48)
		tmp = t_1;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -265000000000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-219], t$95$1, If[LessEqual[a, 5.2e-201], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-48], t$95$1, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.65e11

   1. Initial program 84.1%

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

   2. Taylor expanded in t around inf 72.4%

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

   3. Taylor expanded in z around 0 51.9%

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

   if -2.65e11 < a < 5.3000000000000003e-219 or 5.19999999999999965e-201 < a < 2.70000000000000011e-48

   1. Initial program 68.9%

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

   2. Taylor expanded in x around 0 51.5%

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

      1. associate-*r/ 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. associate-*r/ 59.7%

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

      2. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   if 5.3000000000000003e-219 < a < 5.19999999999999965e-201

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 82.9%

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

      1. associate--l+ 82.9%

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

      2. associate-*r/ 82.9%

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

      3. associate-*r/ 82.9%

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

      4. div-sub 82.9%

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

      5. distribute-lft-out-- 82.9%

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

      6. associate-*r/ 82.9%

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

      7. mul-1-neg 82.9%

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

      8. unsub-neg 82.9%

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

      9. distribute-rgt-out-- 82.9%

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

      10. associate-/l* 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in t around 0 83.2%

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

   6. Taylor expanded in y around inf 83.2%

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

      1. associate-/l* 83.8%

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

   8. Simplified 83.8%

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

   if 2.70000000000000011e-48 < a

   1. Initial program 95.0%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-/l* 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in x around inf 58.8%

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

      1. distribute-lft-in 58.9%

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

      2. *-rgt-identity 58.9%

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

      3. mul-1-neg 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

      5. unsub-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in z around 0 47.7%

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

      1. associate-/l* 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -265000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 17: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+152)
   (+ t (/ a (/ z (- t x))))
   (if (<= z -3.6e-115)
     (* y (/ (- t x) (- a z)))
     (if (<= z 6e+46) (+ x (/ y (/ a (- t x)))) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+152) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -3.6e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.4d+152)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-3.6d-115)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 6d+46) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+152) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -3.6e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+152:
		tmp = t + (a / (z / (t - x)))
	elif z <= -3.6e-115:
		tmp = y * ((t - x) / (a - z))
	elif z <= 6e+46:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+152)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -3.6e-115)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 6e+46)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e+152)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -3.6e-115)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 6e+46)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+152], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-115], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+46], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e152

   1. Initial program 54.8%

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

   2. Taylor expanded in z around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-*r/ 68.1%

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

      3. associate-*r/ 68.1%

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

      4. div-sub 68.1%

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

      5. distribute-lft-out-- 68.1%

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

      6. associate-*r/ 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

      9. distribute-rgt-out-- 68.2%

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

      10. associate-/l* 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. remove-double-neg 61.7%

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

      4. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

   if -1.4000000000000001e152 < z < -3.60000000000000009e-115

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   4. Simplified 57.4%

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

   if -3.60000000000000009e-115 < z < 6.00000000000000047e46

   1. Initial program 89.9%

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

   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* 75.9%

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

   4. Simplified 75.9%

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

   if 6.00000000000000047e46 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 49.0%

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

      1. associate-*r/ 66.9%

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

   4. Simplified 66.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 18: 63.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+152)
   (+ t (/ a (/ z (- t x))))
   (if (<= z -5.4e-101)
     (* y (/ (- t x) (- a z)))
     (if (<= z 9.2e+46) (+ x (/ y (/ a (- t x)))) (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+152) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.4e-101) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.2e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+152)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-5.4d-101)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 9.2d+46) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+152) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.4e-101) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.2e+46) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+152:
		tmp = t + (a / (z / (t - x)))
	elif z <= -5.4e-101:
		tmp = y * ((t - x) / (a - z))
	elif z <= 9.2e+46:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+152)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -5.4e-101)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 9.2e+46)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+152)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -5.4e-101)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 9.2e+46)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+152], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e-101], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+46], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5e152

   1. Initial program 54.8%

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

   2. Taylor expanded in z around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-*r/ 68.1%

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

      3. associate-*r/ 68.1%

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

      4. div-sub 68.1%

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

      5. distribute-lft-out-- 68.1%

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

      6. associate-*r/ 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

      9. distribute-rgt-out-- 68.2%

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

      10. associate-/l* 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. remove-double-neg 61.7%

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

      4. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

   if -2.5e152 < z < -5.4000000000000003e-101

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   4. Simplified 57.4%

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

   if -5.4000000000000003e-101 < z < 9.2000000000000002e46

   1. Initial program 89.9%

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

   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* 75.9%

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

   4. Simplified 75.9%

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

   if 9.2000000000000002e46 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 49.0%

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

      1. associate-*r/ 66.9%

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

   4. Simplified 66.9%

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

      1. clear-num 66.8%

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

      2. un-div-inv 66.9%

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

   6. Applied egg-rr 66.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 19: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{x - t}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+152)
   (+ t (/ (- x t) (/ (- z) a)))
   (if (<= z -9.5e-115)
     (* y (/ (- t x) (- a z)))
     (if (<= z 2.45e+48)
       (+ x (/ y (/ a (- t x))))
       (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+152) {
		tmp = t + ((x - t) / (-z / a));
	} else if (z <= -9.5e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.45e+48) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+152)) then
        tmp = t + ((x - t) / (-z / a))
    else if (z <= (-9.5d-115)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 2.45d+48) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t / ((a - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+152) {
		tmp = t + ((x - t) / (-z / a));
	} else if (z <= -9.5e-115) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.45e+48) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+152:
		tmp = t + ((x - t) / (-z / a))
	elif z <= -9.5e-115:
		tmp = y * ((t - x) / (a - z))
	elif z <= 2.45e+48:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+152)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(Float64(-z) / a)));
	elseif (z <= -9.5e-115)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 2.45e+48)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+152)
		tmp = t + ((x - t) / (-z / a));
	elseif (z <= -9.5e-115)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 2.45e+48)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+152], N[(t + N[(N[(x - t), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-115], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+48], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.29999999999999985e152

   1. Initial program 54.8%

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

   2. Taylor expanded in z around inf 68.1%

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

      1. associate--l+ 68.1%

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

      2. associate-*r/ 68.1%

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

      3. associate-*r/ 68.1%

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

      4. div-sub 68.1%

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

      5. distribute-lft-out-- 68.1%

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

      6. associate-*r/ 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

      9. distribute-rgt-out-- 68.2%

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

      10. associate-/l* 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

   7. Simplified 63.8%

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

   if -2.29999999999999985e152 < z < -9.4999999999999996e-115

   1. Initial program 83.1%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   4. Simplified 57.4%

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

   if -9.4999999999999996e-115 < z < 2.45000000000000015e48

   1. Initial program 89.9%

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

   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* 75.9%

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

   4. Simplified 75.9%

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

   if 2.45000000000000015e48 < z

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 49.0%

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

      1. associate-*r/ 66.9%

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

   4. Simplified 66.9%

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

      1. clear-num 66.8%

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

      2. un-div-inv 66.9%

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

   6. Applied egg-rr 66.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;t + \frac{x - t}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 20: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+95} \lor \neg \left(y \leq 1.32 \cdot 10^{+143}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.4e+95) (not (<= y 1.32e+143)))
   (* y (/ (- t x) (- a z)))
   (+ x (* (- y z) (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.4e+95) || !(y <= 1.32e+143)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.4d+95)) .or. (.not. (y <= 1.32d+143))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = x + ((y - z) * (t / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.4e+95) || !(y <= 1.32e+143)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.4e+95) or not (y <= 1.32e+143):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.4e+95) || !(y <= 1.32e+143))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.4e+95) || ~((y <= 1.32e+143)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.4e+95], N[Not[LessEqual[y, 1.32e+143]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e95 or 1.3200000000000001e143 < y

   1. Initial program 86.6%

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

   2. Taylor expanded in y around inf 85.7%

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

      1. div-sub 85.7%

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

   4. Simplified 85.7%

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

   if -4.3999999999999998e95 < y < 1.3200000000000001e143

   1. Initial program 74.6%

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

   2. Taylor expanded in t around inf 68.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+95} \lor \neg \left(y \leq 1.32 \cdot 10^{+143}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 21: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+33} \lor \neg \left(a \leq 6.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e+33) (not (<= a 6.6e-42)))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e+33) || !(a <= 6.6e-42)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.7d+33)) .or. (.not. (a <= 6.6d-42))) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e+33) || !(a <= 6.6e-42)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.7e+33) or not (a <= 6.6e-42):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e+33) || !(a <= 6.6e-42))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.7e+33) || ~((a <= 6.6e-42)))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e+33], N[Not[LessEqual[a, 6.6e-42]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7e33 or 6.6000000000000005e-42 < a

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 59.1%

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

      1. associate-/l* 79.1%

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

   4. Simplified 79.1%

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

   if -1.7e33 < a < 6.6000000000000005e-42

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 74.0%

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

      1. associate--l+ 74.0%

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

      2. associate-*r/ 74.0%

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

      3. associate-*r/ 74.0%

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

      4. div-sub 74.0%

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

      5. distribute-lft-out-- 74.0%

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

      6. associate-*r/ 74.0%

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

      7. mul-1-neg 74.0%

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

      8. unsub-neg 74.0%

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

      9. distribute-rgt-out-- 74.0%

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

      10. associate-/l* 81.0%

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

   4. Simplified 81.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+33} \lor \neg \left(a \leq 6.6 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 22: 44.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -9.5e-45)
     t_1
     (if (<= a 1.8e-146) (* x (/ (- y a) z)) (if (<= a 3.8e-42) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -9.5e-45) {
		tmp = t_1;
	} else if (a <= 1.8e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 3.8e-42) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-9.5d-45)) then
        tmp = t_1
    else if (a <= 1.8d-146) then
        tmp = x * ((y - a) / z)
    else if (a <= 3.8d-42) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -9.5e-45) {
		tmp = t_1;
	} else if (a <= 1.8e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 3.8e-42) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -9.5e-45:
		tmp = t_1
	elif a <= 1.8e-146:
		tmp = x * ((y - a) / z)
	elif a <= 3.8e-42:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -9.5e-45)
		tmp = t_1;
	elseif (a <= 1.8e-146)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 3.8e-42)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -9.5e-45)
		tmp = t_1;
	elseif (a <= 1.8e-146)
		tmp = x * ((y - a) / z);
	elseif (a <= 3.8e-42)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-45], t$95$1, If[LessEqual[a, 1.8e-146], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-42], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000002e-45 or 3.80000000000000017e-42 < a

   1. Initial program 90.0%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in z around 0 51.9%

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

   if -9.5000000000000002e-45 < a < 1.79999999999999989e-146

   1. Initial program 63.7%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. div-sub 74.2%

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

      5. distribute-lft-out-- 74.2%

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

      6. associate-*r/ 74.2%

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

      7. mul-1-neg 74.2%

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

      8. unsub-neg 74.2%

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

      9. distribute-rgt-out-- 74.2%

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

      10. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 36.6%

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

      1. associate-*r/ 41.9%

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

   7. Simplified 41.9%

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

   if 1.79999999999999989e-146 < a < 3.80000000000000017e-42

   1. Initial program 78.6%

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

   2. Taylor expanded in z around inf 50.4%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 23: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.4e-45)
   (+ x (/ (* y t) a))
   (if (<= a 1.9e-146)
     (* x (/ (- y a) z))
     (if (<= a 2.6e-48) t (- x (* x (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-45) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.9e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.6e-48) {
		tmp = t;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.4d-45)) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.9d-146) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.6d-48) then
        tmp = t
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-45) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.9e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.6e-48) {
		tmp = t;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e-45:
		tmp = x + ((y * t) / a)
	elif a <= 1.9e-146:
		tmp = x * ((y - a) / z)
	elif a <= 2.6e-48:
		tmp = t
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e-45)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.9e-146)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.6e-48)
		tmp = t;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e-45)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.9e-146)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.6e-48)
		tmp = t;
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e-45], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-146], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-48], t, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.39999999999999987e-45

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 74.8%

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

   3. Taylor expanded in z around 0 49.8%

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

   if -4.39999999999999987e-45 < a < 1.89999999999999997e-146

   1. Initial program 63.7%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. div-sub 74.2%

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

      5. distribute-lft-out-- 74.2%

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

      6. associate-*r/ 74.2%

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

      7. mul-1-neg 74.2%

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

      8. unsub-neg 74.2%

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

      9. distribute-rgt-out-- 74.2%

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

      10. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 36.6%

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

      1. associate-*r/ 41.9%

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

   7. Simplified 41.9%

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

   if 1.89999999999999997e-146 < a < 2.59999999999999987e-48

   1. Initial program 76.8%

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

   2. Taylor expanded in z around inf 50.3%

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

   if 2.59999999999999987e-48 < a

   1. Initial program 95.0%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-/l* 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in x around inf 58.8%

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

      1. distribute-lft-in 58.9%

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

      2. *-rgt-identity 58.9%

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

      3. mul-1-neg 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

      5. unsub-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in z around 0 55.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 24: 44.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-44)
   (+ x (/ (* y t) a))
   (if (<= a 1.8e-146)
     (* x (/ (- y a) z))
     (if (<= a 1.4e-48) t (- x (/ x (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-44) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.8e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.4e-48) {
		tmp = t;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d-44)) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.8d-146) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.4d-48) then
        tmp = t
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-44) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.8e-146) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.4e-48) {
		tmp = t;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-44:
		tmp = x + ((y * t) / a)
	elif a <= 1.8e-146:
		tmp = x * ((y - a) / z)
	elif a <= 1.4e-48:
		tmp = t
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-44)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.8e-146)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.4e-48)
		tmp = t;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e-44)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.8e-146)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.4e-48)
		tmp = t;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-44], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-146], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-48], t, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.10000000000000006e-44

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 74.8%

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

   3. Taylor expanded in z around 0 49.8%

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

   if -1.10000000000000006e-44 < a < 1.79999999999999989e-146

   1. Initial program 63.7%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. div-sub 74.2%

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

      5. distribute-lft-out-- 74.2%

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

      6. associate-*r/ 74.2%

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

      7. mul-1-neg 74.2%

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

      8. unsub-neg 74.2%

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

      9. distribute-rgt-out-- 74.2%

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

      10. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 36.6%

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

      1. associate-*r/ 41.9%

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

   7. Simplified 41.9%

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

   if 1.79999999999999989e-146 < a < 1.40000000000000002e-48

   1. Initial program 76.8%

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

   2. Taylor expanded in z around inf 50.3%

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

   if 1.40000000000000002e-48 < a

   1. Initial program 95.0%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-/l* 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in x around inf 58.8%

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

      1. distribute-lft-in 58.9%

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

      2. *-rgt-identity 58.9%

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

      3. mul-1-neg 58.9%

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

      4. distribute-rgt-neg-in 58.9%

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

      5. unsub-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in z around 0 47.7%

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

      1. associate-/l* 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 25: 37.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+184)
   x
   (if (<= a -5.5e+96) t (if (<= a -3.1e+29) x (if (<= a 1.2e-41) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -5.5e+96) {
		tmp = t;
	} else if (a <= -3.1e+29) {
		tmp = x;
	} else if (a <= 1.2e-41) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+184)) then
        tmp = x
    else if (a <= (-5.5d+96)) then
        tmp = t
    else if (a <= (-3.1d+29)) then
        tmp = x
    else if (a <= 1.2d-41) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -5.5e+96) {
		tmp = t;
	} else if (a <= -3.1e+29) {
		tmp = x;
	} else if (a <= 1.2e-41) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+184:
		tmp = x
	elif a <= -5.5e+96:
		tmp = t
	elif a <= -3.1e+29:
		tmp = x
	elif a <= 1.2e-41:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -5.5e+96)
		tmp = t;
	elseif (a <= -3.1e+29)
		tmp = x;
	elseif (a <= 1.2e-41)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -5.5e+96)
		tmp = t;
	elseif (a <= -3.1e+29)
		tmp = x;
	elseif (a <= 1.2e-41)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+184], x, If[LessEqual[a, -5.5e+96], t, If[LessEqual[a, -3.1e+29], x, If[LessEqual[a, 1.2e-41], t, x]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000002e184 or -5.5000000000000002e96 < a < -3.0999999999999999e29 or 1.20000000000000011e-41 < a

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 48.4%

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

   if -1.00000000000000002e184 < a < -5.5000000000000002e96 or -3.0999999999999999e29 < a < 1.20000000000000011e-41

   1. Initial program 69.5%

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

   2. Taylor expanded in z around inf 36.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 37.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+184)
   x
   (if (<= a -1.8e+96)
     (+ x (- t x))
     (if (<= a -1.05e+38) x (if (<= a 9.2e-42) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -1.8e+96) {
		tmp = x + (t - x);
	} else if (a <= -1.05e+38) {
		tmp = x;
	} else if (a <= 9.2e-42) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+184)) then
        tmp = x
    else if (a <= (-1.8d+96)) then
        tmp = x + (t - x)
    else if (a <= (-1.05d+38)) then
        tmp = x
    else if (a <= 9.2d-42) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+184) {
		tmp = x;
	} else if (a <= -1.8e+96) {
		tmp = x + (t - x);
	} else if (a <= -1.05e+38) {
		tmp = x;
	} else if (a <= 9.2e-42) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+184:
		tmp = x
	elif a <= -1.8e+96:
		tmp = x + (t - x)
	elif a <= -1.05e+38:
		tmp = x
	elif a <= 9.2e-42:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -1.8e+96)
		tmp = Float64(x + Float64(t - x));
	elseif (a <= -1.05e+38)
		tmp = x;
	elseif (a <= 9.2e-42)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+184)
		tmp = x;
	elseif (a <= -1.8e+96)
		tmp = x + (t - x);
	elseif (a <= -1.05e+38)
		tmp = x;
	elseif (a <= 9.2e-42)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+184], x, If[LessEqual[a, -1.8e+96], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e+38], x, If[LessEqual[a, 9.2e-42], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.00000000000000002e184 or -1.80000000000000007e96 < a < -1.05e38 or 9.20000000000000015e-42 < a

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 48.4%

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

   if -1.00000000000000002e184 < a < -1.80000000000000007e96

   1. Initial program 76.0%

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

   2. Taylor expanded in z around inf 33.9%

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

   if -1.05e38 < a < 9.20000000000000015e-42

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 36.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.7%

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

2. Taylor expanded in z around inf 24.5%

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

3. Final simplification 24.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023271 
(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)))))