Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.7% → 90.4%

Time: 23.3s

Alternatives: 22

Speedup: 0.6×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.7% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ t_2 := x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- x t) (- z a)) (- z y))))
        (t_2 (+ x (/ (* (- t x) (- z y)) (- z a)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-243)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 2e+269) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = x + (((t - x) * (z - y)) / (z - a));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-243) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+269) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = x + (((t - x) * (z - y)) / (z - a));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-243) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+269) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((x - t) / (z - a)) * (z - y))
	t_2 = x + (((t - x) * (z - y)) / (z - a))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-243:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 2e+269:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(z - y)))
	t_2 = Float64(x + Float64(Float64(Float64(t - x) * Float64(z - y)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-243)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 2e+269)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((x - t) / (z - a)) * (z - y));
	t_2 = x + (((t - x) * (z - y)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-243)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 2e+269)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(t - x), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-243], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+269], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 2.0000000000000001e269 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 39.4%

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

      1. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.99999999999999999e-243 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.0000000000000001e269

   1. Initial program 98.6%

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

   if -1.99999999999999999e-243 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.6%

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

      1. associate-/l* 4.6%

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

   3. Simplified 4.6%

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

   5. Taylor expanded in y around 0 4.6%

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

      1. +-commutative 4.6%

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

      2. div-sub 4.6%

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

      3. mul-1-neg 4.6%

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

      4. associate-/l* 4.6%

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

      5. distribute-lft-neg-out 4.6%

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

      6. distribute-rgt-out 4.6%

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

      7. sub-neg 4.6%

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

      8. associate-/r/ 4.7%

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

   7. Simplified 4.7%

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

   8. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a} \leq -\infty:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a} \leq -2 \cdot 10^{-243}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a} \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot \left(z - y\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -8.3 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -8.3e+74)
     t
     (if (<= z -1.65e-264)
       x
       (if (<= z 4.9e-266)
         t_1
         (if (<= z 6.2e-197)
           x
           (if (<= z 3.6e-144)
             t_1
             (if (<= z 2.8e-27) x (if (<= z 4.8e+155) (* x (/ y z)) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -8.3e+74) {
		tmp = t;
	} else if (z <= -1.65e-264) {
		tmp = x;
	} else if (z <= 4.9e-266) {
		tmp = t_1;
	} else if (z <= 6.2e-197) {
		tmp = x;
	} else if (z <= 3.6e-144) {
		tmp = t_1;
	} else if (z <= 2.8e-27) {
		tmp = x;
	} else if (z <= 4.8e+155) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-8.3d+74)) then
        tmp = t
    else if (z <= (-1.65d-264)) then
        tmp = x
    else if (z <= 4.9d-266) then
        tmp = t_1
    else if (z <= 6.2d-197) then
        tmp = x
    else if (z <= 3.6d-144) then
        tmp = t_1
    else if (z <= 2.8d-27) then
        tmp = x
    else if (z <= 4.8d+155) then
        tmp = x * (y / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -8.3e+74) {
		tmp = t;
	} else if (z <= -1.65e-264) {
		tmp = x;
	} else if (z <= 4.9e-266) {
		tmp = t_1;
	} else if (z <= 6.2e-197) {
		tmp = x;
	} else if (z <= 3.6e-144) {
		tmp = t_1;
	} else if (z <= 2.8e-27) {
		tmp = x;
	} else if (z <= 4.8e+155) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -8.3e+74:
		tmp = t
	elif z <= -1.65e-264:
		tmp = x
	elif z <= 4.9e-266:
		tmp = t_1
	elif z <= 6.2e-197:
		tmp = x
	elif z <= 3.6e-144:
		tmp = t_1
	elif z <= 2.8e-27:
		tmp = x
	elif z <= 4.8e+155:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -8.3e+74)
		tmp = t;
	elseif (z <= -1.65e-264)
		tmp = x;
	elseif (z <= 4.9e-266)
		tmp = t_1;
	elseif (z <= 6.2e-197)
		tmp = x;
	elseif (z <= 3.6e-144)
		tmp = t_1;
	elseif (z <= 2.8e-27)
		tmp = x;
	elseif (z <= 4.8e+155)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -8.3e+74)
		tmp = t;
	elseif (z <= -1.65e-264)
		tmp = x;
	elseif (z <= 4.9e-266)
		tmp = t_1;
	elseif (z <= 6.2e-197)
		tmp = x;
	elseif (z <= 3.6e-144)
		tmp = t_1;
	elseif (z <= 2.8e-27)
		tmp = x;
	elseif (z <= 4.8e+155)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.3e+74], t, If[LessEqual[z, -1.65e-264], x, If[LessEqual[z, 4.9e-266], t$95$1, If[LessEqual[z, 6.2e-197], x, If[LessEqual[z, 3.6e-144], t$95$1, If[LessEqual[z, 2.8e-27], x, If[LessEqual[z, 4.8e+155], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2999999999999998e74 or 4.80000000000000042e155 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -8.2999999999999998e74 < z < -1.65000000000000006e-264 or 4.9000000000000003e-266 < z < 6.20000000000000057e-197 or 3.6e-144 < z < 2.8e-27

   1. Initial program 91.3%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -1.65000000000000006e-264 < z < 4.9000000000000003e-266 or 6.20000000000000057e-197 < z < 3.6e-144

   1. Initial program 92.5%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in y around inf 74.6%

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

      1. div-sub 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in t around inf 51.6%

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

      1. associate-/l* 58.8%

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

   10. Simplified 58.8%

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

   if 2.8e-27 < z < 4.80000000000000042e155

   1. Initial program 64.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in a around 0 38.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+74}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-266}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -2.7e+78)
     t
     (if (<= z 7e-291)
       t_1
       (if (<= z 1.95e-268)
         (* y (/ (- t x) a))
         (if (<= z 2.8e-180)
           t_1
           (if (<= z 6.5e-11)
             (* x (- 1.0 (/ y a)))
             (if (<= z 5.6e+153) (* x (/ (- y a) z)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -2.7e+78) {
		tmp = t;
	} else if (z <= 7e-291) {
		tmp = t_1;
	} else if (z <= 1.95e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.8e-180) {
		tmp = t_1;
	} else if (z <= 6.5e-11) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.6e+153) {
		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 + (t * (y / a))
    if (z <= (-2.7d+78)) then
        tmp = t
    else if (z <= 7d-291) then
        tmp = t_1
    else if (z <= 1.95d-268) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.8d-180) then
        tmp = t_1
    else if (z <= 6.5d-11) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.6d+153) 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 + (t * (y / a));
	double tmp;
	if (z <= -2.7e+78) {
		tmp = t;
	} else if (z <= 7e-291) {
		tmp = t_1;
	} else if (z <= 1.95e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.8e-180) {
		tmp = t_1;
	} else if (z <= 6.5e-11) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.6e+153) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -2.7e+78:
		tmp = t
	elif z <= 7e-291:
		tmp = t_1
	elif z <= 1.95e-268:
		tmp = y * ((t - x) / a)
	elif z <= 2.8e-180:
		tmp = t_1
	elif z <= 6.5e-11:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.6e+153:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -2.7e+78)
		tmp = t;
	elseif (z <= 7e-291)
		tmp = t_1;
	elseif (z <= 1.95e-268)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.8e-180)
		tmp = t_1;
	elseif (z <= 6.5e-11)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.6e+153)
		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 + (t * (y / a));
	tmp = 0.0;
	if (z <= -2.7e+78)
		tmp = t;
	elseif (z <= 7e-291)
		tmp = t_1;
	elseif (z <= 1.95e-268)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.8e-180)
		tmp = t_1;
	elseif (z <= 6.5e-11)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.6e+153)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+78], t, If[LessEqual[z, 7e-291], t$95$1, If[LessEqual[z, 1.95e-268], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-180], t$95$1, If[LessEqual[z, 6.5e-11], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+153], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.70000000000000004e78 or 5.5999999999999997e153 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -2.70000000000000004e78 < z < 6.99999999999999991e-291 or 1.9499999999999999e-268 < z < 2.79999999999999997e-180

   1. Initial program 93.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. div-sub 89.5%

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

      3. mul-1-neg 89.5%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-out 86.5%

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

      6. distribute-rgt-out 91.3%

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

      7. sub-neg 91.3%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 69.9%

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

   9. Taylor expanded in t around inf 60.0%

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

       1. associate-*r/ 62.5%

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

   11. Simplified 62.5%

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

   if 6.99999999999999991e-291 < z < 1.9499999999999999e-268

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 99.8%

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

   if 2.79999999999999997e-180 < z < 6.49999999999999953e-11

   1. Initial program 82.6%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in z around 0 60.9%

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

   if 6.49999999999999953e-11 < z < 5.5999999999999997e153

   1. Initial program 64.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around inf 47.4%

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

      1. mul-1-neg 47.4%

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

      2. unsub-neg 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in z around inf 44.8%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

      3. +-commutative 44.8%

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

      4. distribute-lft-in 44.8%

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

      5. neg-mul-1 44.8%

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

      6. remove-double-neg 44.8%

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

      7. mul-1-neg 44.8%

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

      8. sub-neg 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-291}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-180}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -2e+77)
     t
     (if (<= z 7.5e-291)
       t_1
       (if (<= z 3.6e-268)
         (* y (/ (- t x) a))
         (if (<= z 1.6e-180)
           t_1
           (if (<= z 8.8e-8)
             (* x (- 1.0 (/ y a)))
             (if (<= z 5.5e+155) (* y (/ (- x t) z)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -2e+77) {
		tmp = t;
	} else if (z <= 7.5e-291) {
		tmp = t_1;
	} else if (z <= 3.6e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.6e-180) {
		tmp = t_1;
	} else if (z <= 8.8e-8) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.5e+155) {
		tmp = y * ((x - t) / 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 + (t * (y / a))
    if (z <= (-2d+77)) then
        tmp = t
    else if (z <= 7.5d-291) then
        tmp = t_1
    else if (z <= 3.6d-268) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.6d-180) then
        tmp = t_1
    else if (z <= 8.8d-8) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.5d+155) then
        tmp = y * ((x - t) / 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 + (t * (y / a));
	double tmp;
	if (z <= -2e+77) {
		tmp = t;
	} else if (z <= 7.5e-291) {
		tmp = t_1;
	} else if (z <= 3.6e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.6e-180) {
		tmp = t_1;
	} else if (z <= 8.8e-8) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.5e+155) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -2e+77:
		tmp = t
	elif z <= 7.5e-291:
		tmp = t_1
	elif z <= 3.6e-268:
		tmp = y * ((t - x) / a)
	elif z <= 1.6e-180:
		tmp = t_1
	elif z <= 8.8e-8:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.5e+155:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -2e+77)
		tmp = t;
	elseif (z <= 7.5e-291)
		tmp = t_1;
	elseif (z <= 3.6e-268)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.6e-180)
		tmp = t_1;
	elseif (z <= 8.8e-8)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.5e+155)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -2e+77)
		tmp = t;
	elseif (z <= 7.5e-291)
		tmp = t_1;
	elseif (z <= 3.6e-268)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.6e-180)
		tmp = t_1;
	elseif (z <= 8.8e-8)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.5e+155)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+77], t, If[LessEqual[z, 7.5e-291], t$95$1, If[LessEqual[z, 3.6e-268], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-180], t$95$1, If[LessEqual[z, 8.8e-8], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+155], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999997e77 or 5.5000000000000001e155 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -1.99999999999999997e77 < z < 7.49999999999999981e-291 or 3.6000000000000001e-268 < z < 1.60000000000000008e-180

   1. Initial program 93.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. div-sub 89.5%

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

      3. mul-1-neg 89.5%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-out 86.5%

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

      6. distribute-rgt-out 91.3%

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

      7. sub-neg 91.3%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 69.9%

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

   9. Taylor expanded in t around inf 60.0%

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

       1. associate-*r/ 62.5%

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

   11. Simplified 62.5%

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

   if 7.49999999999999981e-291 < z < 3.6000000000000001e-268

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 99.8%

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

   if 1.60000000000000008e-180 < z < 8.7999999999999994e-8

   1. Initial program 82.6%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in z around 0 60.9%

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

   if 8.7999999999999994e-8 < z < 5.5000000000000001e155

   1. Initial program 64.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in a around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-neg-frac2 54.3%

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

   10. Simplified 54.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-291}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-180}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -3.1e+75)
     t
     (if (<= z 7.2e-291)
       t_1
       (if (<= z 1.9e-268)
         (* y (/ (- t x) a))
         (if (<= z 3.5e-180)
           t_1
           (if (<= z 6e-11)
             (- x (* x (/ y a)))
             (if (<= z 9.5e+153) (* y (/ (- x t) z)) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3.1e+75) {
		tmp = t;
	} else if (z <= 7.2e-291) {
		tmp = t_1;
	} else if (z <= 1.9e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.5e-180) {
		tmp = t_1;
	} else if (z <= 6e-11) {
		tmp = x - (x * (y / a));
	} else if (z <= 9.5e+153) {
		tmp = y * ((x - t) / 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 + (t * (y / a))
    if (z <= (-3.1d+75)) then
        tmp = t
    else if (z <= 7.2d-291) then
        tmp = t_1
    else if (z <= 1.9d-268) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.5d-180) then
        tmp = t_1
    else if (z <= 6d-11) then
        tmp = x - (x * (y / a))
    else if (z <= 9.5d+153) then
        tmp = y * ((x - t) / 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 + (t * (y / a));
	double tmp;
	if (z <= -3.1e+75) {
		tmp = t;
	} else if (z <= 7.2e-291) {
		tmp = t_1;
	} else if (z <= 1.9e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.5e-180) {
		tmp = t_1;
	} else if (z <= 6e-11) {
		tmp = x - (x * (y / a));
	} else if (z <= 9.5e+153) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -3.1e+75:
		tmp = t
	elif z <= 7.2e-291:
		tmp = t_1
	elif z <= 1.9e-268:
		tmp = y * ((t - x) / a)
	elif z <= 3.5e-180:
		tmp = t_1
	elif z <= 6e-11:
		tmp = x - (x * (y / a))
	elif z <= 9.5e+153:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -3.1e+75)
		tmp = t;
	elseif (z <= 7.2e-291)
		tmp = t_1;
	elseif (z <= 1.9e-268)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.5e-180)
		tmp = t_1;
	elseif (z <= 6e-11)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 9.5e+153)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -3.1e+75)
		tmp = t;
	elseif (z <= 7.2e-291)
		tmp = t_1;
	elseif (z <= 1.9e-268)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.5e-180)
		tmp = t_1;
	elseif (z <= 6e-11)
		tmp = x - (x * (y / a));
	elseif (z <= 9.5e+153)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+75], t, If[LessEqual[z, 7.2e-291], t$95$1, If[LessEqual[z, 1.9e-268], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-180], t$95$1, If[LessEqual[z, 6e-11], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+153], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1000000000000001e75 or 9.4999999999999995e153 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -3.1000000000000001e75 < z < 7.1999999999999993e-291 or 1.9000000000000001e-268 < z < 3.5000000000000001e-180

   1. Initial program 93.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. div-sub 89.5%

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

      3. mul-1-neg 89.5%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-out 86.5%

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

      6. distribute-rgt-out 91.3%

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

      7. sub-neg 91.3%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 69.9%

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

   9. Taylor expanded in t around inf 60.0%

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

       1. associate-*r/ 62.5%

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

   11. Simplified 62.5%

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

   if 7.1999999999999993e-291 < z < 1.9000000000000001e-268

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 99.8%

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

   if 3.5000000000000001e-180 < z < 6e-11

   1. Initial program 82.6%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. div-sub 94.0%

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

      3. mul-1-neg 94.0%

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

      4. associate-/l* 91.0%

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

      5. distribute-lft-neg-out 91.0%

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

      6. distribute-rgt-out 94.3%

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

      7. sub-neg 94.3%

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

      8. associate-/r/ 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in z around 0 68.6%

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

   9. Taylor expanded in t around 0 49.7%

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

       1. mul-1-neg 49.7%

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

       2. associate-*r/ 60.9%

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

       3. distribute-lft-neg-in 60.9%

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

   11. Simplified 60.9%

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

   if 6e-11 < z < 9.4999999999999995e153

   1. Initial program 64.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in a around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-neg-frac2 54.3%

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

   10. Simplified 54.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-291}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-180}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-11}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -6.8e+79)
     t
     (if (<= z 9e-291)
       t_1
       (if (<= z 2.1e-268)
         (* y (/ (- t x) a))
         (if (<= z 5.2e-191)
           t_1
           (if (<= z 5.7e-12)
             (- x (* x (/ y a)))
             (if (<= z 6.5e+155) (/ y (/ z (- x t))) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.8e+79) {
		tmp = t;
	} else if (z <= 9e-291) {
		tmp = t_1;
	} else if (z <= 2.1e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 5.2e-191) {
		tmp = t_1;
	} else if (z <= 5.7e-12) {
		tmp = x - (x * (y / a));
	} else if (z <= 6.5e+155) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-6.8d+79)) then
        tmp = t
    else if (z <= 9d-291) then
        tmp = t_1
    else if (z <= 2.1d-268) then
        tmp = y * ((t - x) / a)
    else if (z <= 5.2d-191) then
        tmp = t_1
    else if (z <= 5.7d-12) then
        tmp = x - (x * (y / a))
    else if (z <= 6.5d+155) then
        tmp = y / (z / (x - t))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.8e+79) {
		tmp = t;
	} else if (z <= 9e-291) {
		tmp = t_1;
	} else if (z <= 2.1e-268) {
		tmp = y * ((t - x) / a);
	} else if (z <= 5.2e-191) {
		tmp = t_1;
	} else if (z <= 5.7e-12) {
		tmp = x - (x * (y / a));
	} else if (z <= 6.5e+155) {
		tmp = y / (z / (x - t));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -6.8e+79:
		tmp = t
	elif z <= 9e-291:
		tmp = t_1
	elif z <= 2.1e-268:
		tmp = y * ((t - x) / a)
	elif z <= 5.2e-191:
		tmp = t_1
	elif z <= 5.7e-12:
		tmp = x - (x * (y / a))
	elif z <= 6.5e+155:
		tmp = y / (z / (x - t))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -6.8e+79)
		tmp = t;
	elseif (z <= 9e-291)
		tmp = t_1;
	elseif (z <= 2.1e-268)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 5.2e-191)
		tmp = t_1;
	elseif (z <= 5.7e-12)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 6.5e+155)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -6.8e+79)
		tmp = t;
	elseif (z <= 9e-291)
		tmp = t_1;
	elseif (z <= 2.1e-268)
		tmp = y * ((t - x) / a);
	elseif (z <= 5.2e-191)
		tmp = t_1;
	elseif (z <= 5.7e-12)
		tmp = x - (x * (y / a));
	elseif (z <= 6.5e+155)
		tmp = y / (z / (x - t));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+79], t, If[LessEqual[z, 9e-291], t$95$1, If[LessEqual[z, 2.1e-268], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-191], t$95$1, If[LessEqual[z, 5.7e-12], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+155], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.80000000000000063e79 or 6.50000000000000046e155 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -6.80000000000000063e79 < z < 8.99999999999999948e-291 or 2.09999999999999998e-268 < z < 5.19999999999999972e-191

   1. Initial program 93.0%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. div-sub 89.5%

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

      3. mul-1-neg 89.5%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-out 86.5%

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

      6. distribute-rgt-out 91.3%

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

      7. sub-neg 91.3%

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

      8. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 69.9%

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

   9. Taylor expanded in t around inf 60.0%

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

       1. associate-*r/ 62.5%

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

   11. Simplified 62.5%

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

   if 8.99999999999999948e-291 < z < 2.09999999999999998e-268

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 99.8%

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

   if 5.19999999999999972e-191 < z < 5.7000000000000003e-12

   1. Initial program 82.6%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. div-sub 94.0%

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

      3. mul-1-neg 94.0%

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

      4. associate-/l* 91.0%

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

      5. distribute-lft-neg-out 91.0%

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

      6. distribute-rgt-out 94.3%

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

      7. sub-neg 94.3%

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

      8. associate-/r/ 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in z around 0 68.6%

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

   9. Taylor expanded in t around 0 49.7%

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

       1. mul-1-neg 49.7%

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

       2. associate-*r/ 60.9%

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

       3. distribute-lft-neg-in 60.9%

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

   11. Simplified 60.9%

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

   if 5.7000000000000003e-12 < z < 6.50000000000000046e155

   1. Initial program 64.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   7. Simplified 60.1%

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

      1. clear-num 57.7%

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

      2. div-inv 57.8%

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

   9. Applied egg-rr 57.8%

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

   10. Taylor expanded in a around 0 54.4%

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

       1. neg-mul-1 54.4%

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

       2. distribute-neg-frac2 54.4%

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

   12. Simplified 54.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-191}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-12}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.00055:\\ \;\;\;\;x + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))))
   (if (<= z -3.05e+74)
     t_1
     (if (<= z -0.00055)
       (+ x (/ (- x t) (/ z y)))
       (if (<= z -1.55e-33)
         t_1
         (if (<= z 2.5e-27)
           (+ x (/ (- t x) (/ a y)))
           (if (<= z 5.6e+153) (* y (/ (- x t) (- z a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -3.05e+74) {
		tmp = t_1;
	} else if (z <= -0.00055) {
		tmp = x + ((x - t) / (z / y));
	} else if (z <= -1.55e-33) {
		tmp = t_1;
	} else if (z <= 2.5e-27) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 5.6e+153) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    if (z <= (-3.05d+74)) then
        tmp = t_1
    else if (z <= (-0.00055d0)) then
        tmp = x + ((x - t) / (z / y))
    else if (z <= (-1.55d-33)) then
        tmp = t_1
    else if (z <= 2.5d-27) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 5.6d+153) then
        tmp = y * ((x - t) / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -3.05e+74) {
		tmp = t_1;
	} else if (z <= -0.00055) {
		tmp = x + ((x - t) / (z / y));
	} else if (z <= -1.55e-33) {
		tmp = t_1;
	} else if (z <= 2.5e-27) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 5.6e+153) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	tmp = 0
	if z <= -3.05e+74:
		tmp = t_1
	elif z <= -0.00055:
		tmp = x + ((x - t) / (z / y))
	elif z <= -1.55e-33:
		tmp = t_1
	elif z <= 2.5e-27:
		tmp = x + ((t - x) / (a / y))
	elif z <= 5.6e+153:
		tmp = y * ((x - t) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.05e+74)
		tmp = t_1;
	elseif (z <= -0.00055)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(z / y)));
	elseif (z <= -1.55e-33)
		tmp = t_1;
	elseif (z <= 2.5e-27)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 5.6e+153)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (z <= -3.05e+74)
		tmp = t_1;
	elseif (z <= -0.00055)
		tmp = x + ((x - t) / (z / y));
	elseif (z <= -1.55e-33)
		tmp = t_1;
	elseif (z <= 2.5e-27)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 5.6e+153)
		tmp = y * ((x - t) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.05e+74], t$95$1, If[LessEqual[z, -0.00055], N[(x + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-33], t$95$1, If[LessEqual[z, 2.5e-27], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+153], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0499999999999998e74 or -5.50000000000000033e-4 < z < -1.54999999999999998e-33 or 5.5999999999999997e153 < z

   1. Initial program 44.1%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   if -3.0499999999999998e74 < z < -5.50000000000000033e-4

   1. Initial program 76.5%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. div-sub 81.7%

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

      3. mul-1-neg 81.7%

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

      4. associate-/l* 93.9%

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

      5. distribute-lft-neg-out 93.9%

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

      6. distribute-rgt-out 93.9%

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

      7. sub-neg 93.9%

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

      8. associate-/r/ 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in y around inf 76.1%

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

   9. Taylor expanded in a around 0 64.0%

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

       1. neg-mul-1 64.0%

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

       2. distribute-neg-frac2 64.0%

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

   11. Simplified 64.0%

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

   if -1.54999999999999998e-33 < z < 2.5000000000000001e-27

   1. Initial program 93.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. div-sub 92.8%

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

      3. mul-1-neg 92.8%

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

      4. associate-/l* 87.7%

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

      5. distribute-lft-neg-out 87.7%

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

      6. distribute-rgt-out 92.9%

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

      7. sub-neg 92.9%

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

      8. associate-/r/ 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in z around 0 78.2%

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

   if 2.5000000000000001e-27 < z < 5.5999999999999997e153

   1. Initial program 64.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. div-sub 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq -0.00055:\\ \;\;\;\;x + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ t_2 := t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-258}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- x t) (- z a)) (- z y))))
        (t_2 (+ t (* (/ (- x t) z) (- y a)))))
   (if (<= z -1.25e+218)
     t_2
     (if (<= z -5e-232)
       t_1
       (if (<= z 4e-258)
         (+ x (/ (- x t) (/ (- z a) y)))
         (if (<= z 2.6e+121) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = t + (((x - t) / z) * (y - a));
	double tmp;
	if (z <= -1.25e+218) {
		tmp = t_2;
	} else if (z <= -5e-232) {
		tmp = t_1;
	} else if (z <= 4e-258) {
		tmp = x + ((x - t) / ((z - a) / y));
	} else if (z <= 2.6e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (((x - t) / (z - a)) * (z - y))
    t_2 = t + (((x - t) / z) * (y - a))
    if (z <= (-1.25d+218)) then
        tmp = t_2
    else if (z <= (-5d-232)) then
        tmp = t_1
    else if (z <= 4d-258) then
        tmp = x + ((x - t) / ((z - a) / y))
    else if (z <= 2.6d+121) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((x - t) / (z - a)) * (z - y));
	double t_2 = t + (((x - t) / z) * (y - a));
	double tmp;
	if (z <= -1.25e+218) {
		tmp = t_2;
	} else if (z <= -5e-232) {
		tmp = t_1;
	} else if (z <= 4e-258) {
		tmp = x + ((x - t) / ((z - a) / y));
	} else if (z <= 2.6e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((x - t) / (z - a)) * (z - y))
	t_2 = t + (((x - t) / z) * (y - a))
	tmp = 0
	if z <= -1.25e+218:
		tmp = t_2
	elif z <= -5e-232:
		tmp = t_1
	elif z <= 4e-258:
		tmp = x + ((x - t) / ((z - a) / y))
	elif z <= 2.6e+121:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(x - t) / Float64(z - a)) * Float64(z - y)))
	t_2 = Float64(t + Float64(Float64(Float64(x - t) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -1.25e+218)
		tmp = t_2;
	elseif (z <= -5e-232)
		tmp = t_1;
	elseif (z <= 4e-258)
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(z - a) / y)));
	elseif (z <= 2.6e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((x - t) / (z - a)) * (z - y));
	t_2 = t + (((x - t) / z) * (y - a));
	tmp = 0.0;
	if (z <= -1.25e+218)
		tmp = t_2;
	elseif (z <= -5e-232)
		tmp = t_1;
	elseif (z <= 4e-258)
		tmp = x + ((x - t) / ((z - a) / y));
	elseif (z <= 2.6e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+218], t$95$2, If[LessEqual[z, -5e-232], t$95$1, If[LessEqual[z, 4e-258], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+121], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999996e218 or 2.5999999999999999e121 < z

   1. Initial program 31.4%

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

      1. associate-/l* 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. div-sub 68.0%

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

      7. associate-/l* 82.7%

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

      8. associate-/l* 92.5%

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

      9. distribute-rgt-out-- 92.5%

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

   7. Simplified 92.5%

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

   if -1.24999999999999996e218 < z < -4.9999999999999999e-232 or 3.99999999999999982e-258 < z < 2.5999999999999999e121

   1. Initial program 83.0%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   if -4.9999999999999999e-232 < z < 3.99999999999999982e-258

   1. Initial program 92.8%

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

      1. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. div-sub 78.7%

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

      3. mul-1-neg 78.7%

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

      4. associate-/l* 74.1%

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

      5. distribute-lft-neg-out 74.1%

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

      6. distribute-rgt-out 78.5%

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

      7. sub-neg 78.5%

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

      8. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 99.7%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+218}:\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-232}:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-258}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{x - t}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+52}:\\ \;\;\;\;t \cdot t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-8} \lor \neg \left(t \leq -9 \cdot 10^{-71}\right) \land t \leq 1.75 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))))
   (if (<= t -2.05e+52)
     (* t t_1)
     (if (or (<= t -2.5e-8) (and (not (<= t -9e-71)) (<= t 1.75e-152)))
       (* x (- 1.0 t_1))
       (+ x (* (- z y) (/ t (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double tmp;
	if (t <= -2.05e+52) {
		tmp = t * t_1;
	} else if ((t <= -2.5e-8) || (!(t <= -9e-71) && (t <= 1.75e-152))) {
		tmp = x * (1.0 - t_1);
	} else {
		tmp = x + ((z - y) * (t / (z - 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 = (z - y) / (z - a)
    if (t <= (-2.05d+52)) then
        tmp = t * t_1
    else if ((t <= (-2.5d-8)) .or. (.not. (t <= (-9d-71))) .and. (t <= 1.75d-152)) then
        tmp = x * (1.0d0 - t_1)
    else
        tmp = x + ((z - y) * (t / (z - 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 = (z - y) / (z - a);
	double tmp;
	if (t <= -2.05e+52) {
		tmp = t * t_1;
	} else if ((t <= -2.5e-8) || (!(t <= -9e-71) && (t <= 1.75e-152))) {
		tmp = x * (1.0 - t_1);
	} else {
		tmp = x + ((z - y) * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - y) / (z - a)
	tmp = 0
	if t <= -2.05e+52:
		tmp = t * t_1
	elif (t <= -2.5e-8) or (not (t <= -9e-71) and (t <= 1.75e-152)):
		tmp = x * (1.0 - t_1)
	else:
		tmp = x + ((z - y) * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	tmp = 0.0
	if (t <= -2.05e+52)
		tmp = Float64(t * t_1);
	elseif ((t <= -2.5e-8) || (!(t <= -9e-71) && (t <= 1.75e-152)))
		tmp = Float64(x * Float64(1.0 - t_1));
	else
		tmp = Float64(x + Float64(Float64(z - y) * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - y) / (z - a);
	tmp = 0.0;
	if (t <= -2.05e+52)
		tmp = t * t_1;
	elseif ((t <= -2.5e-8) || (~((t <= -9e-71)) && (t <= 1.75e-152)))
		tmp = x * (1.0 - t_1);
	else
		tmp = x + ((z - y) * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+52], N[(t * t$95$1), $MachinePrecision], If[Or[LessEqual[t, -2.5e-8], And[N[Not[LessEqual[t, -9e-71]], $MachinePrecision], LessEqual[t, 1.75e-152]]], N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e52

   1. Initial program 62.9%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in x around 0 46.8%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   if -2.05e52 < t < -2.4999999999999999e-8 or -9.0000000000000004e-71 < t < 1.7500000000000001e-152

   1. Initial program 75.0%

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

      1. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in x around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

   7. Simplified 74.3%

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

   if -2.4999999999999999e-8 < t < -9.0000000000000004e-71 or 1.7500000000000001e-152 < t

   1. Initial program 74.4%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around inf 76.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-8} \lor \neg \left(t \leq -9 \cdot 10^{-71}\right) \land t \leq 1.75 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - \frac{z - y}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := x \cdot \left(1 - t\_1\right)\\ t_3 := t \cdot t\_1\\ \mathbf{if}\;t \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-70}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z y) (- z a))) (t_2 (* x (- 1.0 t_1))) (t_3 (* t t_1)))
   (if (<= t -1e+52)
     t_3
     (if (<= t -4.5e-44)
       t_2
       (if (<= t -1.35e-70)
         (/ (* t (- z y)) (- z a))
         (if (<= t 3e-6) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x * (1.0 - t_1);
	double t_3 = t * t_1;
	double tmp;
	if (t <= -1e+52) {
		tmp = t_3;
	} else if (t <= -4.5e-44) {
		tmp = t_2;
	} else if (t <= -1.35e-70) {
		tmp = (t * (z - y)) / (z - a);
	} else if (t <= 3e-6) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = (z - y) / (z - a)
    t_2 = x * (1.0d0 - t_1)
    t_3 = t * t_1
    if (t <= (-1d+52)) then
        tmp = t_3
    else if (t <= (-4.5d-44)) then
        tmp = t_2
    else if (t <= (-1.35d-70)) then
        tmp = (t * (z - y)) / (z - a)
    else if (t <= 3d-6) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = x * (1.0 - t_1);
	double t_3 = t * t_1;
	double tmp;
	if (t <= -1e+52) {
		tmp = t_3;
	} else if (t <= -4.5e-44) {
		tmp = t_2;
	} else if (t <= -1.35e-70) {
		tmp = (t * (z - y)) / (z - a);
	} else if (t <= 3e-6) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - y) / (z - a)
	t_2 = x * (1.0 - t_1)
	t_3 = t * t_1
	tmp = 0
	if t <= -1e+52:
		tmp = t_3
	elif t <= -4.5e-44:
		tmp = t_2
	elif t <= -1.35e-70:
		tmp = (t * (z - y)) / (z - a)
	elif t <= 3e-6:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = Float64(x * Float64(1.0 - t_1))
	t_3 = Float64(t * t_1)
	tmp = 0.0
	if (t <= -1e+52)
		tmp = t_3;
	elseif (t <= -4.5e-44)
		tmp = t_2;
	elseif (t <= -1.35e-70)
		tmp = Float64(Float64(t * Float64(z - y)) / Float64(z - a));
	elseif (t <= 3e-6)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - y) / (z - a);
	t_2 = x * (1.0 - t_1);
	t_3 = t * t_1;
	tmp = 0.0;
	if (t <= -1e+52)
		tmp = t_3;
	elseif (t <= -4.5e-44)
		tmp = t_2;
	elseif (t <= -1.35e-70)
		tmp = (t * (z - y)) / (z - a);
	elseif (t <= 3e-6)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * t$95$1), $MachinePrecision]}, If[LessEqual[t, -1e+52], t$95$3, If[LessEqual[t, -4.5e-44], t$95$2, If[LessEqual[t, -1.35e-70], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-6], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999999e51 or 3.0000000000000001e-6 < t

   1. Initial program 66.6%

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

      1. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0 53.0%

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

      1. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   if -9.9999999999999999e51 < t < -4.4999999999999999e-44 or -1.3500000000000001e-70 < t < 3.0000000000000001e-6

   1. Initial program 75.5%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in x around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

   7. Simplified 71.4%

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

   if -4.4999999999999999e-44 < t < -1.3500000000000001e-70

   1. Initial program 91.7%

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

      1. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in x around 0 67.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(1 - \frac{z - y}{z - a}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-70}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(1 - \frac{z - y}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-267}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))))
   (if (<= t -4.7e-91)
     t_1
     (if (<= t -1.16e-267)
       (- x (* x (/ y a)))
       (if (<= t 5.5e-175)
         (* y (/ (- x t) (- z a)))
         (if (<= t 4.7e-21) (* x (- 1.0 (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -4.7e-91) {
		tmp = t_1;
	} else if (t <= -1.16e-267) {
		tmp = x - (x * (y / a));
	} else if (t <= 5.5e-175) {
		tmp = y * ((x - t) / (z - a));
	} else if (t <= 4.7e-21) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    if (t <= (-4.7d-91)) then
        tmp = t_1
    else if (t <= (-1.16d-267)) then
        tmp = x - (x * (y / a))
    else if (t <= 5.5d-175) then
        tmp = y * ((x - t) / (z - a))
    else if (t <= 4.7d-21) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -4.7e-91) {
		tmp = t_1;
	} else if (t <= -1.16e-267) {
		tmp = x - (x * (y / a));
	} else if (t <= 5.5e-175) {
		tmp = y * ((x - t) / (z - a));
	} else if (t <= 4.7e-21) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	tmp = 0
	if t <= -4.7e-91:
		tmp = t_1
	elif t <= -1.16e-267:
		tmp = x - (x * (y / a))
	elif t <= 5.5e-175:
		tmp = y * ((x - t) / (z - a))
	elif t <= 4.7e-21:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (t <= -4.7e-91)
		tmp = t_1;
	elseif (t <= -1.16e-267)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (t <= 5.5e-175)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (t <= 4.7e-21)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (t <= -4.7e-91)
		tmp = t_1;
	elseif (t <= -1.16e-267)
		tmp = x - (x * (y / a));
	elseif (t <= 5.5e-175)
		tmp = y * ((x - t) / (z - a));
	elseif (t <= 4.7e-21)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e-91], t$95$1, If[LessEqual[t, -1.16e-267], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-175], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e-21], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.70000000000000006e-91 or 4.7000000000000003e-21 < t

   1. Initial program 71.1%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 49.8%

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

      1. associate-/l* 68.5%

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

   7. Simplified 68.5%

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

   if -4.70000000000000006e-91 < t < -1.1600000000000001e-267

   1. Initial program 73.4%

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

      1. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. div-sub 75.2%

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

      3. mul-1-neg 75.2%

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

      4. associate-/l* 78.0%

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

      5. distribute-lft-neg-out 78.0%

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

      6. distribute-rgt-out 81.5%

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

      7. sub-neg 81.5%

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

      8. associate-/r/ 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in z around 0 73.6%

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

   9. Taylor expanded in t around 0 64.7%

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

       1. mul-1-neg 64.7%

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

       2. associate-*r/ 73.6%

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

       3. distribute-lft-neg-in 73.6%

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

   11. Simplified 73.6%

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

   if -1.1600000000000001e-267 < t < 5.50000000000000054e-175

   1. Initial program 74.8%

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

      1. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. div-sub 60.8%

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

   7. Simplified 60.8%

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

   if 5.50000000000000054e-175 < t < 4.7000000000000003e-21

   1. Initial program 74.4%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

   7. Simplified 62.9%

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

   8. Taylor expanded in z around 0 56.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-267}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))))
   (if (<= z -3.55e-34)
     t_1
     (if (<= z 5e-27)
       (+ x (* y (/ (- t x) a)))
       (if (<= z 8.5e+153) (* y (/ (- x t) (- z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -3.55e-34) {
		tmp = t_1;
	} else if (z <= 5e-27) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 8.5e+153) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    if (z <= (-3.55d-34)) then
        tmp = t_1
    else if (z <= 5d-27) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 8.5d+153) then
        tmp = y * ((x - t) / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -3.55e-34) {
		tmp = t_1;
	} else if (z <= 5e-27) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 8.5e+153) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	tmp = 0
	if z <= -3.55e-34:
		tmp = t_1
	elif z <= 5e-27:
		tmp = x + (y * ((t - x) / a))
	elif z <= 8.5e+153:
		tmp = y * ((x - t) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.55e-34)
		tmp = t_1;
	elseif (z <= 5e-27)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 8.5e+153)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (z <= -3.55e-34)
		tmp = t_1;
	elseif (z <= 5e-27)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 8.5e+153)
		tmp = y * ((x - t) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.55e-34], t$95$1, If[LessEqual[z, 5e-27], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+153], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.55000000000000018e-34 or 8.49999999999999935e153 < z

   1. Initial program 49.4%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around 0 42.5%

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

      1. associate-/l* 68.8%

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

   7. Simplified 68.8%

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

   if -3.55000000000000018e-34 < z < 5.0000000000000002e-27

   1. Initial program 93.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

   if 5.0000000000000002e-27 < z < 8.49999999999999935e153

   1. Initial program 64.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. div-sub 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))))
   (if (<= z -1.55e-33)
     t_1
     (if (<= z 6.5e-27)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 4.4e+155) (* y (/ (- x t) (- z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -1.55e-33) {
		tmp = t_1;
	} else if (z <= 6.5e-27) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 4.4e+155) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    if (z <= (-1.55d-33)) then
        tmp = t_1
    else if (z <= 6.5d-27) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 4.4d+155) then
        tmp = y * ((x - t) / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (z <= -1.55e-33) {
		tmp = t_1;
	} else if (z <= 6.5e-27) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 4.4e+155) {
		tmp = y * ((x - t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	tmp = 0
	if z <= -1.55e-33:
		tmp = t_1
	elif z <= 6.5e-27:
		tmp = x + ((t - x) / (a / y))
	elif z <= 4.4e+155:
		tmp = y * ((x - t) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.55e-33)
		tmp = t_1;
	elseif (z <= 6.5e-27)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 4.4e+155)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (z <= -1.55e-33)
		tmp = t_1;
	elseif (z <= 6.5e-27)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 4.4e+155)
		tmp = y * ((x - t) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-33], t$95$1, If[LessEqual[z, 6.5e-27], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+155], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999998e-33 or 4.4000000000000005e155 < z

   1. Initial program 49.4%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around 0 42.5%

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

      1. associate-/l* 68.8%

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

   7. Simplified 68.8%

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

   if -1.54999999999999998e-33 < z < 6.50000000000000025e-27

   1. Initial program 93.6%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. div-sub 92.8%

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

      3. mul-1-neg 92.8%

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

      4. associate-/l* 87.7%

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

      5. distribute-lft-neg-out 87.7%

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

      6. distribute-rgt-out 92.9%

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

      7. sub-neg 92.9%

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

      8. associate-/r/ 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in z around 0 78.2%

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

   if 6.50000000000000025e-27 < z < 4.4000000000000005e155

   1. Initial program 64.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. div-sub 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+218} \lor \neg \left(z \leq 1.95 \cdot 10^{+120}\right):\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.26e+218) (not (<= z 1.95e+120)))
   (+ t (* (/ (- x t) z) (- y a)))
   (+ x (/ (- t x) (/ (- z a) (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.26e+218) || !(z <= 1.95e+120)) {
		tmp = t + (((x - t) / z) * (y - a));
	} else {
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.26d+218)) .or. (.not. (z <= 1.95d+120))) then
        tmp = t + (((x - t) / z) * (y - a))
    else
        tmp = x + ((t - x) / ((z - a) / (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.26e+218) || !(z <= 1.95e+120)) {
		tmp = t + (((x - t) / z) * (y - a));
	} else {
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.26e+218) or not (z <= 1.95e+120):
		tmp = t + (((x - t) / z) * (y - a))
	else:
		tmp = x + ((t - x) / ((z - a) / (z - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.26e+218) || !(z <= 1.95e+120))
		tmp = Float64(t + Float64(Float64(Float64(x - t) / z) * Float64(y - a)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(z - a) / Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.26e+218) || ~((z <= 1.95e+120)))
		tmp = t + (((x - t) / z) * (y - a));
	else
		tmp = x + ((t - x) / ((z - a) / (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.26e+218], N[Not[LessEqual[z, 1.95e+120]], $MachinePrecision]], N[(t + N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26000000000000005e218 or 1.9499999999999999e120 < z

   1. Initial program 31.4%

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

      1. associate-/l* 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. div-sub 68.0%

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

      7. associate-/l* 82.7%

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

      8. associate-/l* 92.5%

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

      9. distribute-rgt-out-- 92.5%

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

   7. Simplified 92.5%

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

   if -1.26000000000000005e218 < z < 1.9499999999999999e120

   1. Initial program 84.3%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. div-sub 84.1%

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

      3. mul-1-neg 84.1%

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

      4. associate-/l* 86.6%

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

      5. distribute-lft-neg-out 86.6%

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

      6. distribute-rgt-out 89.8%

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

      7. sub-neg 89.8%

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

      8. associate-/r/ 93.2%

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

   7. Simplified 93.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+218} \lor \neg \left(z \leq 1.95 \cdot 10^{+120}\right):\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{z - a}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.00015:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+22)
   t
   (if (<= z 0.00015)
     (* x (- 1.0 (/ y a)))
     (if (<= z 1.6e+157) (* x (/ (- y a) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+22) {
		tmp = t;
	} else if (z <= 0.00015) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+157) {
		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) :: tmp
    if (z <= (-3.2d+22)) then
        tmp = t
    else if (z <= 0.00015d0) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d+157) 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 tmp;
	if (z <= -3.2e+22) {
		tmp = t;
	} else if (z <= 0.00015) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e+157) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+22:
		tmp = t
	elif z <= 0.00015:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e+157:
		tmp = x * ((y - a) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+22)
		tmp = t;
	elseif (z <= 0.00015)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e+157)
		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)
	tmp = 0.0;
	if (z <= -3.2e+22)
		tmp = t;
	elseif (z <= 0.00015)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e+157)
		tmp = x * ((y - a) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+22], t, If[LessEqual[z, 0.00015], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+157], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e22 or 1.6e157 < z

   1. Initial program 43.3%

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

      1. associate-/l* 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in z around inf 61.3%

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

   if -3.2e22 < z < 1.49999999999999987e-4

   1. Initial program 92.3%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in z around 0 58.4%

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

   if 1.49999999999999987e-4 < z < 1.6e157

   1. Initial program 64.1%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around inf 47.4%

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

      1. mul-1-neg 47.4%

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

      2. unsub-neg 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in z around inf 44.8%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

      3. +-commutative 44.8%

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

      4. distribute-lft-in 44.8%

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

      5. neg-mul-1 44.8%

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

      6. remove-double-neg 44.8%

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

      7. mul-1-neg 44.8%

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

      8. sub-neg 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.00015:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+75)
   t
   (if (<= z 9.5e-32) x (if (<= z 3.6e+55) t (if (<= z 5e+154) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+75) {
		tmp = t;
	} else if (z <= 9.5e-32) {
		tmp = x;
	} else if (z <= 3.6e+55) {
		tmp = t;
	} else if (z <= 5e+154) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+75)) then
        tmp = t
    else if (z <= 9.5d-32) then
        tmp = x
    else if (z <= 3.6d+55) then
        tmp = t
    else if (z <= 5d+154) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+75) {
		tmp = t;
	} else if (z <= 9.5e-32) {
		tmp = x;
	} else if (z <= 3.6e+55) {
		tmp = t;
	} else if (z <= 5e+154) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+75:
		tmp = t
	elif z <= 9.5e-32:
		tmp = x
	elif z <= 3.6e+55:
		tmp = t
	elif z <= 5e+154:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+75)
		tmp = t;
	elseif (z <= 9.5e-32)
		tmp = x;
	elseif (z <= 3.6e+55)
		tmp = t;
	elseif (z <= 5e+154)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+75)
		tmp = t;
	elseif (z <= 9.5e-32)
		tmp = x;
	elseif (z <= 3.6e+55)
		tmp = t;
	elseif (z <= 5e+154)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+75], t, If[LessEqual[z, 9.5e-32], x, If[LessEqual[z, 3.6e+55], t, If[LessEqual[z, 5e+154], x, t]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e75 or 9.4999999999999999e-32 < z < 3.59999999999999987e55 or 5.00000000000000004e154 < z

   1. Initial program 47.2%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 59.8%

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

   if -1.1499999999999999e75 < z < 9.4999999999999999e-32 or 3.59999999999999987e55 < z < 5.00000000000000004e154

   1. Initial program 87.5%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 39.3%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+75} \lor \neg \left(z \leq 7.2 \cdot 10^{+153}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+75) (not (<= z 7.2e+153)))
   (* t (/ (- z y) (- z a)))
   (+ x (/ (- x t) (/ (- z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+75) || !(z <= 7.2e+153)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x + ((x - t) / ((z - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+75)) .or. (.not. (z <= 7.2d+153))) then
        tmp = t * ((z - y) / (z - a))
    else
        tmp = x + ((x - t) / ((z - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+75) || !(z <= 7.2e+153)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x + ((x - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+75) or not (z <= 7.2e+153):
		tmp = t * ((z - y) / (z - a))
	else:
		tmp = x + ((x - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+75) || !(z <= 7.2e+153))
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	else
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+75) || ~((z <= 7.2e+153)))
		tmp = t * ((z - y) / (z - a));
	else
		tmp = x + ((x - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+75], N[Not[LessEqual[z, 7.2e+153]], $MachinePrecision]], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000006e75 or 7.2000000000000001e153 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in x around 0 43.8%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   if -1.40000000000000006e75 < z < 7.2000000000000001e153

   1. Initial program 86.3%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around 0 85.5%

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

      1. +-commutative 85.5%

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

      2. div-sub 86.1%

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

      3. mul-1-neg 86.1%

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

      4. associate-/l* 86.3%

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

      5. distribute-lft-neg-out 86.3%

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

      6. distribute-rgt-out 89.8%

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

      7. sub-neg 89.8%

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

      8. associate-/r/ 93.5%

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

   7. Simplified 93.5%

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

   8. Taylor expanded in y around inf 82.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+75} \lor \neg \left(z \leq 7.2 \cdot 10^{+153}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17} \lor \neg \left(z \leq 9.8 \cdot 10^{-32}\right):\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+17) (not (<= z 9.8e-32)))
   (+ t (* (/ (- x t) z) (- y a)))
   (+ x (/ (- x t) (/ (- z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+17) || !(z <= 9.8e-32)) {
		tmp = t + (((x - t) / z) * (y - a));
	} else {
		tmp = x + ((x - t) / ((z - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+17)) .or. (.not. (z <= 9.8d-32))) then
        tmp = t + (((x - t) / z) * (y - a))
    else
        tmp = x + ((x - t) / ((z - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+17) || !(z <= 9.8e-32)) {
		tmp = t + (((x - t) / z) * (y - a));
	} else {
		tmp = x + ((x - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+17) or not (z <= 9.8e-32):
		tmp = t + (((x - t) / z) * (y - a))
	else:
		tmp = x + ((x - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+17) || !(z <= 9.8e-32))
		tmp = Float64(t + Float64(Float64(Float64(x - t) / z) * Float64(y - a)));
	else
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+17) || ~((z <= 9.8e-32)))
		tmp = t + (((x - t) / z) * (y - a));
	else
		tmp = x + ((x - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+17], N[Not[LessEqual[z, 9.8e-32]], $MachinePrecision]], N[(t + N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e17 or 9.7999999999999996e-32 < z

   1. Initial program 50.7%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 65.4%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. 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. div-sub 65.4%

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

      7. associate-/l* 74.4%

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

      8. associate-/l* 81.3%

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

      9. distribute-rgt-out-- 81.4%

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

   7. Simplified 81.4%

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

   if -8e17 < z < 9.7999999999999996e-32

   1. Initial program 92.7%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. div-sub 92.8%

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

      3. mul-1-neg 92.8%

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

      4. associate-/l* 88.0%

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

      5. distribute-lft-neg-out 88.0%

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

      6. distribute-rgt-out 92.8%

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

      7. sub-neg 92.8%

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

      8. associate-/r/ 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in y around inf 89.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17} \lor \neg \left(z \leq 9.8 \cdot 10^{-32}\right):\\ \;\;\;\;t + \frac{x - t}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.9e+78)
   t
   (if (<= z 5e-27) x (if (<= z 7.8e+155) (* x (/ y z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.9e+78) {
		tmp = t;
	} else if (z <= 5e-27) {
		tmp = x;
	} else if (z <= 7.8e+155) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.9d+78)) then
        tmp = t
    else if (z <= 5d-27) then
        tmp = x
    else if (z <= 7.8d+155) then
        tmp = x * (y / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.9e+78) {
		tmp = t;
	} else if (z <= 5e-27) {
		tmp = x;
	} else if (z <= 7.8e+155) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.9e+78:
		tmp = t
	elif z <= 5e-27:
		tmp = x
	elif z <= 7.8e+155:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.9e+78)
		tmp = t;
	elseif (z <= 5e-27)
		tmp = x;
	elseif (z <= 7.8e+155)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.9e+78)
		tmp = t;
	elseif (z <= 5e-27)
		tmp = x;
	elseif (z <= 7.8e+155)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.9e+78], t, If[LessEqual[z, 5e-27], x, If[LessEqual[z, 7.8e+155], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8999999999999998e78 or 7.7999999999999996e155 < z

   1. Initial program 38.7%

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

      1. associate-/l* 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 66.2%

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

   if -6.8999999999999998e78 < z < 5.0000000000000002e-27

   1. Initial program 91.5%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 39.5%

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

   if 5.0000000000000002e-27 < z < 7.7999999999999996e155

   1. Initial program 64.5%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in a around 0 38.8%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-88} \lor \neg \left(t \leq 2.05 \cdot 10^{-21}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.55e-88) (not (<= t 2.05e-21)))
   (* t (/ (- z y) (- z a)))
   (- x (* x (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e-88) || !(t <= 2.05e-21)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.55d-88)) .or. (.not. (t <= 2.05d-21))) then
        tmp = t * ((z - y) / (z - a))
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e-88) || !(t <= 2.05e-21)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.55e-88) or not (t <= 2.05e-21):
		tmp = t * ((z - y) / (z - a))
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.55e-88) || !(t <= 2.05e-21))
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.55e-88) || ~((t <= 2.05e-21)))
		tmp = t * ((z - y) / (z - a));
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.55e-88], N[Not[LessEqual[t, 2.05e-21]], $MachinePrecision]], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5499999999999999e-88 or 2.04999999999999997e-21 < t

   1. Initial program 71.1%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 49.8%

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

      1. associate-/l* 68.5%

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

   7. Simplified 68.5%

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

   if -1.5499999999999999e-88 < t < 2.04999999999999997e-21

   1. Initial program 74.3%

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

      1. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. div-sub 76.6%

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

      3. mul-1-neg 76.6%

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

      4. associate-/l* 75.7%

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

      5. distribute-lft-neg-out 75.7%

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

      6. distribute-rgt-out 79.4%

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

      7. sub-neg 79.4%

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

      8. associate-/r/ 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in z around 0 62.1%

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

   9. Taylor expanded in t around 0 54.7%

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

       1. mul-1-neg 54.7%

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

       2. associate-*r/ 59.0%

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

       3. distribute-lft-neg-in 59.0%

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

   11. Simplified 59.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-88} \lor \neg \left(t \leq 2.05 \cdot 10^{-21}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.52e+22) t (if (<= z 4e+149) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.52e+22) {
		tmp = t;
	} else if (z <= 4e+149) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.52d+22)) then
        tmp = t
    else if (z <= 4d+149) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.52e+22) {
		tmp = t;
	} else if (z <= 4e+149) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.52e+22:
		tmp = t
	elif z <= 4e+149:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.52e+22)
		tmp = t;
	elseif (z <= 4e+149)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.52e+22)
		tmp = t;
	elseif (z <= 4e+149)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.52e+22], t, If[LessEqual[z, 4e+149], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e22 or 4.0000000000000002e149 < z

   1. Initial program 42.4%

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

      1. associate-/l* 69.0%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in z around inf 60.0%

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

   if -1.52e22 < z < 4.0000000000000002e149

   1. Initial program 88.0%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around 0 53.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 25.6% 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 72.5%

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

   1. associate-/l* 83.0%

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

3. Simplified 83.0%

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

5. Taylor expanded in z around inf 26.3%

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

6. Final simplification 26.3%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))