Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 95.5%

Time: 19.6s

Alternatives: 21

Speedup: 0.8×

Specification

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

Wolfram

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

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

Wolfram

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

Alternative 1: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a - z}{y - z}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+56}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ (- a z) (- y z)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -4e-263)
     t_1
     (if (<= t_2 0.0)
       (+ t (* (- y a) (/ x z)))
       (if (<= t_2 5e+56)
         (+
          (/ (* (- y z) t) (- a z))
          (* x (- (+ (/ z (- a z)) 1.0) (/ y (- a z)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-263) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y - a) * (x / z));
	} else if (t_2 <= 5e+56) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) / ((a - z) / (y - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-263)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + ((y - a) * (x / z))
    else if (t_2 <= 5d+56) then
        tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0d0) - (y / (a - z))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / ((a - z) / (y - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-263) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y - a) * (x / z));
	} else if (t_2 <= 5e+56) {
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / ((a - z) / (y - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-263:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + ((y - a) * (x / z))
	elif t_2 <= 5e+56:
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-263)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	elseif (t_2 <= 5e+56)
		tmp = Float64(Float64(Float64(Float64(y - z) * t) / Float64(a - z)) + Float64(x * Float64(Float64(Float64(z / Float64(a - z)) + 1.0) - Float64(y / Float64(a - z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / ((a - z) / (y - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-263)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + ((y - a) * (x / z));
	elseif (t_2 <= 5e+56)
		tmp = (((y - z) * t) / (a - z)) + (x * (((z / (a - z)) + 1.0) - (y / (a - z))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-263], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+56], N[(N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4e-263 or 5.00000000000000024e56 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*l/ 75.8%

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

      3. associate-*r/ 91.4%

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

      4. clear-num 91.4%

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

      5. un-div-inv 91.7%

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

   3. Applied egg-rr 91.7%

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

   if -4e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.0%

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

   2. Taylor expanded in z around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. associate--l+ 79.9%

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

      3. associate-*r/ 79.9%

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

      4. associate-*r/ 79.9%

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

      5. div-sub 79.9%

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

      6. distribute-lft-out-- 79.9%

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

      7. mul-1-neg 79.9%

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

      8. distribute-neg-frac 79.9%

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

      9. unsub-neg 79.9%

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

      10. distribute-rgt-out-- 80.0%

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

   4. Simplified 80.0%

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

      1. *-un-lft-identity 80.0%

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

      2. associate-/l* 99.4%

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

   6. Applied egg-rr 99.4%

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

      1. *-lft-identity 99.4%

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

      2. associate-/r/ 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in t around 0 99.9%

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

       1. mul-1-neg 99.9%

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

       2. distribute-neg-frac 99.9%

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

   11. Simplified 99.9%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000024e56

   1. Initial program 74.3%

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

   2. Taylor expanded in x around -inf 97.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-263}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{+56}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x \cdot \left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 5500000000.0)
       (+ t (* (- y a) (/ (- x t) z)))
       (if (<= a 1.04e+83)
         (+ x (/ (- t x) (/ a y)))
         (if (<= a 6.4e+174) (+ x (/ (- x t) (+ -1.0 (/ a z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 5500000000.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (a <= 1.04e+83) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 6.4e+174) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 5500000000.0d0) then
        tmp = t + ((y - a) * ((x - t) / z))
    else if (a <= 1.04d+83) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 6.4d+174) then
        tmp = x + ((x - t) / ((-1.0d0) + (a / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 5500000000.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (a <= 1.04e+83) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 6.4e+174) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 5500000000.0:
		tmp = t + ((y - a) * ((x - t) / z))
	elif a <= 1.04e+83:
		tmp = x + ((t - x) / (a / y))
	elif a <= 6.4e+174:
		tmp = x + ((x - t) / (-1.0 + (a / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 5500000000.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (a <= 1.04e+83)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 6.4e+174)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(-1.0 + Float64(a / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 5500000000.0)
		tmp = t + ((y - a) * ((x - t) / z));
	elseif (a <= 1.04e+83)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 6.4e+174)
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 5500000000.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.04e+83], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+174], N[(x + N[(N[(x - t), $MachinePrecision] / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000023e75 or 6.4000000000000001e174 < a

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -5.60000000000000023e75 < a < 5.5e9

   1. Initial program 66.1%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--l+ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. associate-*r/ 72.2%

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

      5. div-sub 74.3%

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

      6. distribute-lft-out-- 74.3%

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

      7. mul-1-neg 74.3%

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

      8. distribute-neg-frac 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.3%

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

   4. Simplified 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. associate-/l* 82.6%

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

   6. Applied egg-rr 82.6%

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

      1. *-lft-identity 82.6%

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

      2. associate-/r/ 80.8%

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

   8. Simplified 80.8%

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

   if 5.5e9 < a < 1.0399999999999999e83

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 87.1%

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

      4. clear-num 87.2%

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

      5. un-div-inv 87.2%

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

   3. Applied egg-rr 87.2%

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

   4. Taylor expanded in z around 0 74.3%

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

   if 1.0399999999999999e83 < a < 6.4000000000000001e174

   1. Initial program 82.8%

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

   2. Taylor expanded in y around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-/l* 82.7%

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

      5. div-sub 82.7%

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

      6. *-inverses 82.7%

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

   4. Simplified 82.7%

      \[\leadsto \color{blue}{x - \frac{t - x}{\frac{a}{z} - 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+83}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 3: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1450000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+172}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -5.8e+75)
     t_1
     (if (<= a 1450000000.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (if (<= a 7e+91)
         (+ x (/ (- t x) (/ a y)))
         (if (<= a 3.2e+172) (+ x (/ (- x t) (+ -1.0 (/ a z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 1450000000.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (a <= 7e+91) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.2e+172) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-5.8d+75)) then
        tmp = t_1
    else if (a <= 1450000000.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if (a <= 7d+91) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 3.2d+172) then
        tmp = x + ((x - t) / ((-1.0d0) + (a / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 1450000000.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (a <= 7e+91) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.2e+172) {
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -5.8e+75:
		tmp = t_1
	elif a <= 1450000000.0:
		tmp = t + ((x - t) / (z / (y - a)))
	elif a <= 7e+91:
		tmp = x + ((t - x) / (a / y))
	elif a <= 3.2e+172:
		tmp = x + ((x - t) / (-1.0 + (a / z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 1450000000.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (a <= 7e+91)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 3.2e+172)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(-1.0 + Float64(a / z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 1450000000.0)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif (a <= 7e+91)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 3.2e+172)
		tmp = x + ((x - t) / (-1.0 + (a / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+75], t$95$1, If[LessEqual[a, 1450000000.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+91], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+172], N[(x + N[(N[(x - t), $MachinePrecision] / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.7999999999999997e75 or 3.19999999999999985e172 < a

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if -5.7999999999999997e75 < a < 1.45e9

   1. Initial program 66.1%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--l+ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. associate-*r/ 72.2%

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

      5. div-sub 74.3%

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

      6. distribute-lft-out-- 74.3%

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

      7. mul-1-neg 74.3%

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

      8. distribute-neg-frac 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.3%

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

   4. Simplified 74.3%

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

      1. sub-neg 74.3%

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

      2. associate-/l* 82.6%

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

   6. Applied egg-rr 82.6%

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

   if 1.45e9 < a < 7.00000000000000001e91

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 87.1%

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

      4. clear-num 87.2%

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

      5. un-div-inv 87.2%

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

   3. Applied egg-rr 87.2%

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

   4. Taylor expanded in z around 0 74.3%

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

   if 7.00000000000000001e91 < a < 3.19999999999999985e172

   1. Initial program 82.8%

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

   2. Taylor expanded in y around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-/l* 82.7%

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

      5. div-sub 82.7%

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

      6. *-inverses 82.7%

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

   4. Simplified 82.7%

      \[\leadsto \color{blue}{x - \frac{t - x}{\frac{a}{z} - 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1450000000:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+91}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+172}:\\ \;\;\;\;x + \frac{x - t}{-1 + \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 4: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 310000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -5.8e+75)
     t_1
     (if (<= a 4.4e-116)
       (- t (/ (* y t) z))
       (if (<= a 310000000.0)
         (* y (/ x z))
         (if (<= a 2.7e+129)
           (* x (- 1.0 (/ y a)))
           (if (<= a 8.6e+155) (* t (/ (- z) (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 4.4e-116) {
		tmp = t - ((y * t) / z);
	} else if (a <= 310000000.0) {
		tmp = y * (x / z);
	} else if (a <= 2.7e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 8.6e+155) {
		tmp = t * (-z / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-5.8d+75)) then
        tmp = t_1
    else if (a <= 4.4d-116) then
        tmp = t - ((y * t) / z)
    else if (a <= 310000000.0d0) then
        tmp = y * (x / z)
    else if (a <= 2.7d+129) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 8.6d+155) then
        tmp = t * (-z / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 4.4e-116) {
		tmp = t - ((y * t) / z);
	} else if (a <= 310000000.0) {
		tmp = y * (x / z);
	} else if (a <= 2.7e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 8.6e+155) {
		tmp = t * (-z / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -5.8e+75:
		tmp = t_1
	elif a <= 4.4e-116:
		tmp = t - ((y * t) / z)
	elif a <= 310000000.0:
		tmp = y * (x / z)
	elif a <= 2.7e+129:
		tmp = x * (1.0 - (y / a))
	elif a <= 8.6e+155:
		tmp = t * (-z / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 4.4e-116)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= 310000000.0)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 2.7e+129)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 8.6e+155)
		tmp = Float64(t * Float64(Float64(-z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 4.4e-116)
		tmp = t - ((y * t) / z);
	elseif (a <= 310000000.0)
		tmp = y * (x / z);
	elseif (a <= 2.7e+129)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 8.6e+155)
		tmp = t * (-z / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+75], t$95$1, If[LessEqual[a, 4.4e-116], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 310000000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+129], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+155], N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.7999999999999997e75 or 8.6000000000000005e155 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 71.1%

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

   3. Taylor expanded in t around inf 68.8%

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

   if -5.7999999999999997e75 < a < 4.4000000000000002e-116

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. associate--l+ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. associate-*r/ 75.2%

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

      5. div-sub 77.8%

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

      6. distribute-lft-out-- 77.8%

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

      7. mul-1-neg 77.8%

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

      8. distribute-neg-frac 77.8%

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

      9. unsub-neg 77.8%

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

      10. distribute-rgt-out-- 77.8%

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

   4. Simplified 77.8%

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

      1. *-un-lft-identity 77.8%

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

      2. associate-/l* 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. *-lft-identity 84.1%

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

      2. associate-/r/ 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in y around inf 74.6%

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

   10. Taylor expanded in t around inf 59.0%

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

   if 4.4000000000000002e-116 < a < 3.1e8

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. associate--l+ 57.6%

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

      3. associate-*r/ 57.6%

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

      4. associate-*r/ 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-lft-out-- 57.6%

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

      7. mul-1-neg 57.6%

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

      8. distribute-neg-frac 57.6%

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

      9. unsub-neg 57.6%

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

      10. distribute-rgt-out-- 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in t around 0 35.6%

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

      1. associate-/l* 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 35.7%

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

      1. associate-*r/ 50.1%

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

   10. Simplified 50.1%

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

   if 3.1e8 < a < 2.7000000000000001e129

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 73.4%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   if 2.7000000000000001e129 < a < 8.6000000000000005e155

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. neg-mul-1 83.6%

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

      2. distribute-neg-frac 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 310000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 5: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 240000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -5.8e+75)
     t_1
     (if (<= a 3.3e-116)
       (* t (/ (- z y) z))
       (if (<= a 240000.0)
         (* y (/ x z))
         (if (<= a 2.7e+129)
           (* x (- 1.0 (/ y a)))
           (if (<= a 2.3e+156) (* t (/ (- z) (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 3.3e-116) {
		tmp = t * ((z - y) / z);
	} else if (a <= 240000.0) {
		tmp = y * (x / z);
	} else if (a <= 2.7e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 2.3e+156) {
		tmp = t * (-z / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-5.8d+75)) then
        tmp = t_1
    else if (a <= 3.3d-116) then
        tmp = t * ((z - y) / z)
    else if (a <= 240000.0d0) then
        tmp = y * (x / z)
    else if (a <= 2.7d+129) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 2.3d+156) then
        tmp = t * (-z / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 3.3e-116) {
		tmp = t * ((z - y) / z);
	} else if (a <= 240000.0) {
		tmp = y * (x / z);
	} else if (a <= 2.7e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 2.3e+156) {
		tmp = t * (-z / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -5.8e+75:
		tmp = t_1
	elif a <= 3.3e-116:
		tmp = t * ((z - y) / z)
	elif a <= 240000.0:
		tmp = y * (x / z)
	elif a <= 2.7e+129:
		tmp = x * (1.0 - (y / a))
	elif a <= 2.3e+156:
		tmp = t * (-z / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 3.3e-116)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 240000.0)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 2.7e+129)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 2.3e+156)
		tmp = Float64(t * Float64(Float64(-z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 3.3e-116)
		tmp = t * ((z - y) / z);
	elseif (a <= 240000.0)
		tmp = y * (x / z);
	elseif (a <= 2.7e+129)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 2.3e+156)
		tmp = t * (-z / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+75], t$95$1, If[LessEqual[a, 3.3e-116], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 240000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+129], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+156], N[(t * N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.7999999999999997e75 or 2.2999999999999999e156 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 71.1%

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

   3. Taylor expanded in t around inf 68.8%

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

   if -5.7999999999999997e75 < a < 3.30000000000000001e-116

   1. Initial program 64.8%

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

   2. Taylor expanded in t around inf 63.7%

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

      1. div-sub 63.7%

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

   4. Simplified 63.7%

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

   5. Taylor expanded in a around 0 59.8%

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

      1. associate-*r/ 59.8%

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

      2. neg-mul-1 59.8%

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

   7. Simplified 59.8%

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

   if 3.30000000000000001e-116 < a < 2.4e5

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. associate--l+ 57.6%

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

      3. associate-*r/ 57.6%

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

      4. associate-*r/ 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-lft-out-- 57.6%

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

      7. mul-1-neg 57.6%

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

      8. distribute-neg-frac 57.6%

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

      9. unsub-neg 57.6%

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

      10. distribute-rgt-out-- 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in t around 0 35.6%

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

      1. associate-/l* 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 35.7%

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

      1. associate-*r/ 50.1%

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

   10. Simplified 50.1%

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

   if 2.4e5 < a < 2.7000000000000001e129

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 73.4%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   if 2.7000000000000001e129 < a < 2.2999999999999999e156

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. neg-mul-1 83.6%

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

      2. distribute-neg-frac 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 240000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{-z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 6: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.55:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -2.3e+83)
     t_1
     (if (<= z -2.3e-144)
       (* y (/ (- t x) (- a z)))
       (if (<= z 3.8e-56)
         (+ x (/ (* y t) a))
         (if (<= z 1.55)
           (* t (/ (- y z) (- a z)))
           (if (<= z 2.4e+50) (* x (- 1.0 (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -2.3e+83) {
		tmp = t_1;
	} else if (z <= -2.3e-144) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.8e-56) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.55) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-2.3d+83)) then
        tmp = t_1
    else if (z <= (-2.3d-144)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 3.8d-56) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.55d0) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.4d+50) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -2.3e+83) {
		tmp = t_1;
	} else if (z <= -2.3e-144) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.8e-56) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.55) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.4e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -2.3e+83:
		tmp = t_1
	elif z <= -2.3e-144:
		tmp = y * ((t - x) / (a - z))
	elif z <= 3.8e-56:
		tmp = x + ((y * t) / a)
	elif z <= 1.55:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.4e+50:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -2.3e+83)
		tmp = t_1;
	elseif (z <= -2.3e-144)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 3.8e-56)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.55)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.4e+50)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -2.3e+83)
		tmp = t_1;
	elseif (z <= -2.3e-144)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 3.8e-56)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.55)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.4e+50)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+83], t$95$1, If[LessEqual[z, -2.3e-144], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-56], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+50], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.29999999999999995e83 or 2.4000000000000002e50 < z

   1. Initial program 54.2%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. associate--l+ 62.6%

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

      3. associate-*r/ 62.6%

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

      4. associate-*r/ 62.6%

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

      5. div-sub 62.6%

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

      6. distribute-lft-out-- 62.6%

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

      7. mul-1-neg 62.6%

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

      8. distribute-neg-frac 62.6%

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

      9. unsub-neg 62.6%

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

      10. distribute-rgt-out-- 62.7%

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

   4. Simplified 62.7%

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

      1. *-un-lft-identity 62.7%

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

      2. associate-/l* 85.7%

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

   6. Applied egg-rr 85.7%

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

      1. *-lft-identity 85.7%

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

      2. associate-/r/ 82.7%

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

   8. Simplified 82.7%

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

   9. Taylor expanded in y around inf 59.4%

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

   10. Taylor expanded in t around 0 55.5%

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

       1. mul-1-neg 55.5%

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

       2. associate-*r/ 64.5%

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

       3. distribute-rgt-neg-in 64.5%

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

       4. distribute-neg-frac 64.5%

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

   12. Simplified 64.5%

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

   if -2.29999999999999995e83 < z < -2.3e-144

   1. Initial program 87.2%

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

   2. Taylor expanded in x around -inf 87.6%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. sub-neg 60.3%

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

      4. div-sub 60.3%

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

   5. Simplified 60.3%

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

   if -2.3e-144 < z < 3.8000000000000002e-56

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 84.2%

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

   3. Taylor expanded in t around inf 71.6%

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

   if 3.8000000000000002e-56 < z < 1.55000000000000004

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   4. Simplified 72.6%

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

   if 1.55000000000000004 < z < 2.4000000000000002e50

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 74.0%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.55:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 7: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -1.8e+83)
     t_1
     (if (<= z -9.5e-102)
       (* y (/ (- t x) (- a z)))
       (if (<= z 3.1e-55)
         (+ x (/ (- t x) (/ a y)))
         (if (<= z 1.25)
           (* t (/ (- y z) (- a z)))
           (if (<= z 2.8e+50) (* x (- 1.0 (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.8e+83) {
		tmp = t_1;
	} else if (z <= -9.5e-102) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.1e-55) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.25) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.8e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-1.8d+83)) then
        tmp = t_1
    else if (z <= (-9.5d-102)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 3.1d-55) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 1.25d0) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.8d+50) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -1.8e+83) {
		tmp = t_1;
	} else if (z <= -9.5e-102) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 3.1e-55) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 1.25) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.8e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -1.8e+83:
		tmp = t_1
	elif z <= -9.5e-102:
		tmp = y * ((t - x) / (a - z))
	elif z <= 3.1e-55:
		tmp = x + ((t - x) / (a / y))
	elif z <= 1.25:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.8e+50:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.8e+83)
		tmp = t_1;
	elseif (z <= -9.5e-102)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 3.1e-55)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 1.25)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.8e+50)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -1.8e+83)
		tmp = t_1;
	elseif (z <= -9.5e-102)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 3.1e-55)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 1.25)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.8e+50)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+83], t$95$1, If[LessEqual[z, -9.5e-102], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-55], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+50], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7999999999999999e83 or 2.7999999999999998e50 < z

   1. Initial program 54.2%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. associate--l+ 62.6%

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

      3. associate-*r/ 62.6%

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

      4. associate-*r/ 62.6%

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

      5. div-sub 62.6%

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

      6. distribute-lft-out-- 62.6%

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

      7. mul-1-neg 62.6%

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

      8. distribute-neg-frac 62.6%

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

      9. unsub-neg 62.6%

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

      10. distribute-rgt-out-- 62.7%

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

   4. Simplified 62.7%

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

      1. *-un-lft-identity 62.7%

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

      2. associate-/l* 85.7%

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

   6. Applied egg-rr 85.7%

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

      1. *-lft-identity 85.7%

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

      2. associate-/r/ 82.7%

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

   8. Simplified 82.7%

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

   9. Taylor expanded in y around inf 59.4%

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

   10. Taylor expanded in t around 0 55.5%

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

       1. mul-1-neg 55.5%

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

       2. associate-*r/ 64.5%

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

       3. distribute-rgt-neg-in 64.5%

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

       4. distribute-neg-frac 64.5%

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

   12. Simplified 64.5%

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

   if -1.7999999999999999e83 < z < -9.50000000000000025e-102

   1. Initial program 88.3%

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

   2. Taylor expanded in x around -inf 88.8%

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

   3. Taylor expanded in y around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. sub-neg 63.5%

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

      4. div-sub 63.5%

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

   5. Simplified 63.5%

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

   if -9.50000000000000025e-102 < z < 3.09999999999999997e-55

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 95.1%

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

      3. associate-*r/ 93.9%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.5%

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

   3. Applied egg-rr 94.5%

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

   4. Taylor expanded in z around 0 83.9%

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

   if 3.09999999999999997e-55 < z < 1.25

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   4. Simplified 72.6%

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

   if 1.25 < z < 2.7999999999999998e50

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 74.0%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 56.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -6.5e+75)
     t_1
     (if (<= a 1.26e+29)
       (+ t (* y (/ x z)))
       (if (<= a 1.9e+129)
         (* x (- 1.0 (/ y a)))
         (if (<= a 9e+155) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -6.5e+75) {
		tmp = t_1;
	} else if (a <= 1.26e+29) {
		tmp = t + (y * (x / z));
	} else if (a <= 1.9e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 9e+155) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-6.5d+75)) then
        tmp = t_1
    else if (a <= 1.26d+29) then
        tmp = t + (y * (x / z))
    else if (a <= 1.9d+129) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 9d+155) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -6.5e+75) {
		tmp = t_1;
	} else if (a <= 1.26e+29) {
		tmp = t + (y * (x / z));
	} else if (a <= 1.9e+129) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 9e+155) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -6.5e+75:
		tmp = t_1
	elif a <= 1.26e+29:
		tmp = t + (y * (x / z))
	elif a <= 1.9e+129:
		tmp = x * (1.0 - (y / a))
	elif a <= 9e+155:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -6.5e+75)
		tmp = t_1;
	elseif (a <= 1.26e+29)
		tmp = Float64(t + Float64(y * Float64(x / z)));
	elseif (a <= 1.9e+129)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 9e+155)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -6.5e+75)
		tmp = t_1;
	elseif (a <= 1.26e+29)
		tmp = t + (y * (x / z));
	elseif (a <= 1.9e+129)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 9e+155)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+75], t$95$1, If[LessEqual[a, 1.26e+29], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+129], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+155], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.4999999999999998e75 or 8.99999999999999947e155 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 71.1%

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

   3. Taylor expanded in t around inf 68.8%

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

   if -6.4999999999999998e75 < a < 1.26e29

   1. Initial program 66.3%

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

   2. Taylor expanded in z around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. associate--l+ 70.9%

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

      3. associate-*r/ 70.9%

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

      4. associate-*r/ 70.9%

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

      5. div-sub 72.9%

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

      6. distribute-lft-out-- 72.9%

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

      7. mul-1-neg 72.9%

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

      8. distribute-neg-frac 72.9%

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

      9. unsub-neg 72.9%

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

      10. distribute-rgt-out-- 72.9%

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

   4. Simplified 72.9%

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

      1. *-un-lft-identity 72.9%

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

      2. associate-/l* 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. *-lft-identity 81.1%

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

      2. associate-/r/ 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in y around inf 70.4%

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

   10. Taylor expanded in t around 0 57.1%

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

       1. mul-1-neg 57.1%

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

       2. associate-*r/ 61.6%

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

       3. distribute-rgt-neg-in 61.6%

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

       4. distribute-neg-frac 61.6%

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

   12. Simplified 61.6%

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

   if 1.26e29 < a < 1.90000000000000003e129

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 78.3%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

   5. Simplified 67.7%

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

   if 1.90000000000000003e129 < a < 8.99999999999999947e155

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 9: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7100000000000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -6e+75)
     t_1
     (if (<= a 7100000000000.0)
       (- t (/ y (/ z (- t x))))
       (if (<= a 2.7e+129)
         (+ x (/ (- t x) (/ a y)))
         (if (<= a 2.3e+156) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -6e+75) {
		tmp = t_1;
	} else if (a <= 7100000000000.0) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 2.7e+129) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 2.3e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-6d+75)) then
        tmp = t_1
    else if (a <= 7100000000000.0d0) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 2.7d+129) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 2.3d+156) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -6e+75) {
		tmp = t_1;
	} else if (a <= 7100000000000.0) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 2.7e+129) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 2.3e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -6e+75:
		tmp = t_1
	elif a <= 7100000000000.0:
		tmp = t - (y / (z / (t - x)))
	elif a <= 2.7e+129:
		tmp = x + ((t - x) / (a / y))
	elif a <= 2.3e+156:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -6e+75)
		tmp = t_1;
	elseif (a <= 7100000000000.0)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 2.7e+129)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 2.3e+156)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -6e+75)
		tmp = t_1;
	elseif (a <= 7100000000000.0)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 2.7e+129)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 2.3e+156)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+75], t$95$1, If[LessEqual[a, 7100000000000.0], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+129], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+156], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6e75 or 2.2999999999999999e156 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   4. Simplified 77.8%

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

   if -6e75 < a < 7.1e12

   1. Initial program 66.1%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--l+ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. associate-*r/ 72.2%

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

      5. div-sub 74.3%

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

      6. distribute-lft-out-- 74.3%

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

      7. mul-1-neg 74.3%

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

      8. distribute-neg-frac 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if 7.1e12 < a < 2.7000000000000001e129

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l/ 82.7%

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

      3. associate-*r/ 91.2%

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

      4. clear-num 91.3%

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

      5. un-div-inv 91.3%

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

   3. Applied egg-rr 91.3%

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

   4. Taylor expanded in z around 0 73.4%

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

   if 2.7000000000000001e129 < a < 2.2999999999999999e156

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 7100000000000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 70.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 58000000000000:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 58000000000000.0)
       (+ t (* (- y a) (/ (- x t) z)))
       (if (<= a 2.7e+129)
         (+ x (/ (- t x) (/ a y)))
         (if (<= a 1e+156) (* t (/ (- y z) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 58000000000000.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (a <= 2.7e+129) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 58000000000000.0d0) then
        tmp = t + ((y - a) * ((x - t) / z))
    else if (a <= 2.7d+129) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 1d+156) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 58000000000000.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else if (a <= 2.7e+129) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1e+156) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 58000000000000.0:
		tmp = t + ((y - a) * ((x - t) / z))
	elif a <= 2.7e+129:
		tmp = x + ((t - x) / (a / y))
	elif a <= 1e+156:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 58000000000000.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	elseif (a <= 2.7e+129)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 1e+156)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 58000000000000.0)
		tmp = t + ((y - a) * ((x - t) / z));
	elseif (a <= 2.7e+129)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 1e+156)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 58000000000000.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+129], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+156], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.60000000000000023e75 or 9.9999999999999998e155 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.8%

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

   4. Simplified 77.8%

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

   if -5.60000000000000023e75 < a < 5.8e13

   1. Initial program 66.1%

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

   2. Taylor expanded in z around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--l+ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. associate-*r/ 72.2%

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

      5. div-sub 74.3%

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

      6. distribute-lft-out-- 74.3%

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

      7. mul-1-neg 74.3%

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

      8. distribute-neg-frac 74.3%

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

      9. unsub-neg 74.3%

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

      10. distribute-rgt-out-- 74.3%

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

   4. Simplified 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. associate-/l* 82.6%

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

   6. Applied egg-rr 82.6%

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

      1. *-lft-identity 82.6%

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

      2. associate-/r/ 80.8%

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

   8. Simplified 80.8%

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

   if 5.8e13 < a < 2.7000000000000001e129

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l/ 82.7%

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

      3. associate-*r/ 91.2%

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

      4. clear-num 91.3%

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

      5. un-div-inv 91.3%

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

   3. Applied egg-rr 91.3%

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

   4. Taylor expanded in z around 0 73.4%

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

   if 2.7000000000000001e129 < a < 9.9999999999999998e155

   1. Initial program 67.7%

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

   2. Taylor expanded in t around inf 100.0%

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

      1. div-sub 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 58000000000000:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 10^{+156}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+167} \lor \neg \left(z \leq 3.5 \cdot 10^{+51}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+167) (not (<= z 3.5e+51)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- y z) (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+167) || !(z <= 3.5e+51)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+167)) .or. (.not. (z <= 3.5d+51))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+167) || !(z <= 3.5e+51)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+167) or not (z <= 3.5e+51):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+167) || !(z <= 3.5e+51))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+167) || ~((z <= 3.5e+51)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+167], N[Not[LessEqual[z, 3.5e+51]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e167 or 3.5e51 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate--l+ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. associate-*r/ 62.7%

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

      5. div-sub 62.7%

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

      6. distribute-lft-out-- 62.7%

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

      7. mul-1-neg 62.7%

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

      8. distribute-neg-frac 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 62.8%

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

   4. Simplified 62.8%

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

      1. sub-neg 62.8%

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

      2. associate-/l* 87.7%

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

   6. Applied egg-rr 87.7%

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

   if -2.6000000000000002e167 < z < 3.5e51

   1. Initial program 89.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+167} \lor \neg \left(z \leq 3.5 \cdot 10^{+51}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 12: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+168} \lor \neg \left(z \leq 3.5 \cdot 10^{+51}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+168) (not (<= z 3.5e+51)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ (- t x) (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+168) || !(z <= 3.5e+51)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.15d+168)) .or. (.not. (z <= 3.5d+51))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+168) || !(z <= 3.5e+51)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+168) or not (z <= 3.5e+51):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+168) || !(z <= 3.5e+51))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+168) || ~((z <= 3.5e+51)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+168], N[Not[LessEqual[z, 3.5e+51]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e168 or 3.5e51 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate--l+ 62.7%

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

      3. associate-*r/ 62.7%

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

      4. associate-*r/ 62.7%

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

      5. div-sub 62.7%

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

      6. distribute-lft-out-- 62.7%

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

      7. mul-1-neg 62.7%

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

      8. distribute-neg-frac 62.7%

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

      9. unsub-neg 62.7%

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

      10. distribute-rgt-out-- 62.8%

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

   4. Simplified 62.8%

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

      1. sub-neg 62.8%

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

      2. associate-/l* 87.7%

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

   6. Applied egg-rr 87.7%

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

   if -1.15e168 < z < 3.5e51

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*l/ 87.4%

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

      3. associate-*r/ 90.4%

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

      4. clear-num 89.7%

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

      5. un-div-inv 90.0%

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

   3. Applied egg-rr 90.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+168} \lor \neg \left(z \leq 3.5 \cdot 10^{+51}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 13: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -6.5e+18)
     t_1
     (if (<= z 4.8e-56)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 3.6)
         (* t (/ (- y z) (- a z)))
         (if (<= z 4.6e+50) (* x (- 1.0 (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -6.5e+18) {
		tmp = t_1;
	} else if (z <= 4.8e-56) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 3.6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.6e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    if (z <= (-6.5d+18)) then
        tmp = t_1
    else if (z <= 4.8d-56) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 3.6d0) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 4.6d+50) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double tmp;
	if (z <= -6.5e+18) {
		tmp = t_1;
	} else if (z <= 4.8e-56) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 3.6) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.6e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -6.5e+18:
		tmp = t_1
	elif z <= 4.8e-56:
		tmp = x + (y / (a / (t - x)))
	elif z <= 3.6:
		tmp = t * ((y - z) / (a - z))
	elif z <= 4.6e+50:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -6.5e+18)
		tmp = t_1;
	elseif (z <= 4.8e-56)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 3.6)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 4.6e+50)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	tmp = 0.0;
	if (z <= -6.5e+18)
		tmp = t_1;
	elseif (z <= 4.8e-56)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 3.6)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 4.6e+50)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+18], t$95$1, If[LessEqual[z, 4.8e-56], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+50], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e18 or 4.59999999999999994e50 < z

   1. Initial program 57.9%

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

   2. Taylor expanded in z around inf 61.3%

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

      1. +-commutative 61.3%

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

      2. associate--l+ 61.3%

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

      3. associate-*r/ 61.3%

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

      4. associate-*r/ 61.3%

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

      5. div-sub 61.3%

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

      6. distribute-lft-out-- 61.3%

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

      7. mul-1-neg 61.3%

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

      8. distribute-neg-frac 61.3%

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

      9. unsub-neg 61.3%

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

      10. distribute-rgt-out-- 61.4%

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

   4. Simplified 61.4%

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

      1. *-un-lft-identity 61.4%

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

      2. associate-/l* 82.1%

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

   6. Applied egg-rr 82.1%

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

      1. *-lft-identity 82.1%

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

      2. associate-/r/ 79.5%

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

   8. Simplified 79.5%

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

   9. Taylor expanded in y around inf 58.7%

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

   10. Taylor expanded in t around 0 54.5%

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

       1. mul-1-neg 54.5%

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

       2. associate-*r/ 62.3%

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

       3. distribute-rgt-neg-in 62.3%

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

       4. distribute-neg-frac 62.3%

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

   12. Simplified 62.3%

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

   if -6.5e18 < z < 4.80000000000000001e-56

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 77.7%

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

   4. Simplified 77.7%

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

   if 4.80000000000000001e-56 < z < 3.60000000000000009

   1. Initial program 83.7%

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

   2. Taylor expanded in t around inf 72.6%

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

      1. div-sub 72.6%

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

   4. Simplified 72.6%

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

   if 3.60000000000000009 < z < 4.59999999999999994e50

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 74.0%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

   5. Simplified 74.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 14: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 31500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -5.8e+75)
     t_1
     (if (<= a 1.9e-117)
       (- t (/ y (/ z t)))
       (if (<= a 31500.0) (* y (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 1.9e-117) {
		tmp = t - (y / (z / t));
	} else if (a <= 31500.0) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-5.8d+75)) then
        tmp = t_1
    else if (a <= 1.9d-117) then
        tmp = t - (y / (z / t))
    else if (a <= 31500.0d0) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.8e+75) {
		tmp = t_1;
	} else if (a <= 1.9e-117) {
		tmp = t - (y / (z / t));
	} else if (a <= 31500.0) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -5.8e+75:
		tmp = t_1
	elif a <= 1.9e-117:
		tmp = t - (y / (z / t))
	elif a <= 31500.0:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 1.9e-117)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (a <= 31500.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -5.8e+75)
		tmp = t_1;
	elseif (a <= 1.9e-117)
		tmp = t - (y / (z / t));
	elseif (a <= 31500.0)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+75], t$95$1, If[LessEqual[a, 1.9e-117], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 31500.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7999999999999997e75 or 31500 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 68.0%

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

   3. Taylor expanded in t around inf 63.6%

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

   if -5.7999999999999997e75 < a < 1.89999999999999986e-117

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. associate--l+ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. associate-*r/ 75.2%

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

      5. div-sub 77.8%

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

      6. distribute-lft-out-- 77.8%

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

      7. mul-1-neg 77.8%

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

      8. distribute-neg-frac 77.8%

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

      9. unsub-neg 77.8%

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

      10. distribute-rgt-out-- 77.8%

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

   4. Simplified 77.8%

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

      1. *-un-lft-identity 77.8%

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

      2. associate-/l* 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. *-lft-identity 84.1%

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

      2. associate-/r/ 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in y around inf 74.6%

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

   10. Taylor expanded in t around inf 59.0%

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

       1. associate-/l* 58.9%

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

   12. Simplified 58.9%

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

   if 1.89999999999999986e-117 < a < 31500

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. associate--l+ 57.6%

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

      3. associate-*r/ 57.6%

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

      4. associate-*r/ 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-lft-out-- 57.6%

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

      7. mul-1-neg 57.6%

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

      8. distribute-neg-frac 57.6%

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

      9. unsub-neg 57.6%

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

      10. distribute-rgt-out-- 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in t around 0 35.6%

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

      1. associate-/l* 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 35.7%

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

      1. associate-*r/ 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq 31500:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 15: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 31000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -5.6e+75)
     t_1
     (if (<= a 1.02e-116)
       (- t (/ (* y t) z))
       (if (<= a 31000.0) (* y (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.02e-116) {
		tmp = t - ((y * t) / z);
	} else if (a <= 31000.0) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-5.6d+75)) then
        tmp = t_1
    else if (a <= 1.02d-116) then
        tmp = t - ((y * t) / z)
    else if (a <= 31000.0d0) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -5.6e+75) {
		tmp = t_1;
	} else if (a <= 1.02e-116) {
		tmp = t - ((y * t) / z);
	} else if (a <= 31000.0) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -5.6e+75:
		tmp = t_1
	elif a <= 1.02e-116:
		tmp = t - ((y * t) / z)
	elif a <= 31000.0:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.02e-116)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	elseif (a <= 31000.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -5.6e+75)
		tmp = t_1;
	elseif (a <= 1.02e-116)
		tmp = t - ((y * t) / z);
	elseif (a <= 31000.0)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+75], t$95$1, If[LessEqual[a, 1.02e-116], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 31000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.60000000000000023e75 or 31000 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 68.0%

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

   3. Taylor expanded in t around inf 63.6%

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

   if -5.60000000000000023e75 < a < 1.02e-116

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. associate--l+ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. associate-*r/ 75.2%

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

      5. div-sub 77.8%

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

      6. distribute-lft-out-- 77.8%

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

      7. mul-1-neg 77.8%

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

      8. distribute-neg-frac 77.8%

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

      9. unsub-neg 77.8%

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

      10. distribute-rgt-out-- 77.8%

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

   4. Simplified 77.8%

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

      1. *-un-lft-identity 77.8%

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

      2. associate-/l* 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. *-lft-identity 84.1%

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

      2. associate-/r/ 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in y around inf 74.6%

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

   10. Taylor expanded in t around inf 59.0%

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

   if 1.02e-116 < a < 31000

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. associate--l+ 57.6%

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

      3. associate-*r/ 57.6%

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

      4. associate-*r/ 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-lft-out-- 57.6%

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

      7. mul-1-neg 57.6%

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

      8. distribute-neg-frac 57.6%

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

      9. unsub-neg 57.6%

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

      10. distribute-rgt-out-- 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in t around 0 35.6%

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

      1. associate-/l* 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 35.7%

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

      1. associate-*r/ 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-116}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 31000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 16: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1080000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e+75)
   x
   (if (<= a 1.95e-116) t (if (<= a 1080000000000.0) (* y (/ x z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+75) {
		tmp = x;
	} else if (a <= 1.95e-116) {
		tmp = t;
	} else if (a <= 1080000000000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d+75)) then
        tmp = x
    else if (a <= 1.95d-116) then
        tmp = t
    else if (a <= 1080000000000.0d0) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e+75) {
		tmp = x;
	} else if (a <= 1.95e-116) {
		tmp = t;
	} else if (a <= 1080000000000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e+75:
		tmp = x
	elif a <= 1.95e-116:
		tmp = t
	elif a <= 1080000000000.0:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e+75)
		tmp = x;
	elseif (a <= 1.95e-116)
		tmp = t;
	elseif (a <= 1080000000000.0)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e+75)
		tmp = x;
	elseif (a <= 1.95e-116)
		tmp = t;
	elseif (a <= 1080000000000.0)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e+75], x, If[LessEqual[a, 1.95e-116], t, If[LessEqual[a, 1080000000000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.2000000000000002e75 or 1.08e12 < a

   1. Initial program 87.5%

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

   2. Taylor expanded in a around inf 49.2%

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

   if -6.2000000000000002e75 < a < 1.95e-116

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf 42.2%

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

   if 1.95e-116 < a < 1.08e12

   1. Initial program 72.1%

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

   2. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. associate--l+ 57.6%

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

      3. associate-*r/ 57.6%

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

      4. associate-*r/ 57.6%

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

      5. div-sub 57.6%

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

      6. distribute-lft-out-- 57.6%

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

      7. mul-1-neg 57.6%

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

      8. distribute-neg-frac 57.6%

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

      9. unsub-neg 57.6%

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

      10. distribute-rgt-out-- 57.6%

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

   4. Simplified 57.6%

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

   5. Taylor expanded in t around 0 35.6%

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

      1. associate-/l* 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 35.7%

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

      1. associate-*r/ 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1080000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 58.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-20} \lor \neg \left(z \leq 2.4 \cdot 10^{+50}\right):\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e-20) (not (<= z 2.4e+50)))
   (+ t (* y (/ x z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e-20) || !(z <= 2.4e+50)) {
		tmp = t + (y * (x / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d-20)) .or. (.not. (z <= 2.4d+50))) then
        tmp = t + (y * (x / z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e-20) || !(z <= 2.4e+50)) {
		tmp = t + (y * (x / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e-20) or not (z <= 2.4e+50):
		tmp = t + (y * (x / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e-20) || !(z <= 2.4e+50))
		tmp = Float64(t + Float64(y * Float64(x / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e-20) || ~((z <= 2.4e+50)))
		tmp = t + (y * (x / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e-20], N[Not[LessEqual[z, 2.4e+50]], $MachinePrecision]], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e-20 or 2.4000000000000002e50 < z

   1. Initial program 59.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. associate--l+ 60.9%

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

      3. associate-*r/ 60.9%

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

      4. associate-*r/ 60.9%

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

      5. div-sub 60.9%

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

      6. distribute-lft-out-- 60.9%

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

      7. mul-1-neg 60.9%

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

      8. distribute-neg-frac 60.9%

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

      9. unsub-neg 60.9%

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

      10. distribute-rgt-out-- 61.0%

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

   4. Simplified 61.0%

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

      1. *-un-lft-identity 61.0%

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

      2. associate-/l* 80.7%

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

   6. Applied egg-rr 80.7%

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

      1. *-lft-identity 80.7%

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

      2. associate-/r/ 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in y around inf 58.3%

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

   10. Taylor expanded in t around 0 54.3%

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

       1. mul-1-neg 54.3%

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

       2. associate-*r/ 61.8%

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

       3. distribute-rgt-neg-in 61.8%

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

       4. distribute-neg-frac 61.8%

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

   12. Simplified 61.8%

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

   if -9.5e-20 < z < 2.4000000000000002e50

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 72.1%

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

   3. Taylor expanded in t around inf 61.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-20} \lor \neg \left(z \leq 2.4 \cdot 10^{+50}\right):\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 18: 46.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+202) t (if (<= z 3.15e+50) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+202) {
		tmp = t;
	} else if (z <= 3.15e+50) {
		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 <= (-8.5d+202)) then
        tmp = t
    else if (z <= 3.15d+50) 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 <= -8.5e+202) {
		tmp = t;
	} else if (z <= 3.15e+50) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+202:
		tmp = t
	elif z <= 3.15e+50:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+202)
		tmp = t;
	elseif (z <= 3.15e+50)
		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 <= -8.5e+202)
		tmp = t;
	elseif (z <= 3.15e+50)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+202], t, If[LessEqual[z, 3.15e+50], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000003e202 or 3.14999999999999993e50 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -8.5000000000000003e202 < z < 3.14999999999999993e50

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 61.9%

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

   3. Taylor expanded in x around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

   5. Simplified 49.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+18) t (if (<= z 3.5e+51) (+ x (/ (* y t) a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+18) {
		tmp = t;
	} else if (z <= 3.5e+51) {
		tmp = x + ((y * t) / 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 <= (-6.5d+18)) then
        tmp = t
    else if (z <= 3.5d+51) then
        tmp = x + ((y * t) / 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 <= -6.5e+18) {
		tmp = t;
	} else if (z <= 3.5e+51) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+18:
		tmp = t
	elif z <= 3.5e+51:
		tmp = x + ((y * t) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+18)
		tmp = t;
	elseif (z <= 3.5e+51)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+18)
		tmp = t;
	elseif (z <= 3.5e+51)
		tmp = x + ((y * t) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+18], t, If[LessEqual[z, 3.5e+51], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e18 or 3.5e51 < z

   1. Initial program 57.9%

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

   2. Taylor expanded in z around inf 42.2%

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

   if -6.5e18 < z < 3.5e51

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 71.2%

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

   3. Taylor expanded in t around inf 60.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 38.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+75) x (if (<= a 1.12e+29) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+75) {
		tmp = x;
	} else if (a <= 1.12e+29) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d+75)) then
        tmp = x
    else if (a <= 1.12d+29) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+75) {
		tmp = x;
	} else if (a <= 1.12e+29) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e+75:
		tmp = x
	elif a <= 1.12e+29:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+75)
		tmp = x;
	elseif (a <= 1.12e+29)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e+75)
		tmp = x;
	elseif (a <= 1.12e+29)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+75], x, If[LessEqual[a, 1.12e+29], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4999999999999998e75 or 1.1200000000000001e29 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 50.0%

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

   if -6.4999999999999998e75 < a < 1.1200000000000001e29

   1. Initial program 66.3%

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

   2. Taylor expanded in z around inf 37.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.5%

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

2. Taylor expanded in z around inf 26.3%

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

3. Final simplification 26.3%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023257 
(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)))))