Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 90.8%

Time: 20.2s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-239} \lor \neg \left(t_2 \leq 4 \cdot 10^{-237}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (or (<= t_2 -1e-239) (not (<= t_2 4e-237)))
     (fma (- y z) t_1 x)
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if ((t_2 <= -1e-239) || !(t_2 <= 4e-237)) {
		tmp = fma((y - z), t_1, x);
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if ((t_2 <= -1e-239) || !(t_2 <= 4e-237))
		tmp = fma(Float64(y - z), t_1, x);
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e-239], N[Not[LessEqual[t$95$2, 4e-237]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-239 or 4e-237 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. fma-def 91.9%

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

   3. Simplified 91.9%

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

   if -1.0000000000000001e-239 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4e-237

   1. Initial program 7.0%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. distribute-lft-out-- 80.4%

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

      3. div-sub 80.5%

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

      4. mul-1-neg 80.5%

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

      5. unsub-neg 80.5%

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

      6. distribute-rgt-out-- 80.8%

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

      7. associate-/l* 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-239} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4 \cdot 10^{-237}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-239} \lor \neg \left(t_1 \leq 4 \cdot 10^{-237}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-239) (not (<= t_1 4e-237)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-239) || !(t_1 <= 4e-237)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-239)) .or. (.not. (t_1 <= 4d-237))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-239) || !(t_1 <= 4e-237)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-239) or not (t_1 <= 4e-237):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-239) || !(t_1 <= 4e-237))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-239) || ~((t_1 <= 4e-237)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-239], N[Not[LessEqual[t$95$1, 4e-237]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-239 or 4e-237 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   if -1.0000000000000001e-239 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4e-237

   1. Initial program 7.0%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. distribute-lft-out-- 80.4%

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

      3. div-sub 80.5%

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

      4. mul-1-neg 80.5%

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

      5. unsub-neg 80.5%

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

      6. distribute-rgt-out-- 80.8%

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

      7. associate-/l* 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-239} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4 \cdot 10^{-237}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.26e+99)
     t
     (if (<= z 1.1e-167)
       t_1
       (if (<= z 1.2e-125)
         (* t (/ y (- a z)))
         (if (<= z 3.9e+64)
           t_1
           (if (<= z 1.65e+106)
             t
             (if (<= z 6.6e+129)
               t_1
               (if (<= z 2.9e+199) (* x (/ (- y a) z)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.26e+99) {
		tmp = t;
	} else if (z <= 1.1e-167) {
		tmp = t_1;
	} else if (z <= 1.2e-125) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.9e+64) {
		tmp = t_1;
	} else if (z <= 1.65e+106) {
		tmp = t;
	} else if (z <= 6.6e+129) {
		tmp = t_1;
	} else if (z <= 2.9e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.26d+99)) then
        tmp = t
    else if (z <= 1.1d-167) then
        tmp = t_1
    else if (z <= 1.2d-125) then
        tmp = t * (y / (a - z))
    else if (z <= 3.9d+64) then
        tmp = t_1
    else if (z <= 1.65d+106) then
        tmp = t
    else if (z <= 6.6d+129) then
        tmp = t_1
    else if (z <= 2.9d+199) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.26e+99) {
		tmp = t;
	} else if (z <= 1.1e-167) {
		tmp = t_1;
	} else if (z <= 1.2e-125) {
		tmp = t * (y / (a - z));
	} else if (z <= 3.9e+64) {
		tmp = t_1;
	} else if (z <= 1.65e+106) {
		tmp = t;
	} else if (z <= 6.6e+129) {
		tmp = t_1;
	} else if (z <= 2.9e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.26e+99:
		tmp = t
	elif z <= 1.1e-167:
		tmp = t_1
	elif z <= 1.2e-125:
		tmp = t * (y / (a - z))
	elif z <= 3.9e+64:
		tmp = t_1
	elif z <= 1.65e+106:
		tmp = t
	elif z <= 6.6e+129:
		tmp = t_1
	elif z <= 2.9e+199:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.26e+99)
		tmp = t;
	elseif (z <= 1.1e-167)
		tmp = t_1;
	elseif (z <= 1.2e-125)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 3.9e+64)
		tmp = t_1;
	elseif (z <= 1.65e+106)
		tmp = t;
	elseif (z <= 6.6e+129)
		tmp = t_1;
	elseif (z <= 2.9e+199)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.26e+99)
		tmp = t;
	elseif (z <= 1.1e-167)
		tmp = t_1;
	elseif (z <= 1.2e-125)
		tmp = t * (y / (a - z));
	elseif (z <= 3.9e+64)
		tmp = t_1;
	elseif (z <= 1.65e+106)
		tmp = t;
	elseif (z <= 6.6e+129)
		tmp = t_1;
	elseif (z <= 2.9e+199)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+99], t, If[LessEqual[z, 1.1e-167], t$95$1, If[LessEqual[z, 1.2e-125], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+64], t$95$1, If[LessEqual[z, 1.65e+106], t, If[LessEqual[z, 6.6e+129], t$95$1, If[LessEqual[z, 2.9e+199], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25999999999999996e99 or 3.8999999999999998e64 < z < 1.65000000000000004e106 or 2.8999999999999999e199 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 61.6%

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

   if -1.25999999999999996e99 < z < 1.1e-167 or 1.2000000000000001e-125 < z < 3.8999999999999998e64 or 1.65000000000000004e106 < z < 6.5999999999999998e129

   1. Initial program 91.5%

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

   2. Taylor expanded in z around 0 64.9%

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

   3. Taylor expanded in x around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. unsub-neg 59.1%

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

   5. Simplified 59.1%

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

   if 1.1e-167 < z < 1.2000000000000001e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 99.8%

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

      4. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 73.8%

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

      1. associate-*r/ 73.8%

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

   7. Simplified 73.8%

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

   if 6.5999999999999998e129 < z < 2.8999999999999999e199

   1. Initial program 59.3%

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

   2. Taylor expanded in z around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. distribute-lft-out-- 60.1%

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

      3. div-sub 60.1%

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

      4. mul-1-neg 60.1%

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

      5. unsub-neg 60.1%

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

      6. distribute-rgt-out-- 60.5%

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

      7. associate-/l* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in t around 0 35.0%

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

      1. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.95e+94)
     t
     (if (<= z 1.02e-181)
       t_1
       (if (<= z 1.4e-127)
         (* y (/ (- t x) a))
         (if (<= z 3.3e+64)
           t_1
           (if (<= z 2.7e+106)
             t
             (if (<= z 3.4e+133)
               t_1
               (if (<= z 3.7e+199) (* x (/ (- y a) z)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.95e+94) {
		tmp = t;
	} else if (z <= 1.02e-181) {
		tmp = t_1;
	} else if (z <= 1.4e-127) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.3e+64) {
		tmp = t_1;
	} else if (z <= 2.7e+106) {
		tmp = t;
	} else if (z <= 3.4e+133) {
		tmp = t_1;
	} else if (z <= 3.7e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2.95d+94)) then
        tmp = t
    else if (z <= 1.02d-181) then
        tmp = t_1
    else if (z <= 1.4d-127) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.3d+64) then
        tmp = t_1
    else if (z <= 2.7d+106) then
        tmp = t
    else if (z <= 3.4d+133) then
        tmp = t_1
    else if (z <= 3.7d+199) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.95e+94) {
		tmp = t;
	} else if (z <= 1.02e-181) {
		tmp = t_1;
	} else if (z <= 1.4e-127) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.3e+64) {
		tmp = t_1;
	} else if (z <= 2.7e+106) {
		tmp = t;
	} else if (z <= 3.4e+133) {
		tmp = t_1;
	} else if (z <= 3.7e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.95e+94:
		tmp = t
	elif z <= 1.02e-181:
		tmp = t_1
	elif z <= 1.4e-127:
		tmp = y * ((t - x) / a)
	elif z <= 3.3e+64:
		tmp = t_1
	elif z <= 2.7e+106:
		tmp = t
	elif z <= 3.4e+133:
		tmp = t_1
	elif z <= 3.7e+199:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.95e+94)
		tmp = t;
	elseif (z <= 1.02e-181)
		tmp = t_1;
	elseif (z <= 1.4e-127)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.3e+64)
		tmp = t_1;
	elseif (z <= 2.7e+106)
		tmp = t;
	elseif (z <= 3.4e+133)
		tmp = t_1;
	elseif (z <= 3.7e+199)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.95e+94)
		tmp = t;
	elseif (z <= 1.02e-181)
		tmp = t_1;
	elseif (z <= 1.4e-127)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.3e+64)
		tmp = t_1;
	elseif (z <= 2.7e+106)
		tmp = t;
	elseif (z <= 3.4e+133)
		tmp = t_1;
	elseif (z <= 3.7e+199)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+94], t, If[LessEqual[z, 1.02e-181], t$95$1, If[LessEqual[z, 1.4e-127], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+64], t$95$1, If[LessEqual[z, 2.7e+106], t, If[LessEqual[z, 3.4e+133], t$95$1, If[LessEqual[z, 3.7e+199], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.94999999999999995e94 or 3.29999999999999988e64 < z < 2.70000000000000006e106 or 3.70000000000000021e199 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 61.6%

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

   if -2.94999999999999995e94 < z < 1.02000000000000003e-181 or 1.4e-127 < z < 3.29999999999999988e64 or 2.70000000000000006e106 < z < 3.39999999999999987e133

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 64.4%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   if 1.02000000000000003e-181 < z < 1.4e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 99.8%

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

      4. associate-/r/ 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in a around inf 88.9%

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

      1. associate-*r/ 88.9%

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

   7. Simplified 88.9%

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

   if 3.39999999999999987e133 < z < 3.70000000000000021e199

   1. Initial program 59.3%

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

   2. Taylor expanded in z around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. distribute-lft-out-- 60.1%

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

      3. div-sub 60.1%

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

      4. mul-1-neg 60.1%

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

      5. unsub-neg 60.1%

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

      6. distribute-rgt-out-- 60.5%

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

      7. associate-/l* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in t around 0 35.0%

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

      1. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -4.5e+97)
     t
     (if (<= z 1.35e-179)
       t_1
       (if (<= z 5.5e-42)
         (+ x (/ t (/ a y)))
         (if (<= z 4.9e+64)
           t_1
           (if (<= z 5e+105)
             t
             (if (<= z 2.3e+129)
               t_1
               (if (<= z 4.8e+199) (* x (/ (- y a) z)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.5e+97) {
		tmp = t;
	} else if (z <= 1.35e-179) {
		tmp = t_1;
	} else if (z <= 5.5e-42) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.9e+64) {
		tmp = t_1;
	} else if (z <= 5e+105) {
		tmp = t;
	} else if (z <= 2.3e+129) {
		tmp = t_1;
	} else if (z <= 4.8e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-4.5d+97)) then
        tmp = t
    else if (z <= 1.35d-179) then
        tmp = t_1
    else if (z <= 5.5d-42) then
        tmp = x + (t / (a / y))
    else if (z <= 4.9d+64) then
        tmp = t_1
    else if (z <= 5d+105) then
        tmp = t
    else if (z <= 2.3d+129) then
        tmp = t_1
    else if (z <= 4.8d+199) then
        tmp = x * ((y - a) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -4.5e+97) {
		tmp = t;
	} else if (z <= 1.35e-179) {
		tmp = t_1;
	} else if (z <= 5.5e-42) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.9e+64) {
		tmp = t_1;
	} else if (z <= 5e+105) {
		tmp = t;
	} else if (z <= 2.3e+129) {
		tmp = t_1;
	} else if (z <= 4.8e+199) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -4.5e+97:
		tmp = t
	elif z <= 1.35e-179:
		tmp = t_1
	elif z <= 5.5e-42:
		tmp = x + (t / (a / y))
	elif z <= 4.9e+64:
		tmp = t_1
	elif z <= 5e+105:
		tmp = t
	elif z <= 2.3e+129:
		tmp = t_1
	elif z <= 4.8e+199:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -4.5e+97)
		tmp = t;
	elseif (z <= 1.35e-179)
		tmp = t_1;
	elseif (z <= 5.5e-42)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4.9e+64)
		tmp = t_1;
	elseif (z <= 5e+105)
		tmp = t;
	elseif (z <= 2.3e+129)
		tmp = t_1;
	elseif (z <= 4.8e+199)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -4.5e+97)
		tmp = t;
	elseif (z <= 1.35e-179)
		tmp = t_1;
	elseif (z <= 5.5e-42)
		tmp = x + (t / (a / y));
	elseif (z <= 4.9e+64)
		tmp = t_1;
	elseif (z <= 5e+105)
		tmp = t;
	elseif (z <= 2.3e+129)
		tmp = t_1;
	elseif (z <= 4.8e+199)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+97], t, If[LessEqual[z, 1.35e-179], t$95$1, If[LessEqual[z, 5.5e-42], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+64], t$95$1, If[LessEqual[z, 5e+105], t, If[LessEqual[z, 2.3e+129], t$95$1, If[LessEqual[z, 4.8e+199], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999976e97 or 4.9000000000000003e64 < z < 5.00000000000000046e105 or 4.8000000000000003e199 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 61.6%

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

   if -4.49999999999999976e97 < z < 1.34999999999999994e-179 or 5.5e-42 < z < 4.9000000000000003e64 or 5.00000000000000046e105 < z < 2.2999999999999999e129

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 68.1%

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

   3. Taylor expanded in x around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. unsub-neg 62.3%

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

   5. Simplified 62.3%

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

   if 1.34999999999999994e-179 < z < 5.5e-42

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 51.1%

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

   3. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 50.1%

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

   5. Simplified 50.1%

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

   if 2.2999999999999999e129 < z < 4.8000000000000003e199

   1. Initial program 59.3%

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

   2. Taylor expanded in z around inf 60.1%

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

      1. associate--l+ 60.1%

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

      2. distribute-lft-out-- 60.1%

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

      3. div-sub 60.1%

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

      4. mul-1-neg 60.1%

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

      5. unsub-neg 60.1%

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

      6. distribute-rgt-out-- 60.5%

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

      7. associate-/l* 75.9%

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

   4. Simplified 75.9%

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

   5. Taylor expanded in t around 0 35.0%

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

      1. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ t_2 := t - \frac{x \cdot a}{z}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z)))
        (t_2 (- t (/ (* x a) z)))
        (t_3 (* y (/ (- x t) z))))
   (if (<= a -5.2e+74)
     (* x (- 1.0 (/ y a)))
     (if (<= a -2.4e-74)
       t_2
       (if (<= a -7.2e-86)
         t_3
         (if (<= a -8e-100)
           t_1
           (if (<= a -1.55e-167)
             t_2
             (if (<= a 1.7e-218)
               t_3
               (if (<= a 7e+29) t_1 (- x (/ x (/ a y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = t - ((x * a) / z);
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -5.2e+74) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.4e-74) {
		tmp = t_2;
	} else if (a <= -7.2e-86) {
		tmp = t_3;
	} else if (a <= -8e-100) {
		tmp = t_1;
	} else if (a <= -1.55e-167) {
		tmp = t_2;
	} else if (a <= 1.7e-218) {
		tmp = t_3;
	} else if (a <= 7e+29) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    t_2 = t - ((x * a) / z)
    t_3 = y * ((x - t) / z)
    if (a <= (-5.2d+74)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-2.4d-74)) then
        tmp = t_2
    else if (a <= (-7.2d-86)) then
        tmp = t_3
    else if (a <= (-8d-100)) then
        tmp = t_1
    else if (a <= (-1.55d-167)) then
        tmp = t_2
    else if (a <= 1.7d-218) then
        tmp = t_3
    else if (a <= 7d+29) then
        tmp = t_1
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = t - ((x * a) / z);
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (a <= -5.2e+74) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.4e-74) {
		tmp = t_2;
	} else if (a <= -7.2e-86) {
		tmp = t_3;
	} else if (a <= -8e-100) {
		tmp = t_1;
	} else if (a <= -1.55e-167) {
		tmp = t_2;
	} else if (a <= 1.7e-218) {
		tmp = t_3;
	} else if (a <= 7e+29) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	t_2 = t - ((x * a) / z)
	t_3 = y * ((x - t) / z)
	tmp = 0
	if a <= -5.2e+74:
		tmp = x * (1.0 - (y / a))
	elif a <= -2.4e-74:
		tmp = t_2
	elif a <= -7.2e-86:
		tmp = t_3
	elif a <= -8e-100:
		tmp = t_1
	elif a <= -1.55e-167:
		tmp = t_2
	elif a <= 1.7e-218:
		tmp = t_3
	elif a <= 7e+29:
		tmp = t_1
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	t_2 = Float64(t - Float64(Float64(x * a) / z))
	t_3 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (a <= -5.2e+74)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -2.4e-74)
		tmp = t_2;
	elseif (a <= -7.2e-86)
		tmp = t_3;
	elseif (a <= -8e-100)
		tmp = t_1;
	elseif (a <= -1.55e-167)
		tmp = t_2;
	elseif (a <= 1.7e-218)
		tmp = t_3;
	elseif (a <= 7e+29)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	t_2 = t - ((x * a) / z);
	t_3 = y * ((x - t) / z);
	tmp = 0.0;
	if (a <= -5.2e+74)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -2.4e-74)
		tmp = t_2;
	elseif (a <= -7.2e-86)
		tmp = t_3;
	elseif (a <= -8e-100)
		tmp = t_1;
	elseif (a <= -1.55e-167)
		tmp = t_2;
	elseif (a <= 1.7e-218)
		tmp = t_3;
	elseif (a <= 7e+29)
		tmp = t_1;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+74], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-74], t$95$2, If[LessEqual[a, -7.2e-86], t$95$3, If[LessEqual[a, -8e-100], t$95$1, If[LessEqual[a, -1.55e-167], t$95$2, If[LessEqual[a, 1.7e-218], t$95$3, If[LessEqual[a, 7e+29], t$95$1, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.2000000000000001e74

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 71.3%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   if -5.2000000000000001e74 < a < -2.3999999999999999e-74 or -8.0000000000000002e-100 < a < -1.55e-167

   1. Initial program 67.1%

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

   2. Taylor expanded in z around inf 62.2%

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

      1. associate--l+ 62.2%

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

      2. distribute-lft-out-- 62.2%

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

      3. div-sub 62.2%

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

      4. mul-1-neg 62.2%

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

      5. unsub-neg 62.2%

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

      6. distribute-rgt-out-- 62.2%

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

      7. associate-/l* 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. sub-neg 56.9%

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

      2. mul-1-neg 56.9%

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

      3. remove-double-neg 56.9%

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

      4. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. *-commutative 57.1%

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

   10. Simplified 57.1%

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

   if -2.3999999999999999e-74 < a < -7.19999999999999932e-86 or -1.55e-167 < a < 1.69999999999999993e-218

   1. Initial program 80.5%

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

   2. Taylor expanded in z around inf 80.5%

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

      1. associate--l+ 80.5%

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

      2. distribute-lft-out-- 80.5%

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

      3. div-sub 80.5%

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

      4. mul-1-neg 80.5%

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

      5. unsub-neg 80.5%

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

      6. distribute-rgt-out-- 80.5%

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

      7. associate-/l* 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in y around -inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. associate-*r/ 68.5%

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

      3. *-commutative 68.5%

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

      4. distribute-rgt-neg-in 68.5%

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

   7. Simplified 68.5%

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

   if -7.19999999999999932e-86 < a < -8.0000000000000002e-100 or 1.69999999999999993e-218 < a < 6.99999999999999958e29

   1. Initial program 74.2%

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

   2. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. distribute-lft-out-- 73.3%

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

      3. div-sub 75.0%

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

      4. mul-1-neg 75.0%

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

      5. unsub-neg 75.0%

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

      6. distribute-rgt-out-- 75.0%

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

      7. associate-/l* 84.8%

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

   4. Simplified 84.8%

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

   5. Taylor expanded in t around inf 65.5%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   if 6.99999999999999958e29 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around 0 60.0%

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

   3. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-100}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-167}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+29}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 56.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ t_2 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-181}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+135}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))) (t_2 (* (- t x) (/ y (- a z)))))
   (if (<= z -3.4e+59)
     t_1
     (if (<= z -3.8e-181)
       (- x (/ x (/ a y)))
       (if (<= z -1.95e-228)
         t_2
         (if (<= z 6.6e-187)
           (* x (- 1.0 (/ y a)))
           (if (<= z 2e+42)
             t_2
             (if (<= z 9e+135) (* (- y z) (/ t (- a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (z <= -3.4e+59) {
		tmp = t_1;
	} else if (z <= -3.8e-181) {
		tmp = x - (x / (a / y));
	} else if (z <= -1.95e-228) {
		tmp = t_2;
	} else if (z <= 6.6e-187) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2e+42) {
		tmp = t_2;
	} else if (z <= 9e+135) {
		tmp = (y - z) * (t / (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 = t + (y * (x / z))
    t_2 = (t - x) * (y / (a - z))
    if (z <= (-3.4d+59)) then
        tmp = t_1
    else if (z <= (-3.8d-181)) then
        tmp = x - (x / (a / y))
    else if (z <= (-1.95d-228)) then
        tmp = t_2
    else if (z <= 6.6d-187) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2d+42) then
        tmp = t_2
    else if (z <= 9d+135) then
        tmp = (y - z) * (t / (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 = t + (y * (x / z));
	double t_2 = (t - x) * (y / (a - z));
	double tmp;
	if (z <= -3.4e+59) {
		tmp = t_1;
	} else if (z <= -3.8e-181) {
		tmp = x - (x / (a / y));
	} else if (z <= -1.95e-228) {
		tmp = t_2;
	} else if (z <= 6.6e-187) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2e+42) {
		tmp = t_2;
	} else if (z <= 9e+135) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	t_2 = (t - x) * (y / (a - z))
	tmp = 0
	if z <= -3.4e+59:
		tmp = t_1
	elif z <= -3.8e-181:
		tmp = x - (x / (a / y))
	elif z <= -1.95e-228:
		tmp = t_2
	elif z <= 6.6e-187:
		tmp = x * (1.0 - (y / a))
	elif z <= 2e+42:
		tmp = t_2
	elif z <= 9e+135:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	t_2 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.4e+59)
		tmp = t_1;
	elseif (z <= -3.8e-181)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= -1.95e-228)
		tmp = t_2;
	elseif (z <= 6.6e-187)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2e+42)
		tmp = t_2;
	elseif (z <= 9e+135)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	t_2 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (z <= -3.4e+59)
		tmp = t_1;
	elseif (z <= -3.8e-181)
		tmp = x - (x / (a / y));
	elseif (z <= -1.95e-228)
		tmp = t_2;
	elseif (z <= 6.6e-187)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2e+42)
		tmp = t_2;
	elseif (z <= 9e+135)
		tmp = (y - z) * (t / (a - z));
	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]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+59], t$95$1, If[LessEqual[z, -3.8e-181], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-228], t$95$2, If[LessEqual[z, 6.6e-187], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+42], t$95$2, If[LessEqual[z, 9e+135], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.40000000000000006e59 or 9.00000000000000014e135 < z

   1. Initial program 56.7%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. associate--l+ 65.4%

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

      2. distribute-lft-out-- 65.4%

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

      3. div-sub 65.4%

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

      4. mul-1-neg 65.4%

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

      5. unsub-neg 65.4%

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

      6. distribute-rgt-out-- 65.7%

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

      7. associate-/l* 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in y around inf 79.4%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-*l/ 73.8%

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

      3. distribute-rgt-neg-in 73.8%

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

   8. Simplified 73.8%

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

   if -3.40000000000000006e59 < z < -3.7999999999999998e-181

   1. Initial program 90.9%

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

   2. Taylor expanded in z around 0 50.5%

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

   3. Taylor expanded in t around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. unsub-neg 43.9%

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

      3. associate-/l* 54.7%

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

   5. Simplified 54.7%

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

   if -3.7999999999999998e-181 < z < -1.95000000000000014e-228 or 6.6e-187 < z < 2.00000000000000009e42

   1. Initial program 90.3%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. div-sub 65.8%

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

      2. associate-*r/ 62.8%

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

      3. associate-/l* 65.8%

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

      4. associate-/r/ 67.5%

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

   4. Simplified 67.5%

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

   if -1.95000000000000014e-228 < z < 6.6e-187

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 93.7%

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

   3. Taylor expanded in x around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if 2.00000000000000009e42 < z < 9.00000000000000014e135

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 59.4%

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

      1. associate-/l* 73.9%

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

      2. associate-/r/ 70.4%

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

   4. Simplified 70.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-181}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-228}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+135}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 55.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ t_2 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))) (t_2 (* (- y z) (/ t (- a z)))))
   (if (<= z -1.4e+58)
     t_1
     (if (<= z 1.1e-167)
       (- x (/ x (/ a y)))
       (if (<= z 3.6e-35)
         t_2
         (if (<= z 1.35e+56)
           (* x (- 1.0 (/ y a)))
           (if (<= z 8.4e+133) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (z <= -1.4e+58) {
		tmp = t_1;
	} else if (z <= 1.1e-167) {
		tmp = x - (x / (a / y));
	} else if (z <= 3.6e-35) {
		tmp = t_2;
	} else if (z <= 1.35e+56) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+133) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * (x / z))
    t_2 = (y - z) * (t / (a - z))
    if (z <= (-1.4d+58)) then
        tmp = t_1
    else if (z <= 1.1d-167) then
        tmp = x - (x / (a / y))
    else if (z <= 3.6d-35) then
        tmp = t_2
    else if (z <= 1.35d+56) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8.4d+133) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * (x / z));
	double t_2 = (y - z) * (t / (a - z));
	double tmp;
	if (z <= -1.4e+58) {
		tmp = t_1;
	} else if (z <= 1.1e-167) {
		tmp = x - (x / (a / y));
	} else if (z <= 3.6e-35) {
		tmp = t_2;
	} else if (z <= 1.35e+56) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8.4e+133) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	t_2 = (y - z) * (t / (a - z))
	tmp = 0
	if z <= -1.4e+58:
		tmp = t_1
	elif z <= 1.1e-167:
		tmp = x - (x / (a / y))
	elif z <= 3.6e-35:
		tmp = t_2
	elif z <= 1.35e+56:
		tmp = x * (1.0 - (y / a))
	elif z <= 8.4e+133:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(x / z)))
	t_2 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.4e+58)
		tmp = t_1;
	elseif (z <= 1.1e-167)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 3.6e-35)
		tmp = t_2;
	elseif (z <= 1.35e+56)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8.4e+133)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * (x / z));
	t_2 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (z <= -1.4e+58)
		tmp = t_1;
	elseif (z <= 1.1e-167)
		tmp = x - (x / (a / y));
	elseif (z <= 3.6e-35)
		tmp = t_2;
	elseif (z <= 1.35e+56)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8.4e+133)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+58], t$95$1, If[LessEqual[z, 1.1e-167], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-35], t$95$2, If[LessEqual[z, 1.35e+56], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+133], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3999999999999999e58 or 8.4e133 < z

   1. Initial program 56.7%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. associate--l+ 65.4%

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

      2. distribute-lft-out-- 65.4%

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

      3. div-sub 65.4%

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

      4. mul-1-neg 65.4%

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

      5. unsub-neg 65.4%

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

      6. distribute-rgt-out-- 65.7%

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

      7. associate-/l* 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in y around inf 79.4%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-*l/ 73.8%

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

      3. distribute-rgt-neg-in 73.8%

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

   8. Simplified 73.8%

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

   if -1.3999999999999999e58 < z < 1.1e-167

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 74.2%

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

   3. Taylor expanded in t around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

      3. associate-/l* 64.5%

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

   5. Simplified 64.5%

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

   if 1.1e-167 < z < 3.60000000000000019e-35 or 1.35000000000000005e56 < z < 8.4e133

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0 58.3%

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

      1. associate-/l* 65.0%

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

      2. associate-/r/ 63.1%

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

   4. Simplified 63.1%

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

   if 3.60000000000000019e-35 < z < 1.35000000000000005e56

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 62.5%

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

   3. Taylor expanded in x around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. unsub-neg 66.3%

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

   5. Simplified 66.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-167}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-35}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+133}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 9: 55.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-180}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+117}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -2.6e+59)
     t_1
     (if (<= z 1.75e-180)
       (- x (/ x (/ a y)))
       (if (<= z 4.2e-41)
         (+ x (/ t (/ a y)))
         (if (<= z 4.6e+64)
           (* x (- 1.0 (/ y a)))
           (if (<= z 3.7e+117) (- t (/ (* y t) z)) 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 <= -2.6e+59) {
		tmp = t_1;
	} else if (z <= 1.75e-180) {
		tmp = x - (x / (a / y));
	} else if (z <= 4.2e-41) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.6e+64) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.7e+117) {
		tmp = t - ((y * t) / 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 = t + (y * (x / z))
    if (z <= (-2.6d+59)) then
        tmp = t_1
    else if (z <= 1.75d-180) then
        tmp = x - (x / (a / y))
    else if (z <= 4.2d-41) then
        tmp = x + (t / (a / y))
    else if (z <= 4.6d+64) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.7d+117) then
        tmp = t - ((y * t) / 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 = t + (y * (x / z));
	double tmp;
	if (z <= -2.6e+59) {
		tmp = t_1;
	} else if (z <= 1.75e-180) {
		tmp = x - (x / (a / y));
	} else if (z <= 4.2e-41) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.6e+64) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.7e+117) {
		tmp = t - ((y * t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -2.6e+59:
		tmp = t_1
	elif z <= 1.75e-180:
		tmp = x - (x / (a / y))
	elif z <= 4.2e-41:
		tmp = x + (t / (a / y))
	elif z <= 4.6e+64:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.7e+117:
		tmp = t - ((y * t) / z)
	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 <= -2.6e+59)
		tmp = t_1;
	elseif (z <= 1.75e-180)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (z <= 4.2e-41)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4.6e+64)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.7e+117)
		tmp = Float64(t - Float64(Float64(y * t) / z));
	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 <= -2.6e+59)
		tmp = t_1;
	elseif (z <= 1.75e-180)
		tmp = x - (x / (a / y));
	elseif (z <= 4.2e-41)
		tmp = x + (t / (a / y));
	elseif (z <= 4.6e+64)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.7e+117)
		tmp = t - ((y * t) / z);
	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, -2.6e+59], t$95$1, If[LessEqual[z, 1.75e-180], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-41], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+64], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+117], N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.59999999999999999e59 or 3.6999999999999999e117 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. distribute-lft-out-- 63.4%

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

      3. div-sub 63.4%

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

      4. mul-1-neg 63.4%

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

      5. unsub-neg 63.4%

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

      6. distribute-rgt-out-- 63.7%

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

      7. associate-/l* 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in y around inf 77.9%

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

   6. Taylor expanded in t around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-*l/ 72.5%

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

      3. distribute-rgt-neg-in 72.5%

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

   8. Simplified 72.5%

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

   if -2.59999999999999999e59 < z < 1.75e-180

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 74.2%

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

   3. Taylor expanded in t around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

      3. associate-/l* 64.5%

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

   5. Simplified 64.5%

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

   if 1.75e-180 < z < 4.20000000000000025e-41

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 51.1%

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

   3. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 50.1%

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

   5. Simplified 50.1%

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

   if 4.20000000000000025e-41 < z < 4.6e64

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 60.9%

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

   3. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   5. Simplified 60.2%

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

   if 4.6e64 < z < 3.6999999999999999e117

   1. Initial program 84.5%

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

   2. Taylor expanded in z around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. div-sub 76.6%

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

      4. mul-1-neg 76.6%

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

      5. unsub-neg 76.6%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in t around inf 71.1%

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

   6. Taylor expanded in y around inf 71.3%

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

      1. *-commutative 71.3%

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

   8. Simplified 71.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-180}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+117}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.25e+95)
     t
     (if (<= z 1.65e-168)
       t_1
       (if (<= z 1.02e-128) (* t (/ y (- a z))) (if (<= z 2.4e+64) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.25e+95) {
		tmp = t;
	} else if (z <= 1.65e-168) {
		tmp = t_1;
	} else if (z <= 1.02e-128) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.4e+64) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.25d+95)) then
        tmp = t
    else if (z <= 1.65d-168) then
        tmp = t_1
    else if (z <= 1.02d-128) then
        tmp = t * (y / (a - z))
    else if (z <= 2.4d+64) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.25e+95) {
		tmp = t;
	} else if (z <= 1.65e-168) {
		tmp = t_1;
	} else if (z <= 1.02e-128) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.4e+64) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.25e+95:
		tmp = t
	elif z <= 1.65e-168:
		tmp = t_1
	elif z <= 1.02e-128:
		tmp = t * (y / (a - z))
	elif z <= 2.4e+64:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.25e+95)
		tmp = t;
	elseif (z <= 1.65e-168)
		tmp = t_1;
	elseif (z <= 1.02e-128)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.4e+64)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.25e+95)
		tmp = t;
	elseif (z <= 1.65e-168)
		tmp = t_1;
	elseif (z <= 1.02e-128)
		tmp = t * (y / (a - z));
	elseif (z <= 2.4e+64)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+95], t, If[LessEqual[z, 1.65e-168], t$95$1, If[LessEqual[z, 1.02e-128], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+64], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25000000000000006e95 or 2.39999999999999999e64 < z

   1. Initial program 61.8%

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

   2. Taylor expanded in z around inf 54.5%

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

   if -1.25000000000000006e95 < z < 1.6500000000000001e-168 or 1.02e-128 < z < 2.39999999999999999e64

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 66.7%

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

   3. Taylor expanded in x around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. unsub-neg 59.2%

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

   5. Simplified 59.2%

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

   if 1.6500000000000001e-168 < z < 1.02e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. div-sub 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 99.8%

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

      4. associate-/r/ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 73.8%

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

      1. associate-*r/ 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 48.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -4.8e-9)
     t_2
     (if (<= a -1.8e-171)
       t_1
       (if (<= a 4.6e-304)
         (* x (/ (- y a) z))
         (if (<= a 2.25e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.8e-9) {
		tmp = t_2;
	} else if (a <= -1.8e-171) {
		tmp = t_1;
	} else if (a <= 4.6e-304) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.25e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-4.8d-9)) then
        tmp = t_2
    else if (a <= (-1.8d-171)) then
        tmp = t_1
    else if (a <= 4.6d-304) then
        tmp = x * ((y - a) / z)
    else if (a <= 2.25d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.8e-9) {
		tmp = t_2;
	} else if (a <= -1.8e-171) {
		tmp = t_1;
	} else if (a <= 4.6e-304) {
		tmp = x * ((y - a) / z);
	} else if (a <= 2.25e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -4.8e-9:
		tmp = t_2
	elif a <= -1.8e-171:
		tmp = t_1
	elif a <= 4.6e-304:
		tmp = x * ((y - a) / z)
	elif a <= 2.25e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -4.8e-9)
		tmp = t_2;
	elseif (a <= -1.8e-171)
		tmp = t_1;
	elseif (a <= 4.6e-304)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 2.25e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -4.8e-9)
		tmp = t_2;
	elseif (a <= -1.8e-171)
		tmp = t_1;
	elseif (a <= 4.6e-304)
		tmp = x * ((y - a) / z);
	elseif (a <= 2.25e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e-9], t$95$2, If[LessEqual[a, -1.8e-171], t$95$1, If[LessEqual[a, 4.6e-304], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8e-9 or 2.2500000000000001e29 < a

   1. Initial program 87.1%

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

   2. Taylor expanded in z around 0 62.5%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   5. Simplified 60.1%

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

   if -4.8e-9 < a < -1.80000000000000002e-171 or 4.5999999999999999e-304 < a < 2.2500000000000001e29

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. distribute-lft-out-- 73.1%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in t around inf 56.1%

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

   6. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   if -1.80000000000000002e-171 < a < 4.5999999999999999e-304

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. distribute-lft-out-- 84.4%

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

      3. div-sub 84.4%

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

      4. mul-1-neg 84.4%

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

      5. unsub-neg 84.4%

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

      6. distribute-rgt-out-- 84.4%

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

      7. associate-/l* 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.7%

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

      1. associate-*r/ 51.8%

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

   7. Simplified 51.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-171}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+29}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 12: 48.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z))))
   (if (<= a -2.8e-10)
     (* x (- 1.0 (/ y a)))
     (if (<= a -2.55e-173)
       t_1
       (if (<= a 4.6e-304)
         (* x (/ (- y a) z))
         (if (<= a 9.2e+28) t_1 (- x (/ x (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -2.8e-10) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.55e-173) {
		tmp = t_1;
	} else if (a <= 4.6e-304) {
		tmp = x * ((y - a) / z);
	} else if (a <= 9.2e+28) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    if (a <= (-2.8d-10)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-2.55d-173)) then
        tmp = t_1
    else if (a <= 4.6d-304) then
        tmp = x * ((y - a) / z)
    else if (a <= 9.2d+28) then
        tmp = t_1
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -2.8e-10) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.55e-173) {
		tmp = t_1;
	} else if (a <= 4.6e-304) {
		tmp = x * ((y - a) / z);
	} else if (a <= 9.2e+28) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	tmp = 0
	if a <= -2.8e-10:
		tmp = x * (1.0 - (y / a))
	elif a <= -2.55e-173:
		tmp = t_1
	elif a <= 4.6e-304:
		tmp = x * ((y - a) / z)
	elif a <= 9.2e+28:
		tmp = t_1
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	tmp = 0.0
	if (a <= -2.8e-10)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -2.55e-173)
		tmp = t_1;
	elseif (a <= 4.6e-304)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 9.2e+28)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	tmp = 0.0;
	if (a <= -2.8e-10)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -2.55e-173)
		tmp = t_1;
	elseif (a <= 4.6e-304)
		tmp = x * ((y - a) / z);
	elseif (a <= 9.2e+28)
		tmp = t_1;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-10], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-173], t$95$1, If[LessEqual[a, 4.6e-304], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+28], t$95$1, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.80000000000000015e-10

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -2.80000000000000015e-10 < a < -2.5499999999999999e-173 or 4.5999999999999999e-304 < a < 9.19999999999999935e28

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. distribute-lft-out-- 73.1%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in t around inf 56.1%

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

   6. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   if -2.5499999999999999e-173 < a < 4.5999999999999999e-304

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. distribute-lft-out-- 84.4%

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

      3. div-sub 84.4%

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

      4. mul-1-neg 84.4%

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

      5. unsub-neg 84.4%

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

      6. distribute-rgt-out-- 84.4%

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

      7. associate-/l* 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.7%

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

      1. associate-*r/ 51.8%

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

   7. Simplified 51.8%

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

   if 9.19999999999999935e28 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around 0 60.0%

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

   3. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+28}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 48.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-302}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z))))
   (if (<= a -3.1e-7)
     (* x (- 1.0 (/ y a)))
     (if (<= a -2.55e-173)
       t_1
       (if (<= a 2.8e-302)
         (/ (* x (- y a)) z)
         (if (<= a 5.8e+28) t_1 (- x (/ x (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -3.1e-7) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.55e-173) {
		tmp = t_1;
	} else if (a <= 2.8e-302) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 5.8e+28) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    if (a <= (-3.1d-7)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-2.55d-173)) then
        tmp = t_1
    else if (a <= 2.8d-302) then
        tmp = (x * (y - a)) / z
    else if (a <= 5.8d+28) then
        tmp = t_1
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -3.1e-7) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -2.55e-173) {
		tmp = t_1;
	} else if (a <= 2.8e-302) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 5.8e+28) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	tmp = 0
	if a <= -3.1e-7:
		tmp = x * (1.0 - (y / a))
	elif a <= -2.55e-173:
		tmp = t_1
	elif a <= 2.8e-302:
		tmp = (x * (y - a)) / z
	elif a <= 5.8e+28:
		tmp = t_1
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	tmp = 0.0
	if (a <= -3.1e-7)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -2.55e-173)
		tmp = t_1;
	elseif (a <= 2.8e-302)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 5.8e+28)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	tmp = 0.0;
	if (a <= -3.1e-7)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -2.55e-173)
		tmp = t_1;
	elseif (a <= 2.8e-302)
		tmp = (x * (y - a)) / z;
	elseif (a <= 5.8e+28)
		tmp = t_1;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e-7], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-173], t$95$1, If[LessEqual[a, 2.8e-302], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5.8e+28], t$95$1, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.1e-7

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -3.1e-7 < a < -2.5499999999999999e-173 or 2.8e-302 < a < 5.8000000000000002e28

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. distribute-lft-out-- 73.1%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in t around inf 56.1%

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

   6. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   if -2.5499999999999999e-173 < a < 2.8e-302

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 84.4%

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

      1. associate--l+ 84.4%

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

      2. distribute-lft-out-- 84.4%

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

      3. div-sub 84.4%

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

      4. mul-1-neg 84.4%

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

      5. unsub-neg 84.4%

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

      6. distribute-rgt-out-- 84.4%

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

      7. associate-/l* 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.7%

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

   if 5.8000000000000002e28 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around 0 60.0%

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

   3. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-173}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-302}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+28}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 14: 50.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot t}{z}\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y t) z))))
   (if (<= a -5.3e-8)
     (* x (- 1.0 (/ y a)))
     (if (<= a -7.3e-168)
       t_1
       (if (<= a 3.7e-217)
         (* y (/ (- x t) z))
         (if (<= a 2.3e+29) t_1 (- x (/ x (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -5.3e-8) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -7.3e-168) {
		tmp = t_1;
	} else if (a <= 3.7e-217) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.3e+29) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y * t) / z)
    if (a <= (-5.3d-8)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-7.3d-168)) then
        tmp = t_1
    else if (a <= 3.7d-217) then
        tmp = y * ((x - t) / z)
    else if (a <= 2.3d+29) then
        tmp = t_1
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * t) / z);
	double tmp;
	if (a <= -5.3e-8) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -7.3e-168) {
		tmp = t_1;
	} else if (a <= 3.7e-217) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.3e+29) {
		tmp = t_1;
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * t) / z)
	tmp = 0
	if a <= -5.3e-8:
		tmp = x * (1.0 - (y / a))
	elif a <= -7.3e-168:
		tmp = t_1
	elif a <= 3.7e-217:
		tmp = y * ((x - t) / z)
	elif a <= 2.3e+29:
		tmp = t_1
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * t) / z))
	tmp = 0.0
	if (a <= -5.3e-8)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -7.3e-168)
		tmp = t_1;
	elseif (a <= 3.7e-217)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 2.3e+29)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * t) / z);
	tmp = 0.0;
	if (a <= -5.3e-8)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -7.3e-168)
		tmp = t_1;
	elseif (a <= 3.7e-217)
		tmp = y * ((x - t) / z);
	elseif (a <= 2.3e+29)
		tmp = t_1;
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e-8], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.3e-168], t$95$1, If[LessEqual[a, 3.7e-217], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+29], t$95$1, N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.2999999999999998e-8

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -5.2999999999999998e-8 < a < -7.3e-168 or 3.6999999999999996e-217 < a < 2.3000000000000001e29

   1. Initial program 70.5%

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

   2. Taylor expanded in z around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. distribute-lft-out-- 69.9%

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

      3. div-sub 71.0%

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

      4. mul-1-neg 71.0%

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

      5. unsub-neg 71.0%

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

      6. distribute-rgt-out-- 71.0%

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

      7. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in t around inf 56.3%

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

   6. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   if -7.3e-168 < a < 3.6999999999999996e-217

   1. Initial program 81.0%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. distribute-lft-out-- 87.0%

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

      3. div-sub 87.0%

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

      4. mul-1-neg 87.0%

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

      5. unsub-neg 87.0%

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

      6. distribute-rgt-out-- 87.0%

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

      7. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around -inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-*r/ 67.9%

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

      3. *-commutative 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

   7. Simplified 67.9%

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

   if 2.3000000000000001e29 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around 0 60.0%

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

   3. Taylor expanded in t around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 57.0%

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

   5. Simplified 57.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -7.3 \cdot 10^{-168}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+29}:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 15: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ x z)))))
   (if (<= z -8.5e+61)
     t_1
     (if (<= z 3e+64)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 3.4e+135) (* (- y z) (/ t (- a z))) 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 <= -8.5e+61) {
		tmp = t_1;
	} else if (z <= 3e+64) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.4e+135) {
		tmp = (y - z) * (t / (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 = t + (y * (x / z))
    if (z <= (-8.5d+61)) then
        tmp = t_1
    else if (z <= 3d+64) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 3.4d+135) then
        tmp = (y - z) * (t / (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 = t + (y * (x / z));
	double tmp;
	if (z <= -8.5e+61) {
		tmp = t_1;
	} else if (z <= 3e+64) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 3.4e+135) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * (x / z))
	tmp = 0
	if z <= -8.5e+61:
		tmp = t_1
	elif z <= 3e+64:
		tmp = x + ((t - x) * (y / a))
	elif z <= 3.4e+135:
		tmp = (y - z) * (t / (a - z))
	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 <= -8.5e+61)
		tmp = t_1;
	elseif (z <= 3e+64)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 3.4e+135)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	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 <= -8.5e+61)
		tmp = t_1;
	elseif (z <= 3e+64)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 3.4e+135)
		tmp = (y - z) * (t / (a - z));
	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, -8.5e+61], t$95$1, If[LessEqual[z, 3e+64], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+135], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000035e61 or 3.4000000000000001e135 < z

   1. Initial program 56.7%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. associate--l+ 65.4%

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

      2. distribute-lft-out-- 65.4%

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

      3. div-sub 65.4%

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

      4. mul-1-neg 65.4%

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

      5. unsub-neg 65.4%

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

      6. distribute-rgt-out-- 65.7%

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

      7. associate-/l* 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in y around inf 79.4%

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

   6. Taylor expanded in t around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-*l/ 73.8%

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

      3. distribute-rgt-neg-in 73.8%

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

   8. Simplified 73.8%

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

   if -8.50000000000000035e61 < z < 3.0000000000000002e64

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 68.6%

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

      1. associate-/l* 72.5%

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

      2. associate-/r/ 73.6%

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

   4. Simplified 73.6%

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

   if 3.0000000000000002e64 < z < 3.4000000000000001e135

   1. Initial program 86.8%

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

   2. Taylor expanded in x around 0 63.1%

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

      1. associate-/l* 76.8%

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

      2. associate-/r/ 72.4%

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

   4. Simplified 72.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+61}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 16: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+76} \lor \neg \left(a \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e+76) (not (<= a 3.6e+28)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+76) || !(a <= 3.6e+28)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d+76)) .or. (.not. (a <= 3.6d+28))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e+76) || !(a <= 3.6e+28)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e+76) or not (a <= 3.6e+28):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e+76) || !(a <= 3.6e+28))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e+76) || ~((a <= 3.6e+28)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e+76], N[Not[LessEqual[a, 3.6e+28]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.9999999999999996e76 or 3.5999999999999999e28 < a

   1. Initial program 88.4%

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

   2. Taylor expanded in a around inf 70.6%

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

      1. associate-/l* 85.7%

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

      2. associate-/r/ 82.4%

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

   4. Simplified 82.4%

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

   if -5.9999999999999996e76 < a < 3.5999999999999999e28

   1. Initial program 74.3%

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

   2. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 73.3%

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

      4. mul-1-neg 73.3%

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

      5. unsub-neg 73.3%

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

      6. distribute-rgt-out-- 73.3%

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

      7. associate-/l* 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in y around inf 74.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+76} \lor \neg \left(a \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 17: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+75} \lor \neg \left(a \leq 1.15 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e+75) (not (<= a 1.15e+29)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e+75) || !(a <= 1.15e+29)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.5d+75)) .or. (.not. (a <= 1.15d+29))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e+75) || !(a <= 1.15e+29)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e+75) or not (a <= 1.15e+29):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e+75) || !(a <= 1.15e+29))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.5e+75) || ~((a <= 1.15e+29)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e+75], N[Not[LessEqual[a, 1.15e+29]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5000000000000001e75 or 1.1500000000000001e29 < a

   1. Initial program 88.4%

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

   2. Taylor expanded in a around inf 70.6%

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

      1. associate-/l* 85.7%

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

      2. associate-/r/ 82.4%

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

   4. Simplified 82.4%

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

   if -5.5000000000000001e75 < a < 1.1500000000000001e29

   1. Initial program 74.3%

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

   2. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. distribute-lft-out-- 72.6%

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

      3. div-sub 73.3%

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

      4. mul-1-neg 73.3%

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

      5. unsub-neg 73.3%

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

      6. distribute-rgt-out-- 73.3%

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

      7. associate-/l* 81.0%

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

   4. Simplified 81.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+75} \lor \neg \left(a \leq 1.15 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 18: 70.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-42} \lor \neg \left(a \leq 2.35 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e-42) (not (<= a 2.35e+29)))
   (+ x (* (- t x) (/ y a)))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-42) || !(a <= 2.35e+29)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.3d-42)) .or. (.not. (a <= 2.35d+29))) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-42) || !(a <= 2.35e+29)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e-42) or not (a <= 2.35e+29):
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e-42) || !(a <= 2.35e+29))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e-42) || ~((a <= 2.35e+29)))
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e-42], N[Not[LessEqual[a, 2.35e+29]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3000000000000002e-42 or 2.3500000000000001e29 < a

   1. Initial program 85.5%

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

   2. Taylor expanded in z around 0 62.2%

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

      1. associate-/l* 69.1%

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

      2. associate-/r/ 72.6%

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

   4. Simplified 72.6%

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

   if -3.3000000000000002e-42 < a < 2.3500000000000001e29

   1. Initial program 75.0%

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

   2. Taylor expanded in z around inf 76.6%

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

      1. associate--l+ 76.6%

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

      2. distribute-lft-out-- 76.6%

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

      3. div-sub 77.4%

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

      4. mul-1-neg 77.4%

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

      5. unsub-neg 77.4%

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

      6. distribute-rgt-out-- 77.4%

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

      7. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in y around inf 78.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-42} \lor \neg \left(a \leq 2.35 \cdot 10^{+29}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 19: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e+96)
   x
   (if (<= a -7.2e-172)
     t
     (if (<= a 3.25e-158) (/ x (/ z y)) (if (<= a 2.6e+38) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e+96) {
		tmp = x;
	} else if (a <= -7.2e-172) {
		tmp = t;
	} else if (a <= 3.25e-158) {
		tmp = x / (z / y);
	} else if (a <= 2.6e+38) {
		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 <= (-1.65d+96)) then
        tmp = x
    else if (a <= (-7.2d-172)) then
        tmp = t
    else if (a <= 3.25d-158) then
        tmp = x / (z / y)
    else if (a <= 2.6d+38) 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 <= -1.65e+96) {
		tmp = x;
	} else if (a <= -7.2e-172) {
		tmp = t;
	} else if (a <= 3.25e-158) {
		tmp = x / (z / y);
	} else if (a <= 2.6e+38) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e+96:
		tmp = x
	elif a <= -7.2e-172:
		tmp = t
	elif a <= 3.25e-158:
		tmp = x / (z / y)
	elif a <= 2.6e+38:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e+96)
		tmp = x;
	elseif (a <= -7.2e-172)
		tmp = t;
	elseif (a <= 3.25e-158)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.6e+38)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e+96)
		tmp = x;
	elseif (a <= -7.2e-172)
		tmp = t;
	elseif (a <= 3.25e-158)
		tmp = x / (z / y);
	elseif (a <= 2.6e+38)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e+96], x, If[LessEqual[a, -7.2e-172], t, If[LessEqual[a, 3.25e-158], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+38], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.64999999999999992e96 or 2.5999999999999999e38 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 48.9%

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

   if -1.64999999999999992e96 < a < -7.20000000000000029e-172 or 3.24999999999999986e-158 < a < 2.5999999999999999e38

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 41.8%

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

   if -7.20000000000000029e-172 < a < 3.24999999999999986e-158

   1. Initial program 80.9%

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

   2. Taylor expanded in z around inf 87.1%

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

      1. associate--l+ 87.1%

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

      2. distribute-lft-out-- 87.1%

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

      3. div-sub 87.1%

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

      4. mul-1-neg 87.1%

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

      5. unsub-neg 87.1%

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

      6. distribute-rgt-out-- 87.1%

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

      7. associate-/l* 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around -inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-*r/ 63.6%

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

      3. *-commutative 63.6%

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

      4. distribute-rgt-neg-in 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 43.6%

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

   10. Simplified 43.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e+95)
   x
   (if (<= a -7.8e-172)
     t
     (if (<= a 3.2e-217) (/ (* x y) z) (if (<= a 1e+37) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e+95) {
		tmp = x;
	} else if (a <= -7.8e-172) {
		tmp = t;
	} else if (a <= 3.2e-217) {
		tmp = (x * y) / z;
	} else if (a <= 1e+37) {
		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 <= (-8.8d+95)) then
        tmp = x
    else if (a <= (-7.8d-172)) then
        tmp = t
    else if (a <= 3.2d-217) then
        tmp = (x * y) / z
    else if (a <= 1d+37) 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 <= -8.8e+95) {
		tmp = x;
	} else if (a <= -7.8e-172) {
		tmp = t;
	} else if (a <= 3.2e-217) {
		tmp = (x * y) / z;
	} else if (a <= 1e+37) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e+95:
		tmp = x
	elif a <= -7.8e-172:
		tmp = t
	elif a <= 3.2e-217:
		tmp = (x * y) / z
	elif a <= 1e+37:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e+95)
		tmp = x;
	elseif (a <= -7.8e-172)
		tmp = t;
	elseif (a <= 3.2e-217)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 1e+37)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e+95)
		tmp = x;
	elseif (a <= -7.8e-172)
		tmp = t;
	elseif (a <= 3.2e-217)
		tmp = (x * y) / z;
	elseif (a <= 1e+37)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e+95], x, If[LessEqual[a, -7.8e-172], t, If[LessEqual[a, 3.2e-217], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1e+37], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.7999999999999996e95 or 9.99999999999999954e36 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 48.9%

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

   if -8.7999999999999996e95 < a < -7.79999999999999946e-172 or 3.2000000000000001e-217 < a < 9.99999999999999954e36

   1. Initial program 72.2%

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

   2. Taylor expanded in z around inf 40.7%

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

   if -7.79999999999999946e-172 < a < 3.2000000000000001e-217

   1. Initial program 81.0%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. distribute-lft-out-- 87.0%

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

      3. div-sub 87.0%

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

      4. mul-1-neg 87.0%

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

      5. unsub-neg 87.0%

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

      6. distribute-rgt-out-- 87.0%

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

      7. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   5. Taylor expanded in y around -inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-*r/ 67.9%

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

      3. *-commutative 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in t around 0 47.9%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 10^{+37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 38.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.12e+107) x (if (<= a 7e+32) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e+107) {
		tmp = x;
	} else if (a <= 7e+32) {
		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 <= (-1.12d+107)) then
        tmp = x
    else if (a <= 7d+32) 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 <= -1.12e+107) {
		tmp = x;
	} else if (a <= 7e+32) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.12e+107:
		tmp = x
	elif a <= 7e+32:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.12e+107)
		tmp = x;
	elseif (a <= 7e+32)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.12e+107)
		tmp = x;
	elseif (a <= 7e+32)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.12e+107], x, If[LessEqual[a, 7e+32], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.11999999999999997e107 or 7.0000000000000002e32 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 48.9%

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

   if -1.11999999999999997e107 < a < 7.0000000000000002e32

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 34.9%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 24.4% 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 80.3%

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

2. Taylor expanded in z around inf 25.5%

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

3. Final simplification 25.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023336 
(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)))))