Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.7% → 90.1%

Time: 19.6s

Alternatives: 20

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: 79.7% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-241} \lor \neg \left(t_2 \leq 5 \cdot 10^{-214}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (or (<= t_2 -5e-241) (not (<= t_2 5e-214)))
     (fma (- y z) t_1 x)
     (- t (/ x (/ z (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if ((t_2 <= -5e-241) || !(t_2 <= 5e-214)) {
		tmp = fma((y - z), t_1, x);
	} else {
		tmp = t - (x / (z / (a - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if ((t_2 <= -5e-241) || !(t_2 <= 5e-214))
		tmp = fma(Float64(y - z), t_1, x);
	else
		tmp = Float64(t - Float64(x / Float64(z / Float64(a - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e-241], N[Not[LessEqual[t$95$2, 5e-214]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(t - N[(x / N[(z / N[(a - y), $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)))) < -4.9999999999999998e-241 or 4.9999999999999998e-214 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. fma-def 92.7%

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

   3. Simplified 92.7%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-214

   1. Initial program 9.6%

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

   2. Taylor expanded in z around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. div-sub 76.6%

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

      4. mul-1-neg 76.6%

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

      5. unsub-neg 76.6%

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

      6. distribute-rgt-out-- 76.6%

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

      7. associate-/l* 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in t around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-/l* 92.0%

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

      3. associate-/r/ 86.9%

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

      4. distribute-rgt-neg-in 86.9%

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

      5. sub-neg 86.9%

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

      6. distribute-neg-out 86.9%

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

      7. mul-1-neg 86.9%

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

      8. remove-double-neg 86.9%

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

      9. +-commutative 86.9%

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

      10. mul-1-neg 86.9%

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

      11. sub-neg 86.9%

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

   7. Simplified 86.9%

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

      1. associate-*l/ 76.6%

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

      2. associate-/l* 92.0%

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

   9. Applied egg-rr 92.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-241} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-214}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \]

Alternative 2: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-241} \lor \neg \left(t_1 \leq 5 \cdot 10^{-214}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-241) (not (<= t_1 5e-214)))
     t_1
     (- t (/ x (/ z (- a y)))))))

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-241) || !(t_1 <= 5e-214)) {
		tmp = t_1;
	} else {
		tmp = t - (x / (z / (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 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-241)) .or. (.not. (t_1 <= 5d-214))) then
        tmp = t_1
    else
        tmp = t - (x / (z / (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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-241) || !(t_1 <= 5e-214)) {
		tmp = t_1;
	} else {
		tmp = t - (x / (z / (a - y)));
	}
	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-241) or not (t_1 <= 5e-214):
		tmp = t_1
	else:
		tmp = t - (x / (z / (a - y)))
	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-241) || !(t_1 <= 5e-214))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x / Float64(z / Float64(a - y))));
	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-241) || ~((t_1 <= 5e-214)))
		tmp = t_1;
	else
		tmp = t - (x / (z / (a - y)));
	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-241], N[Not[LessEqual[t$95$1, 5e-214]], $MachinePrecision]], t$95$1, N[(t - N[(x / N[(z / N[(a - y), $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)))) < -4.9999999999999998e-241 or 4.9999999999999998e-214 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.7%

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

   if -4.9999999999999998e-241 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-214

   1. Initial program 9.6%

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

   2. Taylor expanded in z around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. div-sub 76.6%

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

      4. mul-1-neg 76.6%

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

      5. unsub-neg 76.6%

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

      6. distribute-rgt-out-- 76.6%

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

      7. associate-/l* 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in t around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-/l* 92.0%

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

      3. associate-/r/ 86.9%

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

      4. distribute-rgt-neg-in 86.9%

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

      5. sub-neg 86.9%

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

      6. distribute-neg-out 86.9%

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

      7. mul-1-neg 86.9%

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

      8. remove-double-neg 86.9%

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

      9. +-commutative 86.9%

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

      10. mul-1-neg 86.9%

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

      11. sub-neg 86.9%

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

   7. Simplified 86.9%

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

      1. associate-*l/ 76.6%

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

      2. associate-/l* 92.0%

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

   9. Applied egg-rr 92.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-241} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-214}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -280:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- t x) (/ z (- y a)))))
        (t_2 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -5.4e+134)
     t_2
     (if (<= a -280.0)
       t_1
       (if (<= a -2.75e-30)
         (+ x (/ y (/ a (- t x))))
         (if (<= a 8.5e-110)
           t_1
           (if (<= a 3e+54) (/ t (/ (- a z) (- y z))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / (y - a)));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -5.4e+134) {
		tmp = t_2;
	} else if (a <= -280.0) {
		tmp = t_1;
	} else if (a <= -2.75e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 8.5e-110) {
		tmp = t_1;
	} else if (a <= 3e+54) {
		tmp = t / ((a - z) / (y - z));
	} 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 - ((t - x) / (z / (y - a)))
    t_2 = x + ((y - z) * ((t - x) / a))
    if (a <= (-5.4d+134)) then
        tmp = t_2
    else if (a <= (-280.0d0)) then
        tmp = t_1
    else if (a <= (-2.75d-30)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= 8.5d-110) then
        tmp = t_1
    else if (a <= 3d+54) then
        tmp = t / ((a - z) / (y - z))
    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 - ((t - x) / (z / (y - a)));
	double t_2 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -5.4e+134) {
		tmp = t_2;
	} else if (a <= -280.0) {
		tmp = t_1;
	} else if (a <= -2.75e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 8.5e-110) {
		tmp = t_1;
	} else if (a <= 3e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) / (z / (y - a)))
	t_2 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -5.4e+134:
		tmp = t_2
	elif a <= -280.0:
		tmp = t_1
	elif a <= -2.75e-30:
		tmp = x + (y / (a / (t - x)))
	elif a <= 8.5e-110:
		tmp = t_1
	elif a <= 3e+54:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -5.4e+134)
		tmp = t_2;
	elseif (a <= -280.0)
		tmp = t_1;
	elseif (a <= -2.75e-30)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= 8.5e-110)
		tmp = t_1;
	elseif (a <= 3e+54)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t - x) / (z / (y - a)));
	t_2 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -5.4e+134)
		tmp = t_2;
	elseif (a <= -280.0)
		tmp = t_1;
	elseif (a <= -2.75e-30)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= 8.5e-110)
		tmp = t_1;
	elseif (a <= 3e+54)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+134], t$95$2, If[LessEqual[a, -280.0], t$95$1, If[LessEqual[a, -2.75e-30], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-110], t$95$1, If[LessEqual[a, 3e+54], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.4e134 or 2.9999999999999999e54 < a

   1. Initial program 89.5%

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

   2. Taylor expanded in a around inf 68.3%

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

      1. associate-/l* 83.2%

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

      2. associate-/r/ 80.4%

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

   4. Simplified 80.4%

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

   if -5.4e134 < a < -280 or -2.74999999999999988e-30 < a < 8.50000000000000029e-110

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. distribute-lft-out-- 70.9%

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

      3. div-sub 70.9%

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

      4. mul-1-neg 70.9%

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

      5. unsub-neg 70.9%

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

      6. distribute-rgt-out-- 70.9%

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

      7. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

   if -280 < a < -2.74999999999999988e-30

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 87.4%

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

      1. associate-/l* 87.5%

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

   4. Simplified 87.5%

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

   if 8.50000000000000029e-110 < a < 2.9999999999999999e54

   1. Initial program 84.5%

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

   2. Taylor expanded in x around 0 68.1%

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

      1. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -280:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 4: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{z}{a - z}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -2800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-106}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- t x) (/ z (- a z))))))
   (if (<= a -1.15e+136)
     (+ x (* (- y z) (/ (- t x) a)))
     (if (<= a -2800.0)
       t_1
       (if (<= a -2.85e-30)
         (+ x (/ y (/ a (- t x))))
         (if (<= a 1.32e-106)
           (- t (/ (- t x) (/ z (- y a))))
           (if (<= a 5.5e+54) (/ t (/ (- a z) (- y z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * (z / (a - z)));
	double tmp;
	if (a <= -1.15e+136) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= -2800.0) {
		tmp = t_1;
	} else if (a <= -2.85e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 1.32e-106) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 5.5e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t - x) * (z / (a - z)))
    if (a <= (-1.15d+136)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= (-2800.0d0)) then
        tmp = t_1
    else if (a <= (-2.85d-30)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= 1.32d-106) then
        tmp = t - ((t - x) / (z / (y - a)))
    else if (a <= 5.5d+54) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * (z / (a - z)));
	double tmp;
	if (a <= -1.15e+136) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= -2800.0) {
		tmp = t_1;
	} else if (a <= -2.85e-30) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 1.32e-106) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (a <= 5.5e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t - x) * (z / (a - z)))
	tmp = 0
	if a <= -1.15e+136:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= -2800.0:
		tmp = t_1
	elif a <= -2.85e-30:
		tmp = x + (y / (a / (t - x)))
	elif a <= 1.32e-106:
		tmp = t - ((t - x) / (z / (y - a)))
	elif a <= 5.5e+54:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t - x) * Float64(z / Float64(a - z))))
	tmp = 0.0
	if (a <= -1.15e+136)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= -2800.0)
		tmp = t_1;
	elseif (a <= -2.85e-30)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= 1.32e-106)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	elseif (a <= 5.5e+54)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t - x) * (z / (a - z)));
	tmp = 0.0;
	if (a <= -1.15e+136)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= -2800.0)
		tmp = t_1;
	elseif (a <= -2.85e-30)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= 1.32e-106)
		tmp = t - ((t - x) / (z / (y - a)));
	elseif (a <= 5.5e+54)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t - x), $MachinePrecision] * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+136], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2800.0], t$95$1, If[LessEqual[a, -2.85e-30], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e-106], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+54], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.15e136

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 63.1%

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

      1. associate-/l* 85.0%

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

      2. associate-/r/ 81.8%

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

   4. Simplified 81.8%

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

   if -1.15e136 < a < -2800 or 5.50000000000000026e54 < a

   1. Initial program 82.3%

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

   2. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

      3. associate-/l* 73.0%

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

      4. associate-/r/ 77.7%

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

   4. Simplified 77.7%

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

   if -2800 < a < -2.84999999999999989e-30

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 87.4%

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

      1. associate-/l* 87.5%

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

   4. Simplified 87.5%

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

   if -2.84999999999999989e-30 < a < 1.32000000000000001e-106

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. distribute-lft-out-- 77.6%

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

      3. div-sub 77.6%

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

      4. mul-1-neg 77.6%

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

      5. unsub-neg 77.6%

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

      6. distribute-rgt-out-- 77.6%

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

      7. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

   if 1.32000000000000001e-106 < a < 5.50000000000000026e54

   1. Initial program 84.5%

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

   2. Taylor expanded in x around 0 68.1%

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

      1. associate-/l* 82.8%

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

   4. Simplified 82.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -2800:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z}{a - z}\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-106}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z}{a - z}\\ \end{array} \]

Alternative 5: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+231}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= z -3.6e+231)
     (/ (- t) (+ (/ a z) -1.0))
     (if (<= z -2e-8)
       t_1
       (if (<= z 5.5e-46)
         (+ x (/ y (/ a t)))
         (if (<= z 1.7e+99) t_1 (- t (/ a (/ z x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (z <= -3.6e+231) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -2e-8) {
		tmp = t_1;
	} else if (z <= 5.5e-46) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.7e+99) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (z <= (-3.6d+231)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if (z <= (-2d-8)) then
        tmp = t_1
    else if (z <= 5.5d-46) then
        tmp = x + (y / (a / t))
    else if (z <= 1.7d+99) then
        tmp = t_1
    else
        tmp = t - (a / (z / 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 = (y - z) * (t / (a - z));
	double tmp;
	if (z <= -3.6e+231) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -2e-8) {
		tmp = t_1;
	} else if (z <= 5.5e-46) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.7e+99) {
		tmp = t_1;
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if z <= -3.6e+231:
		tmp = -t / ((a / z) + -1.0)
	elif z <= -2e-8:
		tmp = t_1
	elif z <= 5.5e-46:
		tmp = x + (y / (a / t))
	elif z <= 1.7e+99:
		tmp = t_1
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.6e+231)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif (z <= -2e-8)
		tmp = t_1;
	elseif (z <= 5.5e-46)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.7e+99)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (z <= -3.6e+231)
		tmp = -t / ((a / z) + -1.0);
	elseif (z <= -2e-8)
		tmp = t_1;
	elseif (z <= 5.5e-46)
		tmp = x + (y / (a / t));
	elseif (z <= 1.7e+99)
		tmp = t_1;
	else
		tmp = t - (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+231], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-8], t$95$1, If[LessEqual[z, 5.5e-46], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+99], t$95$1, N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999999e231

   1. Initial program 51.3%

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

   2. Taylor expanded in x around 0 39.9%

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

      1. associate-/l* 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in y around 0 39.9%

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

      1. mul-1-neg 39.9%

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

      2. associate-/l* 82.7%

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

      3. distribute-neg-frac 82.7%

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

      4. div-sub 82.8%

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

      5. sub-neg 82.8%

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

      6. *-inverses 82.8%

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

      7. metadata-eval 82.8%

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

   7. Simplified 82.8%

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

   if -3.5999999999999999e231 < z < -2e-8 or 5.49999999999999983e-46 < z < 1.69999999999999992e99

   1. Initial program 84.6%

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

   2. Taylor expanded in x around 0 45.1%

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

      1. associate-/l* 62.7%

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

      2. associate-/r/ 61.5%

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

   4. Simplified 61.5%

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

   if -2e-8 < z < 5.49999999999999983e-46

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 78.7%

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

      1. associate-/l* 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in t around inf 66.8%

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

   if 1.69999999999999992e99 < z

   1. Initial program 58.1%

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

   2. Taylor expanded in z around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. distribute-lft-out-- 63.0%

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

      3. div-sub 63.0%

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

      4. mul-1-neg 63.0%

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

      5. unsub-neg 63.0%

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

      6. distribute-rgt-out-- 63.0%

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

      7. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 74.7%

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

      3. associate-/r/ 71.8%

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

      4. distribute-rgt-neg-in 71.8%

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

      5. sub-neg 71.8%

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

      6. distribute-neg-out 71.8%

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

      7. mul-1-neg 71.8%

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

      8. remove-double-neg 71.8%

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

      9. +-commutative 71.8%

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

      10. mul-1-neg 71.8%

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

      11. sub-neg 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in a around inf 56.5%

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

      1. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+231}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+99}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.16 \cdot 10^{-119}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -2.85e-30)
     t_1
     (if (<= a 2.16e-119)
       (+ t (/ (- x t) (/ z y)))
       (if (<= a 3.3e+54) (/ t (/ (- a z) (- y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -2.85e-30) {
		tmp = t_1;
	} else if (a <= 2.16e-119) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 3.3e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / a))
    if (a <= (-2.85d-30)) then
        tmp = t_1
    else if (a <= 2.16d-119) then
        tmp = t + ((x - t) / (z / y))
    else if (a <= 3.3d+54) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -2.85e-30) {
		tmp = t_1;
	} else if (a <= 2.16e-119) {
		tmp = t + ((x - t) / (z / y));
	} else if (a <= 3.3e+54) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -2.85e-30:
		tmp = t_1
	elif a <= 2.16e-119:
		tmp = t + ((x - t) / (z / y))
	elif a <= 3.3e+54:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.85e-30)
		tmp = t_1;
	elseif (a <= 2.16e-119)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif (a <= 3.3e+54)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.85e-30)
		tmp = t_1;
	elseif (a <= 2.16e-119)
		tmp = t + ((x - t) / (z / y));
	elseif (a <= 3.3e+54)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e-30], t$95$1, If[LessEqual[a, 2.16e-119], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+54], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.84999999999999989e-30 or 3.3e54 < a

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 63.6%

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

      1. associate-/l* 74.4%

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

      2. associate-/r/ 72.4%

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

   4. Simplified 72.4%

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

   if -2.84999999999999989e-30 < a < 2.1599999999999999e-119

   1. Initial program 72.8%

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

   2. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   if 2.1599999999999999e-119 < a < 3.3e54

   1. Initial program 82.9%

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

   2. Taylor expanded in x around 0 67.4%

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

      1. associate-/l* 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.16 \cdot 10^{-119}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 7: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -2.85e-30)
     x
     (if (<= a -1.8e-99)
       t
       (if (<= a -4.5e-173)
         t_1
         (if (<= a -1.85e-239)
           t
           (if (<= a 1.55e-266) t_1 (if (<= a 4e+54) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2.85e-30) {
		tmp = x;
	} else if (a <= -1.8e-99) {
		tmp = t;
	} else if (a <= -4.5e-173) {
		tmp = t_1;
	} else if (a <= -1.85e-239) {
		tmp = t;
	} else if (a <= 1.55e-266) {
		tmp = t_1;
	} else if (a <= 4e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-2.85d-30)) then
        tmp = x
    else if (a <= (-1.8d-99)) then
        tmp = t
    else if (a <= (-4.5d-173)) then
        tmp = t_1
    else if (a <= (-1.85d-239)) then
        tmp = t
    else if (a <= 1.55d-266) then
        tmp = t_1
    else if (a <= 4d+54) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -2.85e-30) {
		tmp = x;
	} else if (a <= -1.8e-99) {
		tmp = t;
	} else if (a <= -4.5e-173) {
		tmp = t_1;
	} else if (a <= -1.85e-239) {
		tmp = t;
	} else if (a <= 1.55e-266) {
		tmp = t_1;
	} else if (a <= 4e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -2.85e-30:
		tmp = x
	elif a <= -1.8e-99:
		tmp = t
	elif a <= -4.5e-173:
		tmp = t_1
	elif a <= -1.85e-239:
		tmp = t
	elif a <= 1.55e-266:
		tmp = t_1
	elif a <= 4e+54:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -2.85e-30)
		tmp = x;
	elseif (a <= -1.8e-99)
		tmp = t;
	elseif (a <= -4.5e-173)
		tmp = t_1;
	elseif (a <= -1.85e-239)
		tmp = t;
	elseif (a <= 1.55e-266)
		tmp = t_1;
	elseif (a <= 4e+54)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -2.85e-30)
		tmp = x;
	elseif (a <= -1.8e-99)
		tmp = t;
	elseif (a <= -4.5e-173)
		tmp = t_1;
	elseif (a <= -1.85e-239)
		tmp = t;
	elseif (a <= 1.55e-266)
		tmp = t_1;
	elseif (a <= 4e+54)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e-30], x, If[LessEqual[a, -1.8e-99], t, If[LessEqual[a, -4.5e-173], t$95$1, If[LessEqual[a, -1.85e-239], t, If[LessEqual[a, 1.55e-266], t$95$1, If[LessEqual[a, 4e+54], t, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.84999999999999989e-30 or 4.0000000000000003e54 < a

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 50.2%

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

   if -2.84999999999999989e-30 < a < -1.8e-99 or -4.50000000000000018e-173 < a < -1.85000000000000008e-239 or 1.54999999999999998e-266 < a < 4.0000000000000003e54

   1. Initial program 75.3%

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

   2. Taylor expanded in z around inf 47.4%

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

   if -1.8e-99 < a < -4.50000000000000018e-173 or -1.85000000000000008e-239 < a < 1.54999999999999998e-266

   1. Initial program 77.1%

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

   2. Taylor expanded in x around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. unsub-neg 41.1%

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

   4. Simplified 41.1%

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

   5. Taylor expanded in a around 0 51.9%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-239}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-266}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 54.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := t - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- t (* y (/ t z)))))
   (if (<= z -3.2e-7)
     t_2
     (if (<= z 2.85e-39)
       t_1
       (if (<= z 1.1e+27) (* t (/ (- y z) a)) (if (<= z 1.05e+47) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = t - (y * (t / z));
	double tmp;
	if (z <= -3.2e-7) {
		tmp = t_2;
	} else if (z <= 2.85e-39) {
		tmp = t_1;
	} else if (z <= 1.1e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.05e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = t - (y * (t / z))
    if (z <= (-3.2d-7)) then
        tmp = t_2
    else if (z <= 2.85d-39) then
        tmp = t_1
    else if (z <= 1.1d+27) then
        tmp = t * ((y - z) / a)
    else if (z <= 1.05d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = t - (y * (t / z));
	double tmp;
	if (z <= -3.2e-7) {
		tmp = t_2;
	} else if (z <= 2.85e-39) {
		tmp = t_1;
	} else if (z <= 1.1e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 1.05e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = t - (y * (t / z))
	tmp = 0
	if z <= -3.2e-7:
		tmp = t_2
	elif z <= 2.85e-39:
		tmp = t_1
	elif z <= 1.1e+27:
		tmp = t * ((y - z) / a)
	elif z <= 1.05e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(t - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -3.2e-7)
		tmp = t_2;
	elseif (z <= 2.85e-39)
		tmp = t_1;
	elseif (z <= 1.1e+27)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 1.05e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = t - (y * (t / z));
	tmp = 0.0;
	if (z <= -3.2e-7)
		tmp = t_2;
	elseif (z <= 2.85e-39)
		tmp = t_1;
	elseif (z <= 1.1e+27)
		tmp = t * ((y - z) / a);
	elseif (z <= 1.05e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-7], t$95$2, If[LessEqual[z, 2.85e-39], t$95$1, If[LessEqual[z, 1.1e+27], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000001e-7 or 1.05e47 < z

   1. Initial program 71.5%

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

   2. Taylor expanded in x around 0 42.6%

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

      1. associate-/l* 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in a around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. associate-/l* 59.4%

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

      3. distribute-neg-frac 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

      3. associate-*l/ 59.4%

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

      4. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -3.2000000000000001e-7 < z < 2.8499999999999998e-39 or 1.0999999999999999e27 < z < 1.05e47

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0 77.0%

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

      1. associate-/l* 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in t around inf 65.8%

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

   if 2.8499999999999998e-39 < z < 1.0999999999999999e27

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 67.7%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in a around inf 42.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 54.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-6)
   (- t (* y (/ t z)))
   (if (<= z 2.85e-39)
     (+ x (/ y (/ a t)))
     (if (<= z 4.5e+27)
       (* t (/ (- y z) a))
       (if (<= z 2.5e+51) (* x (/ y z)) (- t (/ a (/ z x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-6) {
		tmp = t - (y * (t / z));
	} else if (z <= 2.85e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.5e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.5e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d-6)) then
        tmp = t - (y * (t / z))
    else if (z <= 2.85d-39) then
        tmp = x + (y / (a / t))
    else if (z <= 4.5d+27) then
        tmp = t * ((y - z) / a)
    else if (z <= 2.5d+51) then
        tmp = x * (y / z)
    else
        tmp = t - (a / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-6) {
		tmp = t - (y * (t / z));
	} else if (z <= 2.85e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 4.5e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.5e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e-6:
		tmp = t - (y * (t / z))
	elif z <= 2.85e-39:
		tmp = x + (y / (a / t))
	elif z <= 4.5e+27:
		tmp = t * ((y - z) / a)
	elif z <= 2.5e+51:
		tmp = x * (y / z)
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-6)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= 2.85e-39)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4.5e+27)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 2.5e+51)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e-6)
		tmp = t - (y * (t / z));
	elseif (z <= 2.85e-39)
		tmp = x + (y / (a / t));
	elseif (z <= 4.5e+27)
		tmp = t * ((y - z) / a);
	elseif (z <= 2.5e+51)
		tmp = x * (y / z);
	else
		tmp = t - (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-6], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e-39], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+27], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+51], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5000000000000002e-6

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

   5. Taylor expanded in a around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 60.8%

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

      3. distribute-neg-frac 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

      3. associate-*l/ 60.8%

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

      4. *-commutative 60.8%

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

   10. Simplified 60.8%

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

   if -2.5000000000000002e-6 < z < 2.8499999999999998e-39

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 78.0%

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

      1. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in t around inf 66.2%

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

   if 2.8499999999999998e-39 < z < 4.4999999999999999e27

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 67.7%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in a around inf 42.8%

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

   if 4.4999999999999999e27 < z < 2.5e51

   1. Initial program 85.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in a around 0 45.6%

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

   if 2.5e51 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. distribute-lft-out-- 61.9%

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

      3. div-sub 61.9%

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

      4. mul-1-neg 61.9%

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

      5. unsub-neg 61.9%

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

      6. distribute-rgt-out-- 61.9%

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

      7. associate-/l* 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. associate-/l* 70.0%

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

      3. associate-/r/ 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

      5. sub-neg 67.9%

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

      6. distribute-neg-out 67.9%

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

      7. mul-1-neg 67.9%

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

      8. remove-double-neg 67.9%

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

      9. +-commutative 67.9%

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

      10. mul-1-neg 67.9%

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

      11. sub-neg 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 59.1%

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

   10. Simplified 59.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 10: 54.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e-7)
   (* t (/ (- z y) z))
   (if (<= z 2.35e-39)
     (+ x (/ y (/ a t)))
     (if (<= z 2.2e+27)
       (* t (/ (- y z) a))
       (if (<= z 9.8e+51) (* x (/ y z)) (- t (/ a (/ z x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-7) {
		tmp = t * ((z - y) / z);
	} else if (z <= 2.35e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.2e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.8e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d-7)) then
        tmp = t * ((z - y) / z)
    else if (z <= 2.35d-39) then
        tmp = x + (y / (a / t))
    else if (z <= 2.2d+27) then
        tmp = t * ((y - z) / a)
    else if (z <= 9.8d+51) then
        tmp = x * (y / z)
    else
        tmp = t - (a / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-7) {
		tmp = t * ((z - y) / z);
	} else if (z <= 2.35e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 2.2e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 9.8e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t - (a / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e-7:
		tmp = t * ((z - y) / z)
	elif z <= 2.35e-39:
		tmp = x + (y / (a / t))
	elif z <= 2.2e+27:
		tmp = t * ((y - z) / a)
	elif z <= 9.8e+51:
		tmp = x * (y / z)
	else:
		tmp = t - (a / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e-7)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= 2.35e-39)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 2.2e+27)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 9.8e+51)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t - Float64(a / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e-7)
		tmp = t * ((z - y) / z);
	elseif (z <= 2.35e-39)
		tmp = x + (y / (a / t));
	elseif (z <= 2.2e+27)
		tmp = t * ((y - z) / a);
	elseif (z <= 9.8e+51)
		tmp = x * (y / z);
	else
		tmp = t - (a / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e-7], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-39], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+27], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+51], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(a / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.99999999999999977e-7

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. clear-num 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in a around 0 60.8%

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

      1. mul-1-neg 60.8%

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

   9. Simplified 60.8%

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

   if -4.99999999999999977e-7 < z < 2.3500000000000001e-39

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 78.0%

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

      1. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in t around inf 66.2%

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

   if 2.3500000000000001e-39 < z < 2.1999999999999999e27

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 67.7%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in a around inf 42.8%

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

   if 2.1999999999999999e27 < z < 9.79999999999999967e51

   1. Initial program 85.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in a around 0 45.6%

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

   if 9.79999999999999967e51 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. distribute-lft-out-- 61.9%

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

      3. div-sub 61.9%

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

      4. mul-1-neg 61.9%

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

      5. unsub-neg 61.9%

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

      6. distribute-rgt-out-- 61.9%

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

      7. associate-/l* 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. associate-/l* 70.0%

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

      3. associate-/r/ 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

      5. sub-neg 67.9%

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

      6. distribute-neg-out 67.9%

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

      7. mul-1-neg 67.9%

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

      8. remove-double-neg 67.9%

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

      9. +-commutative 67.9%

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

      10. mul-1-neg 67.9%

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

      11. sub-neg 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in a around inf 51.2%

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

      1. associate-/l* 59.1%

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

   10. Simplified 59.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{\frac{z}{x}}\\ \end{array} \]

Alternative 11: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e-6)
   t
   (if (<= z 2.85e-39)
     (+ x (/ y (/ a t)))
     (if (<= z 1.65e+27)
       (* t (/ (- y z) a))
       (if (<= z 2.5e+51) (* x (/ y z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-6) {
		tmp = t;
	} else if (z <= 2.85e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.65e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.5e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.75d-6)) then
        tmp = t
    else if (z <= 2.85d-39) then
        tmp = x + (y / (a / t))
    else if (z <= 1.65d+27) then
        tmp = t * ((y - z) / a)
    else if (z <= 2.5d+51) then
        tmp = x * (y / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-6) {
		tmp = t;
	} else if (z <= 2.85e-39) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.65e+27) {
		tmp = t * ((y - z) / a);
	} else if (z <= 2.5e+51) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e-6:
		tmp = t
	elif z <= 2.85e-39:
		tmp = x + (y / (a / t))
	elif z <= 1.65e+27:
		tmp = t * ((y - z) / a)
	elif z <= 2.5e+51:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e-6)
		tmp = t;
	elseif (z <= 2.85e-39)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.65e+27)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= 2.5e+51)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e-6)
		tmp = t;
	elseif (z <= 2.85e-39)
		tmp = x + (y / (a / t));
	elseif (z <= 1.65e+27)
		tmp = t * ((y - z) / a);
	elseif (z <= 2.5e+51)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e-6], t, If[LessEqual[z, 2.85e-39], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+27], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+51], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.74999999999999997e-6 or 2.5e51 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in z around inf 49.0%

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

   if -1.74999999999999997e-6 < z < 2.8499999999999998e-39

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 78.0%

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

      1. associate-/l* 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in t around inf 66.2%

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

   if 2.8499999999999998e-39 < z < 1.6499999999999999e27

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 67.7%

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

      3. clear-num 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in a around inf 42.8%

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

   if 1.6499999999999999e27 < z < 2.5e51

   1. Initial program 85.9%

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

   2. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in a around 0 45.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e-8) (not (<= z 5.5e-46)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e-8) || !(z <= 5.5e-46)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (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) :: tmp
    if ((z <= (-5.2d-8)) .or. (.not. (z <= 5.5d-46))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (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 tmp;
	if ((z <= -5.2e-8) || !(z <= 5.5e-46)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e-8) or not (z <= 5.5e-46):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e-8) || !(z <= 5.5e-46))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e-8) || ~((z <= 5.5e-46)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e-8], N[Not[LessEqual[z, 5.5e-46]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000002e-8 or 5.49999999999999983e-46 < z

   1. Initial program 73.9%

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

   2. Taylor expanded in x around 0 44.3%

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

      1. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

      1. clear-num 65.9%

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

      2. associate-/r/ 66.0%

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

      3. clear-num 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -5.2000000000000002e-8 < z < 5.49999999999999983e-46

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 78.7%

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

      1. associate-/l* 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in t around inf 66.8%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 13: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-7} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e-7) (not (<= z 5.5e-46)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e-7) || !(z <= 5.5e-46)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - 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 ((z <= (-1.15d-7)) .or. (.not. (z <= 5.5d-46))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - 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 ((z <= -1.15e-7) || !(z <= 5.5e-46)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e-7) or not (z <= 5.5e-46):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e-7) || !(z <= 5.5e-46))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e-7) || ~((z <= 5.5e-46)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e-7], N[Not[LessEqual[z, 5.5e-46]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999997e-7 or 5.49999999999999983e-46 < z

   1. Initial program 73.9%

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

   2. Taylor expanded in x around 0 44.3%

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

      1. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

      1. clear-num 65.9%

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

      2. associate-/r/ 66.0%

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

      3. clear-num 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -1.14999999999999997e-7 < z < 5.49999999999999983e-46

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 78.7%

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

      1. associate-/l* 79.5%

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

      2. associate-/r/ 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-7} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e-7)
   (* t (/ (- y z) (- a z)))
   (if (<= z 2.1e-14) (+ x (* (- t x) (/ y a))) (+ t (* (/ x z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.1e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x / z) * (y - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d-7)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.1d-14) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x / z) * (y - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-7) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.1e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x / z) * (y - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e-7:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.1e-14:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x / z) * (y - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e-7)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.1e-14)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x / z) * Float64(y - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e-7)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.1e-14)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x / z) * (y - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e-7], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-14], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999977e-7

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. clear-num 70.3%

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

   6. Applied egg-rr 70.3%

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

   if -4.99999999999999977e-7 < z < 2.0999999999999999e-14

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 76.9%

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

      2. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

   if 2.0999999999999999e-14 < z

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.7%

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

      1. associate--l+ 59.7%

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

      2. distribute-lft-out-- 59.7%

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

      3. div-sub 59.7%

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

      4. mul-1-neg 59.7%

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

      5. unsub-neg 59.7%

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

      6. distribute-rgt-out-- 59.7%

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

      7. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in t around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 64.3%

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

      3. associate-/r/ 62.8%

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

      4. distribute-rgt-neg-in 62.8%

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

      5. sub-neg 62.8%

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

      6. distribute-neg-out 62.8%

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

      7. mul-1-neg 62.8%

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

      8. remove-double-neg 62.8%

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

      9. +-commutative 62.8%

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

      10. mul-1-neg 62.8%

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

      11. sub-neg 62.8%

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

   7. Simplified 62.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{z} \cdot \left(y - a\right)\\ \end{array} \]

Alternative 15: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e-6)
   (* t (/ (- y z) (- a z)))
   (if (<= z 4.2e-14) (+ x (* (- t x) (/ y a))) (- t (/ x (/ z (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.2e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (x / (z / (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 (z <= (-1.75d-6)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 4.2d-14) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t - (x / (z / (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 (z <= -1.75e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.2e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (x / (z / (a - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e-6:
		tmp = t * ((y - z) / (a - z))
	elif z <= 4.2e-14:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t - (x / (z / (a - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e-6)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 4.2e-14)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t - Float64(x / Float64(z / Float64(a - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e-6)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 4.2e-14)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t - (x / (z / (a - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e-6], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-14], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999997e-6

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. clear-num 70.3%

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

   6. Applied egg-rr 70.3%

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

   if -1.74999999999999997e-6 < z < 4.1999999999999998e-14

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 76.9%

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

      2. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

   if 4.1999999999999998e-14 < z

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.7%

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

      1. associate--l+ 59.7%

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

      2. distribute-lft-out-- 59.7%

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

      3. div-sub 59.7%

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

      4. mul-1-neg 59.7%

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

      5. unsub-neg 59.7%

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

      6. distribute-rgt-out-- 59.7%

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

      7. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in t around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 64.3%

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

      3. associate-/r/ 62.8%

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

      4. distribute-rgt-neg-in 62.8%

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

      5. sub-neg 62.8%

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

      6. distribute-neg-out 62.8%

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

      7. mul-1-neg 62.8%

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

      8. remove-double-neg 62.8%

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

      9. +-commutative 62.8%

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

      10. mul-1-neg 62.8%

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

      11. sub-neg 62.8%

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

   7. Simplified 62.8%

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

      1. associate-*l/ 55.5%

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

      2. associate-/l* 64.3%

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

   9. Applied egg-rr 64.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{\frac{z}{a - y}}\\ \end{array} \]

Alternative 16: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e-6)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.36e-14) (+ x (* (- t x) (/ y a))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.36e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.75d-6)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.36d-14) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.36e-14) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e-6:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.36e-14:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e-6)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.36e-14)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e-6)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.36e-14)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e-6], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e-14], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999997e-6

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. clear-num 70.3%

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

   6. Applied egg-rr 70.3%

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

   if -1.74999999999999997e-6 < z < 1.36e-14

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 76.9%

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

      2. associate-/r/ 78.0%

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

   4. Simplified 78.0%

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

   if 1.36e-14 < z

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.7%

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

      1. associate--l+ 59.7%

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

      2. distribute-lft-out-- 59.7%

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

      3. div-sub 59.7%

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

      4. mul-1-neg 59.7%

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

      5. unsub-neg 59.7%

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

      6. distribute-rgt-out-- 59.7%

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

      7. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in y around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-14}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 17: 49.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+62) t (if (<= z 3.6e+37) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+62) {
		tmp = t;
	} else if (z <= 3.6e+37) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.7d+62)) then
        tmp = t
    else if (z <= 3.6d+37) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+62) {
		tmp = t;
	} else if (z <= 3.6e+37) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+62:
		tmp = t
	elif z <= 3.6e+37:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+62)
		tmp = t;
	elseif (z <= 3.6e+37)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+62)
		tmp = t;
	elseif (z <= 3.6e+37)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+62], t, If[LessEqual[z, 3.6e+37], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7000000000000003e62 or 3.59999999999999998e37 < z

   1. Initial program 68.5%

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

   2. Taylor expanded in z around inf 49.5%

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

   if -4.7000000000000003e62 < z < 3.59999999999999998e37

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. sub-neg 52.5%

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

   7. Simplified 52.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 56.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e-8)
   (* t (/ (- z y) z))
   (if (<= z 2.1e-15) (+ x (/ y (/ a t))) (+ t (* y (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-8) {
		tmp = t * ((z - y) / z);
	} else if (z <= 2.1e-15) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d-8)) then
        tmp = t * ((z - y) / z)
    else if (z <= 2.1d-15) then
        tmp = x + (y / (a / t))
    else
        tmp = t + (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-8) {
		tmp = t * ((z - y) / z);
	} else if (z <= 2.1e-15) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e-8:
		tmp = t * ((z - y) / z)
	elif z <= 2.1e-15:
		tmp = x + (y / (a / t))
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e-8)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= 2.1e-15)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e-8)
		tmp = t * ((z - y) / z);
	elseif (z <= 2.1e-15)
		tmp = x + (y / (a / t));
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e-8], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-15], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999973e-8

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 70.2%

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

   4. Simplified 70.2%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. clear-num 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in a around 0 60.8%

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

      1. mul-1-neg 60.8%

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

   9. Simplified 60.8%

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

   if -2.99999999999999973e-8 < z < 2.09999999999999981e-15

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 75.9%

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

      1. associate-/l* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in t around inf 64.1%

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

   if 2.09999999999999981e-15 < z

   1. Initial program 75.3%

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

   2. Taylor expanded in z around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. distribute-lft-out-- 58.8%

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

      3. div-sub 58.8%

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

      4. mul-1-neg 58.8%

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

      5. unsub-neg 58.8%

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

      6. distribute-rgt-out-- 58.9%

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

      7. associate-/l* 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in t around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-/l* 63.5%

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

      3. associate-/r/ 61.9%

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

      4. distribute-rgt-neg-in 61.9%

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

      5. sub-neg 61.9%

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

      6. distribute-neg-out 61.9%

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

      7. mul-1-neg 61.9%

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

      8. remove-double-neg 61.9%

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

      9. +-commutative 61.9%

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

      10. mul-1-neg 61.9%

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

      11. sub-neg 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in a around 0 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-*r/ 56.1%

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

      3. associate-*l* 56.1%

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

      4. neg-mul-1 56.1%

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

   10. Simplified 56.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 19: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.85e-30) x (if (<= a 2.9e+54) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e-30) {
		tmp = x;
	} else if (a <= 2.9e+54) {
		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 <= (-2.85d-30)) then
        tmp = x
    else if (a <= 2.9d+54) 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 <= -2.85e-30) {
		tmp = x;
	} else if (a <= 2.9e+54) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.85e-30:
		tmp = x
	elif a <= 2.9e+54:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.85e-30)
		tmp = x;
	elseif (a <= 2.9e+54)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.85e-30)
		tmp = x;
	elseif (a <= 2.9e+54)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.85e-30], x, If[LessEqual[a, 2.9e+54], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.84999999999999989e-30 or 2.8999999999999999e54 < a

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 50.2%

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

   if -2.84999999999999989e-30 < a < 2.8999999999999999e54

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 40.4%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.7%

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

2. Taylor expanded in z around inf 29.2%

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

3. Final simplification 29.2%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023318 
(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)))))