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

Percentage Accurate: 67.7% → 90.7%

Time: 13.3s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-298} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-298) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (+ (* (- y x) a) (* z (- x y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-298) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-298) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-298], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-298 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.3%

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

   3. Simplified 89.3%

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

   if -5.0000000000000002e-298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in t around -inf 99.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-298} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (* (/ (- z t) (- a t)) (- 1.0 (/ x y))))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-298)
       t_2
       (if (<= t_2 0.0) (+ y (/ (+ (* (- y x) a) (* z (- x y))) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (((z - t) / (a - t)) * (1.0 - (x / y))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} 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 + (y * (((z - t) / (a - t)) * (1.0 - (x / y))));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (((z - t) / (a - t)) * (1.0 - (x / y))))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-298:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(1.0 - Float64(x / y)))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) + Float64(z * Float64(x - y))) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (((z - t) / (a - t)) * (1.0 - (x / y))));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((((y - x) * a) + (z * (x - y))) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-298], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 59.3%

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

   3. Taylor expanded in y around -inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. *-commutative 71.3%

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

      3. distribute-rgt-neg-in 71.3%

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

      4. +-commutative 71.3%

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

      5. times-frac 80.6%

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

      6. distribute-rgt-out 85.2%

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

   5. Simplified 85.2%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000002e-298

   1. Initial program 92.2%

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

   if -5.0000000000000002e-298 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

   3. Taylor expanded in t around -inf 99.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-298}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a + z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-12} \lor \neg \left(a \leq -8 \cdot 10^{-56}\right) \land \left(a \leq -1.85 \cdot 10^{-128} \lor \neg \left(a \leq 3.55 \cdot 10^{-22}\right)\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e-12)
         (and (not (<= a -8e-56))
              (or (<= a -1.85e-128) (not (<= a 3.55e-22)))))
   (- x (* y (/ (- z t) (- t a))))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-12) || (!(a <= -8e-56) && ((a <= -1.85e-128) || !(a <= 3.55e-22)))) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (z * ((x - y) / 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 ((a <= (-1.05d-12)) .or. (.not. (a <= (-8d-56))) .and. (a <= (-1.85d-128)) .or. (.not. (a <= 3.55d-22))) then
        tmp = x - (y * ((z - t) / (t - a)))
    else
        tmp = y + (z * ((x - y) / 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 ((a <= -1.05e-12) || (!(a <= -8e-56) && ((a <= -1.85e-128) || !(a <= 3.55e-22)))) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.05e-12) or (not (a <= -8e-56) and ((a <= -1.85e-128) or not (a <= 3.55e-22))):
		tmp = x - (y * ((z - t) / (t - a)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e-12) || (!(a <= -8e-56) && ((a <= -1.85e-128) || !(a <= 3.55e-22))))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.05e-12) || (~((a <= -8e-56)) && ((a <= -1.85e-128) || ~((a <= 3.55e-22)))))
		tmp = x - (y * ((z - t) / (t - a)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e-12], And[N[Not[LessEqual[a, -8e-56]], $MachinePrecision], Or[LessEqual[a, -1.85e-128], N[Not[LessEqual[a, 3.55e-22]], $MachinePrecision]]]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04999999999999997e-12 or -8.0000000000000003e-56 < a < -1.85e-128 or 3.5499999999999999e-22 < a

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. associate-/l* 82.8%

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

   5. Simplified 82.8%

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

   if -1.04999999999999997e-12 < a < -8.0000000000000003e-56 or -1.85e-128 < a < 3.5499999999999999e-22

   1. Initial program 60.1%

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

   3. Taylor expanded in t around -inf 78.6%

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

   4. Taylor expanded in a around 0 73.8%

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

      1. associate-/l* 80.5%

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

      2. associate-*r* 80.5%

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

      3. mul-1-neg 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in z around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-*r/ 80.5%

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

      3. sub-neg 80.5%

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

   9. Simplified 80.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-12} \lor \neg \left(a \leq -8 \cdot 10^{-56}\right) \land \left(a \leq -1.85 \cdot 10^{-128} \lor \neg \left(a \leq 3.55 \cdot 10^{-22}\right)\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+126} \lor \neg \left(x \leq 1.36 \cdot 10^{-36} \lor \neg \left(x \leq 40000\right) \land x \leq 1.02 \cdot 10^{+152}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.25e+126)
         (not
          (or (<= x 1.36e-36) (and (not (<= x 40000.0)) (<= x 1.02e+152)))))
   (* x (- 1.0 (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.25e+126) || !((x <= 1.36e-36) || (!(x <= 40000.0) && (x <= 1.02e+152)))) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.25d+126)) .or. (.not. (x <= 1.36d-36) .or. (.not. (x <= 40000.0d0)) .and. (x <= 1.02d+152))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.25e+126) || !((x <= 1.36e-36) || (!(x <= 40000.0) && (x <= 1.02e+152)))) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.25e+126) or not ((x <= 1.36e-36) or (not (x <= 40000.0) and (x <= 1.02e+152))):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.25e+126) || !((x <= 1.36e-36) || (!(x <= 40000.0) && (x <= 1.02e+152))))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.25e+126) || ~(((x <= 1.36e-36) || (~((x <= 40000.0)) && (x <= 1.02e+152)))))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.25e+126], N[Not[Or[LessEqual[x, 1.36e-36], And[N[Not[LessEqual[x, 40000.0]], $MachinePrecision], LessEqual[x, 1.02e+152]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999994e126 or 1.36000000000000007e-36 < x < 4e4 or 1.01999999999999999e152 < x

   1. Initial program 56.4%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in t around 0 57.1%

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

   if -1.24999999999999994e126 < x < 1.36000000000000007e-36 or 4e4 < x < 1.01999999999999999e152

   1. Initial program 68.6%

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

      1. associate-/l* 89.1%

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

      2. add-cube-cbrt 88.0%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 88.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 88.0%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 88.0%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in x around 0 46.4%

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

      1. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+126} \lor \neg \left(x \leq 1.36 \cdot 10^{-36} \lor \neg \left(x \leq 40000\right) \land x \leq 1.02 \cdot 10^{+152}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \frac{t}{t - a}\\ \mathbf{if}\;t \leq -4.25 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (/ t (- t a)))))
   (if (<= t -4.25e-13)
     t_2
     (if (<= t 1.56e-236)
       t_1
       (if (<= t 2.3e-200) (* y (/ z (- a t))) (if (<= t 4e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (t / (t - a));
	double tmp;
	if (t <= -4.25e-13) {
		tmp = t_2;
	} else if (t <= 1.56e-236) {
		tmp = t_1;
	} else if (t <= 2.3e-200) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+112) {
		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 * (1.0d0 - (z / a))
    t_2 = y * (t / (t - a))
    if (t <= (-4.25d-13)) then
        tmp = t_2
    else if (t <= 1.56d-236) then
        tmp = t_1
    else if (t <= 2.3d-200) then
        tmp = y * (z / (a - t))
    else if (t <= 4d+112) 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 * (1.0 - (z / a));
	double t_2 = y * (t / (t - a));
	double tmp;
	if (t <= -4.25e-13) {
		tmp = t_2;
	} else if (t <= 1.56e-236) {
		tmp = t_1;
	} else if (t <= 2.3e-200) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (t / (t - a))
	tmp = 0
	if t <= -4.25e-13:
		tmp = t_2
	elif t <= 1.56e-236:
		tmp = t_1
	elif t <= 2.3e-200:
		tmp = y * (z / (a - t))
	elif t <= 4e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(t / Float64(t - a)))
	tmp = 0.0
	if (t <= -4.25e-13)
		tmp = t_2;
	elseif (t <= 1.56e-236)
		tmp = t_1;
	elseif (t <= 2.3e-200)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (t / (t - a));
	tmp = 0.0;
	if (t <= -4.25e-13)
		tmp = t_2;
	elseif (t <= 1.56e-236)
		tmp = t_1;
	elseif (t <= 2.3e-200)
		tmp = y * (z / (a - t));
	elseif (t <= 4e+112)
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.25e-13], t$95$2, If[LessEqual[t, 1.56e-236], t$95$1, If[LessEqual[t, 2.3e-200], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2500000000000001e-13 or 3.9999999999999997e112 < t

   1. Initial program 34.9%

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

      1. associate-/l* 74.0%

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

      2. add-cube-cbrt 72.9%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 72.8%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 72.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 72.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in x around 0 34.2%

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

      1. associate-/l* 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 60.4%

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

      1. neg-mul-1 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. neg-sub0 60.4%

         \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} \]

      4. associate--r- 60.4%

         \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - a\right) + t}} \]

      5. neg-sub0 60.4%

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

   10. Simplified 60.4%

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

   if -4.2500000000000001e-13 < t < 1.5599999999999999e-236 or 2.30000000000000007e-200 < t < 3.9999999999999997e112

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. unsub-neg 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around 0 56.2%

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

   if 1.5599999999999999e-236 < t < 2.30000000000000007e-200

   1. Initial program 91.2%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 99.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 99.6%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 71.8%

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

      1. associate-/l* 90.1%

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

   10. Simplified 90.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -2.1e+72)
     t_2
     (if (<= t 5.6e-237)
       t_1
       (if (<= t 6e-200) (* y (/ z (- a t))) (if (<= t 4e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -2.1e+72) {
		tmp = t_2;
	} else if (t <= 5.6e-237) {
		tmp = t_1;
	} else if (t <= 6e-200) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+112) {
		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 * (1.0d0 - (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-2.1d+72)) then
        tmp = t_2
    else if (t <= 5.6d-237) then
        tmp = t_1
    else if (t <= 6d-200) then
        tmp = y * (z / (a - t))
    else if (t <= 4d+112) 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 * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -2.1e+72) {
		tmp = t_2;
	} else if (t <= 5.6e-237) {
		tmp = t_1;
	} else if (t <= 6e-200) {
		tmp = y * (z / (a - t));
	} else if (t <= 4e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -2.1e+72:
		tmp = t_2
	elif t <= 5.6e-237:
		tmp = t_1
	elif t <= 6e-200:
		tmp = y * (z / (a - t))
	elif t <= 4e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -2.1e+72)
		tmp = t_2;
	elseif (t <= 5.6e-237)
		tmp = t_1;
	elseif (t <= 6e-200)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 4e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -2.1e+72)
		tmp = t_2;
	elseif (t <= 5.6e-237)
		tmp = t_1;
	elseif (t <= 6e-200)
		tmp = y * (z / (a - t));
	elseif (t <= 4e+112)
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+72], t$95$2, If[LessEqual[t, 5.6e-237], t$95$1, If[LessEqual[t, 6e-200], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1000000000000001e72 or 3.9999999999999997e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in a around 0 21.2%

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

      1. mul-1-neg 21.2%

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

      2. unsub-neg 21.2%

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

      3. associate-/l* 54.3%

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

      4. div-sub 54.3%

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

      5. sub-neg 54.3%

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

      6. *-inverses 54.3%

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

      7. metadata-eval 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in y around inf 59.8%

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

   if -2.1000000000000001e72 < t < 5.59999999999999995e-237 or 5.99999999999999989e-200 < t < 3.9999999999999997e112

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in t around 0 54.2%

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

   if 5.59999999999999995e-237 < t < 5.99999999999999989e-200

   1. Initial program 91.2%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 99.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 99.6%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 71.8%

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

      1. associate-/l* 90.1%

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

   10. Simplified 90.1%

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

Alternative 7: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.8e+72)
     t_2
     (if (<= t 5.6e-237)
       t_1
       (if (<= t 3.8e-200) (* y (/ z a)) (if (<= t 4e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+72) {
		tmp = t_2;
	} else if (t <= 5.6e-237) {
		tmp = t_1;
	} else if (t <= 3.8e-200) {
		tmp = y * (z / a);
	} else if (t <= 4e+112) {
		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 * (1.0d0 - (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-3.8d+72)) then
        tmp = t_2
    else if (t <= 5.6d-237) then
        tmp = t_1
    else if (t <= 3.8d-200) then
        tmp = y * (z / a)
    else if (t <= 4d+112) 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 * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+72) {
		tmp = t_2;
	} else if (t <= 5.6e-237) {
		tmp = t_1;
	} else if (t <= 3.8e-200) {
		tmp = y * (z / a);
	} else if (t <= 4e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -3.8e+72:
		tmp = t_2
	elif t <= 5.6e-237:
		tmp = t_1
	elif t <= 3.8e-200:
		tmp = y * (z / a)
	elif t <= 4e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.8e+72)
		tmp = t_2;
	elseif (t <= 5.6e-237)
		tmp = t_1;
	elseif (t <= 3.8e-200)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -3.8e+72)
		tmp = t_2;
	elseif (t <= 5.6e-237)
		tmp = t_1;
	elseif (t <= 3.8e-200)
		tmp = y * (z / a);
	elseif (t <= 4e+112)
		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[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+72], t$95$2, If[LessEqual[t, 5.6e-237], t$95$1, If[LessEqual[t, 3.8e-200], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000006e72 or 3.9999999999999997e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in a around 0 21.2%

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

      1. mul-1-neg 21.2%

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

      2. unsub-neg 21.2%

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

      3. associate-/l* 54.3%

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

      4. div-sub 54.3%

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

      5. sub-neg 54.3%

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

      6. *-inverses 54.3%

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

      7. metadata-eval 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in y around inf 59.8%

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

   if -3.80000000000000006e72 < t < 5.59999999999999995e-237 or 3.8e-200 < t < 3.9999999999999997e112

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in t around 0 54.2%

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

   if 5.59999999999999995e-237 < t < 3.8e-200

   1. Initial program 91.2%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 99.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 99.6%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 71.8%

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

      1. associate-/l* 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in a around inf 61.3%

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

       1. associate-/l* 70.1%

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

   13. Simplified 70.1%

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

Alternative 8: 48.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.55e+74)
     y
     (if (<= t 1.56e-236)
       t_1
       (if (<= t 6.8e-200) (* y (/ z a)) (if (<= t 4.4e+112) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.55e+74) {
		tmp = y;
	} else if (t <= 1.56e-236) {
		tmp = t_1;
	} else if (t <= 6.8e-200) {
		tmp = y * (z / a);
	} else if (t <= 4.4e+112) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.55d+74)) then
        tmp = y
    else if (t <= 1.56d-236) then
        tmp = t_1
    else if (t <= 6.8d-200) then
        tmp = y * (z / a)
    else if (t <= 4.4d+112) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.55e+74) {
		tmp = y;
	} else if (t <= 1.56e-236) {
		tmp = t_1;
	} else if (t <= 6.8e-200) {
		tmp = y * (z / a);
	} else if (t <= 4.4e+112) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.55e+74:
		tmp = y
	elif t <= 1.56e-236:
		tmp = t_1
	elif t <= 6.8e-200:
		tmp = y * (z / a)
	elif t <= 4.4e+112:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.55e+74)
		tmp = y;
	elseif (t <= 1.56e-236)
		tmp = t_1;
	elseif (t <= 6.8e-200)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4.4e+112)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.55e+74)
		tmp = y;
	elseif (t <= 1.56e-236)
		tmp = t_1;
	elseif (t <= 6.8e-200)
		tmp = y * (z / a);
	elseif (t <= 4.4e+112)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+74], y, If[LessEqual[t, 1.56e-236], t$95$1, If[LessEqual[t, 6.8e-200], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+112], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000011e74 or 4.3999999999999999e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -1.55000000000000011e74 < t < 1.5599999999999999e-236 or 6.8000000000000006e-200 < t < 4.3999999999999999e112

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in t around 0 54.2%

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

   if 1.5599999999999999e-236 < t < 6.8000000000000006e-200

   1. Initial program 91.2%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 99.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 99.6%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 71.8%

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

      1. associate-/l* 90.1%

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

   10. Simplified 90.1%

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

   11. Taylor expanded in a around inf 61.3%

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

       1. associate-/l* 70.1%

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

   13. Simplified 70.1%

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

Alternative 9: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -7.5e+158)
     t_1
     (if (<= t -7.5e-28)
       (- x (* y (/ (- z t) (- t a))))
       (if (<= t 5.8e+112) (+ x (* z (/ (- x y) (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -7.5e+158) {
		tmp = t_1;
	} else if (t <= -7.5e-28) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else if (t <= 5.8e+112) {
		tmp = x + (z * ((x - y) / (t - 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 = y + (z * ((x - y) / t))
    if (t <= (-7.5d+158)) then
        tmp = t_1
    else if (t <= (-7.5d-28)) then
        tmp = x - (y * ((z - t) / (t - a)))
    else if (t <= 5.8d+112) then
        tmp = x + (z * ((x - y) / (t - 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 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -7.5e+158) {
		tmp = t_1;
	} else if (t <= -7.5e-28) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else if (t <= 5.8e+112) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if t <= -7.5e+158:
		tmp = t_1
	elif t <= -7.5e-28:
		tmp = x - (y * ((z - t) / (t - a)))
	elif t <= 5.8e+112:
		tmp = x + (z * ((x - y) / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -7.5e+158)
		tmp = t_1;
	elseif (t <= -7.5e-28)
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	elseif (t <= 5.8e+112)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -7.5e+158)
		tmp = t_1;
	elseif (t <= -7.5e-28)
		tmp = x - (y * ((z - t) / (t - a)));
	elseif (t <= 5.8e+112)
		tmp = x + (z * ((x - y) / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+158], t$95$1, If[LessEqual[t, -7.5e-28], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+112], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5000000000000004e158 or 5.8000000000000004e112 < t

   1. Initial program 27.2%

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

   3. Taylor expanded in t around -inf 63.4%

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

   4. Taylor expanded in a around 0 63.5%

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

      1. associate-/l* 78.7%

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

      2. associate-*r* 78.7%

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

      3. mul-1-neg 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in z around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. associate-*r/ 78.7%

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

      3. sub-neg 78.7%

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

   9. Simplified 78.7%

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

   if -7.5000000000000004e158 < t < -7.5000000000000003e-28

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf 58.0%

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

      1. associate-/l* 69.7%

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

   5. Simplified 69.7%

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

   if -7.5000000000000003e-28 < t < 5.8000000000000004e112

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+158}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -8.8e-13)
     t_1
     (if (<= t 1.25e-236)
       (* x (- 1.0 (/ z a)))
       (if (<= t 5.9e+91) (* z (/ (- x y) (- t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.8e-13) {
		tmp = t_1;
	} else if (t <= 1.25e-236) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.9e+91) {
		tmp = z * ((x - y) / (t - 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 = y * ((z - t) / (a - t))
    if (t <= (-8.8d-13)) then
        tmp = t_1
    else if (t <= 1.25d-236) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5.9d+91) then
        tmp = z * ((x - y) / (t - 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -8.8e-13) {
		tmp = t_1;
	} else if (t <= 1.25e-236) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.9e+91) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -8.8e-13:
		tmp = t_1
	elif t <= 1.25e-236:
		tmp = x * (1.0 - (z / a))
	elif t <= 5.9e+91:
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -8.8e-13)
		tmp = t_1;
	elseif (t <= 1.25e-236)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5.9e+91)
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -8.8e-13)
		tmp = t_1;
	elseif (t <= 1.25e-236)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5.9e+91)
		tmp = z * ((x - y) / (t - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e-13], t$95$1, If[LessEqual[t, 1.25e-236], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e+91], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.79999999999999986e-13 or 5.9000000000000002e91 < t

   1. Initial program 35.8%

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

      1. associate-/l* 74.5%

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

      2. add-cube-cbrt 73.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 73.4%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 73.4%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 73.4%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in x around 0 32.7%

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

      1. associate-/l* 64.9%

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

   7. Simplified 64.9%

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

   if -8.79999999999999986e-13 < t < 1.2499999999999999e-236

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 66.2%

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

   if 1.2499999999999999e-236 < t < 5.9000000000000002e91

   1. Initial program 84.4%

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

      1. associate-/l* 89.1%

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

      2. add-cube-cbrt 88.4%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 88.4%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 88.4%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 88.4%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 57.3%

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

      1. div-sub 57.3%

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

   7. Simplified 57.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+72)
   y
   (if (<= t -2e-292)
     x
     (if (<= t 2.1e-154) (* y (/ z a)) (if (<= t 4e+112) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+72) {
		tmp = y;
	} else if (t <= -2e-292) {
		tmp = x;
	} else if (t <= 2.1e-154) {
		tmp = y * (z / a);
	} else if (t <= 4e+112) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-2.3d+72)) then
        tmp = y
    else if (t <= (-2d-292)) then
        tmp = x
    else if (t <= 2.1d-154) then
        tmp = y * (z / a)
    else if (t <= 4d+112) then
        tmp = x
    else
        tmp = 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 (t <= -2.3e+72) {
		tmp = y;
	} else if (t <= -2e-292) {
		tmp = x;
	} else if (t <= 2.1e-154) {
		tmp = y * (z / a);
	} else if (t <= 4e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+72:
		tmp = y
	elif t <= -2e-292:
		tmp = x
	elif t <= 2.1e-154:
		tmp = y * (z / a)
	elif t <= 4e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+72)
		tmp = y;
	elseif (t <= -2e-292)
		tmp = x;
	elseif (t <= 2.1e-154)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+72)
		tmp = y;
	elseif (t <= -2e-292)
		tmp = x;
	elseif (t <= 2.1e-154)
		tmp = y * (z / a);
	elseif (t <= 4e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+72], y, If[LessEqual[t, -2e-292], x, If[LessEqual[t, 2.1e-154], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+112], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e72 or 3.9999999999999997e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -2.3e72 < t < -2.0000000000000001e-292 or 2.09999999999999984e-154 < t < 3.9999999999999997e112

   1. Initial program 80.7%

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

   3. Taylor expanded in a around inf 42.5%

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

   if -2.0000000000000001e-292 < t < 2.09999999999999984e-154

   1. Initial program 97.4%

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

      1. associate-/l* 100.0%

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

      2. add-cube-cbrt 99.3%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 99.3%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 99.3%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in z around inf 72.7%

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

      1. div-sub 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in y around inf 47.0%

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

      1. associate-/l* 52.3%

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

   10. Simplified 52.3%

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

   11. Taylor expanded in a around inf 42.3%

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

       1. associate-/l* 47.5%

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

   13. Simplified 47.5%

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

Alternative 12: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.26e+73)
   y
   (if (<= t 1.56e-236)
     x
     (if (<= t 2.5e-187) (* x (/ z t)) (if (<= t 5.5e+112) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.26e+73) {
		tmp = y;
	} else if (t <= 1.56e-236) {
		tmp = x;
	} else if (t <= 2.5e-187) {
		tmp = x * (z / t);
	} else if (t <= 5.5e+112) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1.26d+73)) then
        tmp = y
    else if (t <= 1.56d-236) then
        tmp = x
    else if (t <= 2.5d-187) then
        tmp = x * (z / t)
    else if (t <= 5.5d+112) then
        tmp = x
    else
        tmp = 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 (t <= -1.26e+73) {
		tmp = y;
	} else if (t <= 1.56e-236) {
		tmp = x;
	} else if (t <= 2.5e-187) {
		tmp = x * (z / t);
	} else if (t <= 5.5e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.26e+73:
		tmp = y
	elif t <= 1.56e-236:
		tmp = x
	elif t <= 2.5e-187:
		tmp = x * (z / t)
	elif t <= 5.5e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.26e+73)
		tmp = y;
	elseif (t <= 1.56e-236)
		tmp = x;
	elseif (t <= 2.5e-187)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 5.5e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.26e+73)
		tmp = y;
	elseif (t <= 1.56e-236)
		tmp = x;
	elseif (t <= 2.5e-187)
		tmp = x * (z / t);
	elseif (t <= 5.5e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.26e+73], y, If[LessEqual[t, 1.56e-236], x, If[LessEqual[t, 2.5e-187], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+112], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25999999999999993e73 or 5.50000000000000026e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -1.25999999999999993e73 < t < 1.5599999999999999e-236 or 2.4999999999999998e-187 < t < 5.50000000000000026e112

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 41.6%

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

   if 1.5599999999999999e-236 < t < 2.4999999999999998e-187

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in a around 0 55.9%

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

Alternative 13: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.68 \cdot 10^{-15} \lor \neg \left(a \leq 1.2 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.68e-15) (not (<= a 1.2e-13)))
   (- x (* y (/ (- z t) (- t a))))
   (+ y (* (/ (- z a) t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.68e-15) || !(a <= 1.2e-13)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (((z - a) / t) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.68d-15)) .or. (.not. (a <= 1.2d-13))) then
        tmp = x - (y * ((z - t) / (t - a)))
    else
        tmp = y + (((z - a) / t) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.68e-15) || !(a <= 1.2e-13)) {
		tmp = x - (y * ((z - t) / (t - a)));
	} else {
		tmp = y + (((z - a) / t) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.68e-15) or not (a <= 1.2e-13):
		tmp = x - (y * ((z - t) / (t - a)))
	else:
		tmp = y + (((z - a) / t) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.68e-15) || !(a <= 1.2e-13))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(y + Float64(Float64(Float64(z - a) / t) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.68e-15) || ~((a <= 1.2e-13)))
		tmp = x - (y * ((z - t) / (t - a)));
	else
		tmp = y + (((z - a) / t) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.68e-15], N[Not[LessEqual[a, 1.2e-13]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6800000000000001e-15 or 1.1999999999999999e-13 < a

   1. Initial program 66.5%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. associate-/l* 84.1%

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

   5. Simplified 84.1%

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

   if -1.6800000000000001e-15 < a < 1.1999999999999999e-13

   1. Initial program 61.9%

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

      1. associate-/l* 76.8%

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

      2. add-cube-cbrt 75.8%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 75.8%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 75.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 75.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in t around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.2%

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

      4. mul-1-neg 74.2%

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

      5. *-commutative 74.2%

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

      6. div-sub 75.1%

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

      7. *-commutative 75.1%

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

      8. mul-1-neg 75.1%

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

      9. distribute-lft-out-- 75.1%

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

      10. mul-1-neg 75.1%

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

      11. distribute-rgt-out-- 75.1%

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

      12. distribute-neg-frac 75.1%

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

      13. sub-neg 75.1%

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

   7. Simplified 83.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.68 \cdot 10^{-15} \lor \neg \left(a \leq 1.2 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z - a}{t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+80} \lor \neg \left(a \leq 2.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.25e+80) (not (<= a 2.5e-14)))
   (+ x (* z (/ (- y x) a)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.25e+80) || !(a <= 2.5e-14)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + (z * ((x - y) / 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 ((a <= (-2.25d+80)) .or. (.not. (a <= 2.5d-14))) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = y + (z * ((x - y) / 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 ((a <= -2.25e+80) || !(a <= 2.5e-14)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.25e+80) or not (a <= 2.5e-14):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.25e+80) || !(a <= 2.5e-14))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.25e+80) || ~((a <= 2.5e-14)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.25e+80], N[Not[LessEqual[a, 2.5e-14]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25000000000000003e80 or 2.5000000000000001e-14 < a

   1. Initial program 66.2%

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

   3. Taylor expanded in t around 0 59.4%

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

      1. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   if -2.25000000000000003e80 < a < 2.5000000000000001e-14

   1. Initial program 62.8%

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

   3. Taylor expanded in t around -inf 71.3%

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

   4. Taylor expanded in a around 0 65.5%

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

      1. associate-/l* 70.9%

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

      2. associate-*r* 70.9%

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

      3. mul-1-neg 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in z around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. associate-*r/ 70.9%

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

      3. sub-neg 70.9%

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

   9. Simplified 70.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+80} \lor \neg \left(a \leq 2.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-33} \lor \neg \left(t \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-33) (not (<= t 1.05e+23)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-33) || !(t <= 1.05e+23)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / 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 <= (-1.3d-33)) .or. (.not. (t <= 1.05d+23))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - x) / 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 <= -1.3e-33) || !(t <= 1.05e+23)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e-33) or not (t <= 1.05e+23):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-33) || !(t <= 1.05e+23))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e-33) || ~((t <= 1.05e+23)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-33], N[Not[LessEqual[t, 1.05e+23]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999997e-33 or 1.0500000000000001e23 < t

   1. Initial program 41.3%

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

      1. associate-/l* 76.2%

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

      2. add-cube-cbrt 75.0%

         \[\leadsto x + \color{blue}{\left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}\right)} \cdot \frac{z - t}{a - t} \]

      3. associate-*l* 75.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

      4. pow2 75.0%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right) \]

   4. Applied egg-rr 75.0%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \left(\sqrt[3]{y - x} \cdot \frac{z - t}{a - t}\right)} \]

   5. Taylor expanded in x around 0 34.7%

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

      1. associate-/l* 62.2%

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

   7. Simplified 62.2%

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

   if -1.29999999999999997e-33 < t < 1.0500000000000001e23

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-33} \lor \neg \left(t \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+73}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.85e+73) y (if (<= t 4e+112) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+73) {
		tmp = y;
	} else if (t <= 4e+112) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1.85d+73)) then
        tmp = y
    else if (t <= 4d+112) then
        tmp = x
    else
        tmp = 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 (t <= -1.85e+73) {
		tmp = y;
	} else if (t <= 4e+112) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.85e+73:
		tmp = y
	elif t <= 4e+112:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.85e+73)
		tmp = y;
	elseif (t <= 4e+112)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.85e+73)
		tmp = y;
	elseif (t <= 4e+112)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.85e+73], y, If[LessEqual[t, 4e+112], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.84999999999999987e73 or 3.9999999999999997e112 < t

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -1.84999999999999987e73 < t < 3.9999999999999997e112

   1. Initial program 84.3%

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

   3. Taylor expanded in a around inf 39.0%

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

Alternative 17: 25.1% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 64.4%

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

3. Taylor expanded in a around inf 28.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	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[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))