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

Percentage Accurate: 68.0% → 90.3%

Time: 16.1s

Alternatives: 19

Speedup: 0.6×

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: 68.0% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-283} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -1e-283) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ (* (- y x) (- a z)) 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 <= -1e-283) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((y - x) * (a - z)) / 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 <= -1e-283) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / 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, -1e-283], 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[(y - x), $MachinePrecision] * N[(a - z), $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))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-/l* 90.7%

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

      3. fma-define 90.7%

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

   3. Simplified 90.7%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. +-commutative 55.1%

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

      2. +-commutative 55.1%

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

      3. distribute-lft-in 55.1%

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

      4. mul-1-neg 55.1%

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

      5. distribute-rgt-neg-in 55.1%

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

      6. associate-/l* 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-rgt-identity 55.1%

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

      9. associate-+l+ 4.7%

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

   5. Simplified 3.2%

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

   6. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   8. Simplified 99.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-283} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+274}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e-283)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 4e+274) t_2 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 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 4e+274) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (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 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 4e+274) {
		tmp = t_2;
	} 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 <= -1e-283:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 4e+274:
		tmp = t_2
	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 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 4e+274)
		tmp = t_2;
	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 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 4e+274)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(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, -1e-283], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+274], t$95$2, 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 3.99999999999999969e274 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 38.6%

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

   3. Taylor expanded in y around -inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. *-commutative 58.6%

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

      3. distribute-rgt-neg-in 58.6%

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

      4. +-commutative 58.6%

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

      5. times-frac 71.4%

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

      6. distribute-rgt-out 77.6%

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

   5. Simplified 77.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.99999999999999969e274

   1. Initial program 98.8%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. +-commutative 55.1%

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

      2. +-commutative 55.1%

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

      3. distribute-lft-in 55.1%

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

      4. mul-1-neg 55.1%

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

      5. distribute-rgt-neg-in 55.1%

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

      6. associate-/l* 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-rgt-identity 55.1%

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

      9. associate-+l+ 4.7%

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

   5. Simplified 3.2%

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

   6. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   8. Simplified 99.7%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+274}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{a - t} \cdot \left(1 - \frac{x}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x - y}{t} \cdot \left(a - z\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ (- x y) t) (- a z))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-283)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 5e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (((x - y) / t) * (a - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (((x - y) / t) * (a - z));
	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 <= -1e-283) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (((x - y) / t) * (a - z))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-283:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 5e+305:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(Float64(x - y) / t) * Float64(a - z)))
	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 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (((x - y) / t) * (a - z));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-283)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 5e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $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, -1e-283], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+305], t$95$2, 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 5.00000000000000009e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.6%

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

   3. Taylor expanded in t around inf 53.2%

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

      1. associate--l+ 53.2%

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

      2. distribute-lft-out-- 53.2%

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

      3. div-sub 54.3%

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

      4. mul-1-neg 54.3%

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

      5. unsub-neg 54.3%

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

      6. div-sub 53.2%

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

      7. associate-/l* 59.3%

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

      8. associate-/l* 58.0%

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

      9. distribute-rgt-out-- 67.7%

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

   5. Simplified 67.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.00000000000000009e305

   1. Initial program 98.8%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. +-commutative 55.1%

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

      2. +-commutative 55.1%

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

      3. distribute-lft-in 55.1%

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

      4. mul-1-neg 55.1%

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

      5. distribute-rgt-neg-in 55.1%

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

      6. associate-/l* 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-rgt-identity 55.1%

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

      9. associate-+l+ 4.7%

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

   5. Simplified 3.2%

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

   6. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   8. Simplified 99.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* x (* (/ (- z t) (- a t)) (+ -1.0 (/ y x)))))
     (if (<= t_1 -1e-283)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 5e+305) t_1 (- y (* (/ (- x y) t) (- a z)))))))))

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 <= -((double) INFINITY)) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t_1 <= -1e-283) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = t_1;
	} else {
		tmp = y - (((x - y) / t) * (a - z));
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t_1 <= -1e-283) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 5e+305) {
		tmp = t_1;
	} else {
		tmp = y - (((x - y) / t) * (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))))
	elif t_1 <= -1e-283:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 5e+305:
		tmp = t_1
	else:
		tmp = y - (((x - y) / t) * (a - z))
	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 <= Float64(-Inf))
		tmp = Float64(x + Float64(x * Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(-1.0 + Float64(y / x)))));
	elseif (t_1 <= -1e-283)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 5e+305)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) / t) * Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	elseif (t_1 <= -1e-283)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 5e+305)
		tmp = t_1;
	else
		tmp = y - (((x - y) / t) * (a - z));
	end
	tmp_2 = 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[LessEqual[t$95$1, (-Infinity)], N[(x + N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-283], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], t$95$1, N[(y - N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 38.3%

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

   3. Taylor expanded in x around inf 33.0%

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

      1. times-frac 62.1%

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

      2. distribute-rgt-out 70.2%

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

   5. Simplified 70.2%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999947e-284 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 5.00000000000000009e305

   1. Initial program 98.8%

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

   if -9.99999999999999947e-284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. +-commutative 55.1%

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

      2. +-commutative 55.1%

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

      3. distribute-lft-in 55.1%

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

      4. mul-1-neg 55.1%

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

      5. distribute-rgt-neg-in 55.1%

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

      6. associate-/l* 55.1%

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

      7. mul-1-neg 55.1%

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

      8. *-rgt-identity 55.1%

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

      9. associate-+l+ 4.7%

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

   5. Simplified 3.2%

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

   6. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   8. Simplified 99.7%

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

   if 5.00000000000000009e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 34.8%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. distribute-lft-out-- 63.2%

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

      3. div-sub 63.2%

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

      4. mul-1-neg 63.2%

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

      5. unsub-neg 63.2%

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

      6. div-sub 63.2%

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

      7. associate-/l* 69.6%

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

      8. associate-/l* 65.0%

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

      9. distribute-rgt-out-- 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ t a) 1.0))))
   (if (<= t -4e+30)
     y
     (if (<= t -6.5e-28)
       t_1
       (if (<= t -5e-97)
         (* x (/ (- z a) t))
         (if (<= t -1.8e-242)
           t_1
           (if (<= t 1.75e-168) (* y (/ z a)) (if (<= t 7.8e-28) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((t / a) + 1.0);
	double tmp;
	if (t <= -4e+30) {
		tmp = y;
	} else if (t <= -6.5e-28) {
		tmp = t_1;
	} else if (t <= -5e-97) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.8e-242) {
		tmp = t_1;
	} else if (t <= 1.75e-168) {
		tmp = y * (z / a);
	} else if (t <= 7.8e-28) {
		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 * ((t / a) + 1.0d0)
    if (t <= (-4d+30)) then
        tmp = y
    else if (t <= (-6.5d-28)) then
        tmp = t_1
    else if (t <= (-5d-97)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.8d-242)) then
        tmp = t_1
    else if (t <= 1.75d-168) then
        tmp = y * (z / a)
    else if (t <= 7.8d-28) 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 * ((t / a) + 1.0);
	double tmp;
	if (t <= -4e+30) {
		tmp = y;
	} else if (t <= -6.5e-28) {
		tmp = t_1;
	} else if (t <= -5e-97) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.8e-242) {
		tmp = t_1;
	} else if (t <= 1.75e-168) {
		tmp = y * (z / a);
	} else if (t <= 7.8e-28) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((t / a) + 1.0)
	tmp = 0
	if t <= -4e+30:
		tmp = y
	elif t <= -6.5e-28:
		tmp = t_1
	elif t <= -5e-97:
		tmp = x * ((z - a) / t)
	elif t <= -1.8e-242:
		tmp = t_1
	elif t <= 1.75e-168:
		tmp = y * (z / a)
	elif t <= 7.8e-28:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(t / a) + 1.0))
	tmp = 0.0
	if (t <= -4e+30)
		tmp = y;
	elseif (t <= -6.5e-28)
		tmp = t_1;
	elseif (t <= -5e-97)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.8e-242)
		tmp = t_1;
	elseif (t <= 1.75e-168)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7.8e-28)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((t / a) + 1.0);
	tmp = 0.0;
	if (t <= -4e+30)
		tmp = y;
	elseif (t <= -6.5e-28)
		tmp = t_1;
	elseif (t <= -5e-97)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.8e-242)
		tmp = t_1;
	elseif (t <= 1.75e-168)
		tmp = y * (z / a);
	elseif (t <= 7.8e-28)
		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[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+30], y, If[LessEqual[t, -6.5e-28], t$95$1, If[LessEqual[t, -5e-97], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-242], t$95$1, If[LessEqual[t, 1.75e-168], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-28], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.0000000000000001e30 or 7.79999999999999998e-28 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in t around inf 47.2%

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

   if -4.0000000000000001e30 < t < -6.50000000000000043e-28 or -4.9999999999999995e-97 < t < -1.80000000000000007e-242 or 1.74999999999999991e-168 < t < 7.79999999999999998e-28

   1. Initial program 84.2%

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

   3. Taylor expanded in x around -inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. +-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in z around 0 38.9%

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

      1. +-commutative 38.9%

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

   8. Simplified 38.9%

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

   9. Taylor expanded in t around 0 41.6%

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

   if -6.50000000000000043e-28 < t < -4.9999999999999995e-97

   1. Initial program 90.6%

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

   3. Taylor expanded in x around -inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

      3. +-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in t around -inf 45.0%

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

      1. associate-/l* 49.2%

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

   8. Simplified 49.2%

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

   if -1.80000000000000007e-242 < t < 1.74999999999999991e-168

   1. Initial program 91.3%

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

   3. Taylor expanded in t around 0 86.9%

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

   4. Taylor expanded in y around inf 68.7%

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

   5. Taylor expanded in x around 0 45.3%

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

      1. associate-*r/ 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* z (/ (- x y) (- t a)))))
   (if (<= a -1.4e+58)
     (+ x (* y (/ z a)))
     (if (<= a -3.2e-265)
       t_1
       (if (<= a 1.08e-277)
         t_2
         (if (<= a 1.1e-58)
           t_1
           (if (<= a 4.7e+83) t_2 (+ x (* z (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -1.4e+58) {
		tmp = x + (y * (z / a));
	} else if (a <= -3.2e-265) {
		tmp = t_1;
	} else if (a <= 1.08e-277) {
		tmp = t_2;
	} else if (a <= 1.1e-58) {
		tmp = t_1;
	} else if (a <= 4.7e+83) {
		tmp = t_2;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((x - y) / (t - a))
    if (a <= (-1.4d+58)) then
        tmp = x + (y * (z / a))
    else if (a <= (-3.2d-265)) then
        tmp = t_1
    else if (a <= 1.08d-277) then
        tmp = t_2
    else if (a <= 1.1d-58) then
        tmp = t_1
    else if (a <= 4.7d+83) then
        tmp = t_2
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -1.4e+58) {
		tmp = x + (y * (z / a));
	} else if (a <= -3.2e-265) {
		tmp = t_1;
	} else if (a <= 1.08e-277) {
		tmp = t_2;
	} else if (a <= 1.1e-58) {
		tmp = t_1;
	} else if (a <= 4.7e+83) {
		tmp = t_2;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((x - y) / (t - a))
	tmp = 0
	if a <= -1.4e+58:
		tmp = x + (y * (z / a))
	elif a <= -3.2e-265:
		tmp = t_1
	elif a <= 1.08e-277:
		tmp = t_2
	elif a <= 1.1e-58:
		tmp = t_1
	elif a <= 4.7e+83:
		tmp = t_2
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (a <= -1.4e+58)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -3.2e-265)
		tmp = t_1;
	elseif (a <= 1.08e-277)
		tmp = t_2;
	elseif (a <= 1.1e-58)
		tmp = t_1;
	elseif (a <= 4.7e+83)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (a <= -1.4e+58)
		tmp = x + (y * (z / a));
	elseif (a <= -3.2e-265)
		tmp = t_1;
	elseif (a <= 1.08e-277)
		tmp = t_2;
	elseif (a <= 1.1e-58)
		tmp = t_1;
	elseif (a <= 4.7e+83)
		tmp = t_2;
	else
		tmp = x + (z * (y / a));
	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]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+58], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-265], t$95$1, If[LessEqual[a, 1.08e-277], t$95$2, If[LessEqual[a, 1.1e-58], t$95$1, If[LessEqual[a, 4.7e+83], t$95$2, N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3999999999999999e58

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 67.5%

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

      1. associate-/l* 69.6%

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

   6. Simplified 69.6%

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

   if -1.3999999999999999e58 < a < -3.2e-265 or 1.0800000000000001e-277 < a < 1.10000000000000003e-58

   1. Initial program 68.0%

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

   3. Taylor expanded in y around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. *-commutative 67.9%

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

      3. distribute-rgt-neg-in 67.9%

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

      4. +-commutative 67.9%

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

      5. times-frac 69.5%

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

      6. distribute-rgt-out 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in x around 0 49.2%

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

      1. associate-/l* 64.1%

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

   8. Simplified 64.1%

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

   if -3.2e-265 < a < 1.0800000000000001e-277 or 1.10000000000000003e-58 < a < 4.6999999999999999e83

   1. Initial program 76.3%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. +-commutative 76.1%

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

      3. distribute-lft-in 76.1%

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

      4. mul-1-neg 76.1%

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

      5. distribute-rgt-neg-in 76.1%

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

      6. associate-/l* 71.3%

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

      7. mul-1-neg 71.3%

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

      8. *-rgt-identity 71.3%

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

      9. associate-+l+ 68.9%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in z around inf 75.6%

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

      1. div-sub 75.6%

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

   8. Simplified 75.6%

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

   if 4.6999999999999999e83 < a

   1. Initial program 60.6%

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

   3. Taylor expanded in t around 0 60.3%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 70.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+176)
   y
   (if (<= t 4.1e-19)
     (+ x (* y (/ z a)))
     (if (<= t 8.5e+79)
       y
       (if (<= t 5.5e+162)
         (+ x (/ (* y z) a))
         (if (<= t 6.2e+183) (* x (/ (- z a) t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+176) {
		tmp = y;
	} else if (t <= 4.1e-19) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.5e+79) {
		tmp = y;
	} else if (t <= 5.5e+162) {
		tmp = x + ((y * z) / a);
	} else if (t <= 6.2e+183) {
		tmp = x * ((z - a) / t);
	} 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 <= (-5.6d+176)) then
        tmp = y
    else if (t <= 4.1d-19) then
        tmp = x + (y * (z / a))
    else if (t <= 8.5d+79) then
        tmp = y
    else if (t <= 5.5d+162) then
        tmp = x + ((y * z) / a)
    else if (t <= 6.2d+183) then
        tmp = x * ((z - a) / t)
    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 <= -5.6e+176) {
		tmp = y;
	} else if (t <= 4.1e-19) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.5e+79) {
		tmp = y;
	} else if (t <= 5.5e+162) {
		tmp = x + ((y * z) / a);
	} else if (t <= 6.2e+183) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+176:
		tmp = y
	elif t <= 4.1e-19:
		tmp = x + (y * (z / a))
	elif t <= 8.5e+79:
		tmp = y
	elif t <= 5.5e+162:
		tmp = x + ((y * z) / a)
	elif t <= 6.2e+183:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+176)
		tmp = y;
	elseif (t <= 4.1e-19)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 8.5e+79)
		tmp = y;
	elseif (t <= 5.5e+162)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 6.2e+183)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+176)
		tmp = y;
	elseif (t <= 4.1e-19)
		tmp = x + (y * (z / a));
	elseif (t <= 8.5e+79)
		tmp = y;
	elseif (t <= 5.5e+162)
		tmp = x + ((y * z) / a);
	elseif (t <= 6.2e+183)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+176], y, If[LessEqual[t, 4.1e-19], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+79], y, If[LessEqual[t, 5.5e+162], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+183], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.6000000000000005e176 or 4.09999999999999985e-19 < t < 8.4999999999999998e79 or 6.1999999999999997e183 < t

   1. Initial program 48.0%

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

   3. Taylor expanded in t around inf 59.8%

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

   if -5.6000000000000005e176 < t < 4.09999999999999985e-19

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 63.5%

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

   4. Taylor expanded in y around inf 50.9%

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

      1. associate-/l* 56.3%

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

   6. Simplified 56.3%

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

   if 8.4999999999999998e79 < t < 5.49999999999999966e162

   1. Initial program 58.2%

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

   3. Taylor expanded in t around 0 39.1%

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

   4. Taylor expanded in y around inf 45.8%

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

   if 5.49999999999999966e162 < t < 6.1999999999999997e183

   1. Initial program 28.3%

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

   3. Taylor expanded in x around -inf 74.3%

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

      1. associate-*r* 74.3%

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

      2. neg-mul-1 74.3%

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

      3. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around -inf 9.3%

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

      1. associate-/l* 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+162}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -5.6e+176)
     y
     (if (<= t -8.5e+96)
       t_1
       (if (<= t -6.4e+39)
         y
         (if (<= t -1.3e-65)
           (- x (* x (/ z a)))
           (if (<= t 4.1e-19) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -5.6e+176) {
		tmp = y;
	} else if (t <= -8.5e+96) {
		tmp = t_1;
	} else if (t <= -6.4e+39) {
		tmp = y;
	} else if (t <= -1.3e-65) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.1e-19) {
		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 + (y * (z / a))
    if (t <= (-5.6d+176)) then
        tmp = y
    else if (t <= (-8.5d+96)) then
        tmp = t_1
    else if (t <= (-6.4d+39)) then
        tmp = y
    else if (t <= (-1.3d-65)) then
        tmp = x - (x * (z / a))
    else if (t <= 4.1d-19) 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 + (y * (z / a));
	double tmp;
	if (t <= -5.6e+176) {
		tmp = y;
	} else if (t <= -8.5e+96) {
		tmp = t_1;
	} else if (t <= -6.4e+39) {
		tmp = y;
	} else if (t <= -1.3e-65) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.1e-19) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -5.6e+176:
		tmp = y
	elif t <= -8.5e+96:
		tmp = t_1
	elif t <= -6.4e+39:
		tmp = y
	elif t <= -1.3e-65:
		tmp = x - (x * (z / a))
	elif t <= 4.1e-19:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -5.6e+176)
		tmp = y;
	elseif (t <= -8.5e+96)
		tmp = t_1;
	elseif (t <= -6.4e+39)
		tmp = y;
	elseif (t <= -1.3e-65)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 4.1e-19)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -5.6e+176)
		tmp = y;
	elseif (t <= -8.5e+96)
		tmp = t_1;
	elseif (t <= -6.4e+39)
		tmp = y;
	elseif (t <= -1.3e-65)
		tmp = x - (x * (z / a));
	elseif (t <= 4.1e-19)
		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[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+176], y, If[LessEqual[t, -8.5e+96], t$95$1, If[LessEqual[t, -6.4e+39], y, If[LessEqual[t, -1.3e-65], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-19], t$95$1, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000005e176 or -8.50000000000000025e96 < t < -6.39999999999999986e39 or 4.09999999999999985e-19 < t

   1. Initial program 49.9%

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

   3. Taylor expanded in t around inf 51.5%

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

   if -5.6000000000000005e176 < t < -8.50000000000000025e96 or -1.30000000000000005e-65 < t < 4.09999999999999985e-19

   1. Initial program 88.6%

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

   3. Taylor expanded in t around 0 71.0%

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

   4. Taylor expanded in y around inf 58.8%

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

      1. associate-/l* 62.9%

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

   6. Simplified 62.9%

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

   if -6.39999999999999986e39 < t < -1.30000000000000005e-65

   1. Initial program 74.7%

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

   3. Taylor expanded in t around 0 57.8%

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

   4. Taylor expanded in y around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

      3. associate-/l* 57.6%

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

   6. Simplified 57.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+96}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+39}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-65}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e-55)
   (+ x (* y (/ z a)))
   (if (<= a -4.4e-264)
     y
     (if (<= a 8.2e-93)
       (* x (/ z (- t a)))
       (if (<= a 1.45e-69)
         y
         (if (<= a 4.4e+83) (* z (/ (- y x) a)) (+ x (* z (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-55) {
		tmp = x + (y * (z / a));
	} else if (a <= -4.4e-264) {
		tmp = y;
	} else if (a <= 8.2e-93) {
		tmp = x * (z / (t - a));
	} else if (a <= 1.45e-69) {
		tmp = y;
	} else if (a <= 4.4e+83) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8d-55)) then
        tmp = x + (y * (z / a))
    else if (a <= (-4.4d-264)) then
        tmp = y
    else if (a <= 8.2d-93) then
        tmp = x * (z / (t - a))
    else if (a <= 1.45d-69) then
        tmp = y
    else if (a <= 4.4d+83) then
        tmp = z * ((y - x) / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-55) {
		tmp = x + (y * (z / a));
	} else if (a <= -4.4e-264) {
		tmp = y;
	} else if (a <= 8.2e-93) {
		tmp = x * (z / (t - a));
	} else if (a <= 1.45e-69) {
		tmp = y;
	} else if (a <= 4.4e+83) {
		tmp = z * ((y - x) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e-55:
		tmp = x + (y * (z / a))
	elif a <= -4.4e-264:
		tmp = y
	elif a <= 8.2e-93:
		tmp = x * (z / (t - a))
	elif a <= 1.45e-69:
		tmp = y
	elif a <= 4.4e+83:
		tmp = z * ((y - x) / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e-55)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= -4.4e-264)
		tmp = y;
	elseif (a <= 8.2e-93)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (a <= 1.45e-69)
		tmp = y;
	elseif (a <= 4.4e+83)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e-55)
		tmp = x + (y * (z / a));
	elseif (a <= -4.4e-264)
		tmp = y;
	elseif (a <= 8.2e-93)
		tmp = x * (z / (t - a));
	elseif (a <= 1.45e-69)
		tmp = y;
	elseif (a <= 4.4e+83)
		tmp = z * ((y - x) / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e-55], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-264], y, If[LessEqual[a, 8.2e-93], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-69], y, If[LessEqual[a, 4.4e+83], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.99999999999999996e-55

   1. Initial program 77.7%

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

   3. Taylor expanded in t around 0 60.8%

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

   4. Taylor expanded in y around inf 58.5%

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

      1. associate-/l* 59.9%

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

   6. Simplified 59.9%

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

   if -7.99999999999999996e-55 < a < -4.39999999999999988e-264 or 8.1999999999999998e-93 < a < 1.4499999999999999e-69

   1. Initial program 60.5%

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

   3. Taylor expanded in t around inf 53.5%

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

   if -4.39999999999999988e-264 < a < 8.1999999999999998e-93

   1. Initial program 72.5%

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

   3. Taylor expanded in x around -inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

      3. +-commutative 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in z around inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. associate-*r/ 48.4%

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

      3. *-commutative 48.4%

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

      4. distribute-lft-neg-in 48.4%

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

      5. distribute-frac-neg 48.4%

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

   8. Simplified 48.4%

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

   if 1.4499999999999999e-69 < a < 4.39999999999999997e83

   1. Initial program 81.8%

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

   3. Taylor expanded in t around 0 55.5%

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

   4. Taylor expanded in z around inf 50.6%

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

      1. div-sub 50.6%

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

   6. Simplified 50.6%

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

   if 4.39999999999999997e83 < a

   1. Initial program 60.6%

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

   3. Taylor expanded in t around 0 60.3%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 70.5%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ t a) 1.0))))
   (if (<= t -3.05e+35)
     y
     (if (<= t -1.95e-59)
       t_1
       (if (<= t 3.5e-170) (* y (/ z a)) (if (<= t 7.6e-29) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((t / a) + 1.0);
	double tmp;
	if (t <= -3.05e+35) {
		tmp = y;
	} else if (t <= -1.95e-59) {
		tmp = t_1;
	} else if (t <= 3.5e-170) {
		tmp = y * (z / a);
	} else if (t <= 7.6e-29) {
		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 * ((t / a) + 1.0d0)
    if (t <= (-3.05d+35)) then
        tmp = y
    else if (t <= (-1.95d-59)) then
        tmp = t_1
    else if (t <= 3.5d-170) then
        tmp = y * (z / a)
    else if (t <= 7.6d-29) 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 * ((t / a) + 1.0);
	double tmp;
	if (t <= -3.05e+35) {
		tmp = y;
	} else if (t <= -1.95e-59) {
		tmp = t_1;
	} else if (t <= 3.5e-170) {
		tmp = y * (z / a);
	} else if (t <= 7.6e-29) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((t / a) + 1.0)
	tmp = 0
	if t <= -3.05e+35:
		tmp = y
	elif t <= -1.95e-59:
		tmp = t_1
	elif t <= 3.5e-170:
		tmp = y * (z / a)
	elif t <= 7.6e-29:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(t / a) + 1.0))
	tmp = 0.0
	if (t <= -3.05e+35)
		tmp = y;
	elseif (t <= -1.95e-59)
		tmp = t_1;
	elseif (t <= 3.5e-170)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7.6e-29)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((t / a) + 1.0);
	tmp = 0.0;
	if (t <= -3.05e+35)
		tmp = y;
	elseif (t <= -1.95e-59)
		tmp = t_1;
	elseif (t <= 3.5e-170)
		tmp = y * (z / a);
	elseif (t <= 7.6e-29)
		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[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.05e+35], y, If[LessEqual[t, -1.95e-59], t$95$1, If[LessEqual[t, 3.5e-170], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-29], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.04999999999999989e35 or 7.59999999999999951e-29 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in t around inf 47.2%

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

   if -3.04999999999999989e35 < t < -1.95000000000000009e-59 or 3.49999999999999985e-170 < t < 7.59999999999999951e-29

   1. Initial program 79.1%

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

   3. Taylor expanded in x around -inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. neg-mul-1 67.0%

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

      3. +-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around 0 40.3%

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

      1. +-commutative 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in t around 0 44.4%

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

   if -1.95000000000000009e-59 < t < 3.49999999999999985e-170

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.9%

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

   4. Taylor expanded in y around inf 60.4%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 40.2%

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

   7. Simplified 40.2%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+35}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+30)
   y
   (if (<= t 1.1e-127)
     (* z (/ (- y x) a))
     (if (<= t 1.3e-29)
       (* x (+ (/ t a) 1.0))
       (if (<= t 1.1e+49) (* x (/ (- z a) t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+30) {
		tmp = y;
	} else if (t <= 1.1e-127) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.3e-29) {
		tmp = x * ((t / a) + 1.0);
	} else if (t <= 1.1e+49) {
		tmp = x * ((z - a) / t);
	} 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 <= (-9.5d+30)) then
        tmp = y
    else if (t <= 1.1d-127) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.3d-29) then
        tmp = x * ((t / a) + 1.0d0)
    else if (t <= 1.1d+49) then
        tmp = x * ((z - a) / t)
    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 <= -9.5e+30) {
		tmp = y;
	} else if (t <= 1.1e-127) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.3e-29) {
		tmp = x * ((t / a) + 1.0);
	} else if (t <= 1.1e+49) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+30:
		tmp = y
	elif t <= 1.1e-127:
		tmp = z * ((y - x) / a)
	elif t <= 1.3e-29:
		tmp = x * ((t / a) + 1.0)
	elif t <= 1.1e+49:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+30)
		tmp = y;
	elseif (t <= 1.1e-127)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.3e-29)
		tmp = Float64(x * Float64(Float64(t / a) + 1.0));
	elseif (t <= 1.1e+49)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+30)
		tmp = y;
	elseif (t <= 1.1e-127)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.3e-29)
		tmp = x * ((t / a) + 1.0);
	elseif (t <= 1.1e+49)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+30], y, If[LessEqual[t, 1.1e-127], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-29], N[(x * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+49], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5000000000000003e30 or 1.1e49 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 49.3%

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

   if -9.5000000000000003e30 < t < 1.1000000000000001e-127

   1. Initial program 86.6%

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

   3. Taylor expanded in t around 0 72.1%

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

   4. Taylor expanded in z around inf 47.0%

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

      1. div-sub 48.8%

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

   6. Simplified 48.8%

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

   if 1.1000000000000001e-127 < t < 1.3000000000000001e-29

   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 59.6%

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

      1. associate-*r* 59.6%

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

      2. neg-mul-1 59.6%

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

      3. +-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in z around 0 43.4%

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

      1. +-commutative 43.4%

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

   8. Simplified 43.4%

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

   9. Taylor expanded in t around 0 49.6%

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

   if 1.3000000000000001e-29 < t < 1.1e49

   1. Initial program 71.9%

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

   3. Taylor expanded in x around -inf 52.1%

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

      1. associate-*r* 52.1%

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

      2. neg-mul-1 52.1%

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

      3. +-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in t around -inf 43.1%

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

      1. associate-/l* 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(\frac{t}{a} + 1\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-79}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-60}:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-79)
   (+ x (* y (/ (- z t) (- a t))))
   (if (<= a 6e-60)
     (- y (* (/ (- x y) t) (- a z)))
     (if (<= a 6.5e+93)
       (+ x (/ (* (- y x) z) (- a t)))
       (+ x (* (- t z) (/ y (- t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-79) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (a <= 6e-60) {
		tmp = y - (((x - y) / t) * (a - z));
	} else if (a <= 6.5e+93) {
		tmp = x + (((y - x) * z) / (a - t));
	} else {
		tmp = x + ((t - z) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d-79)) then
        tmp = x + (y * ((z - t) / (a - t)))
    else if (a <= 6d-60) then
        tmp = y - (((x - y) / t) * (a - z))
    else if (a <= 6.5d+93) then
        tmp = x + (((y - x) * z) / (a - t))
    else
        tmp = x + ((t - z) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-79) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else if (a <= 6e-60) {
		tmp = y - (((x - y) / t) * (a - z));
	} else if (a <= 6.5e+93) {
		tmp = x + (((y - x) * z) / (a - t));
	} else {
		tmp = x + ((t - z) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-79:
		tmp = x + (y * ((z - t) / (a - t)))
	elif a <= 6e-60:
		tmp = y - (((x - y) / t) * (a - z))
	elif a <= 6.5e+93:
		tmp = x + (((y - x) * z) / (a - t))
	else:
		tmp = x + ((t - z) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-79)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	elseif (a <= 6e-60)
		tmp = Float64(y - Float64(Float64(Float64(x - y) / t) * Float64(a - z)));
	elseif (a <= 6.5e+93)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-79)
		tmp = x + (y * ((z - t) / (a - t)));
	elseif (a <= 6e-60)
		tmp = y - (((x - y) / t) * (a - z));
	elseif (a <= 6.5e+93)
		tmp = x + (((y - x) * z) / (a - t));
	else
		tmp = x + ((t - z) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-79], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-60], N[(y - N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+93], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.80000000000000012e-79

   1. Initial program 78.9%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   if -2.80000000000000012e-79 < a < 6.00000000000000038e-60

   1. Initial program 63.8%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 77.4%

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

      4. mul-1-neg 77.4%

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

      5. unsub-neg 77.4%

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

      6. div-sub 76.3%

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

      7. associate-/l* 80.5%

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

      8. associate-/l* 74.8%

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

      9. distribute-rgt-out-- 81.5%

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

   5. Simplified 81.5%

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

   if 6.00000000000000038e-60 < a < 6.4999999999999998e93

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 74.7%

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

   if 6.4999999999999998e93 < a

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

      1. associate-/l* 90.5%

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

   7. Applied egg-rr 90.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-79}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-60}:\\ \;\;\;\;y - \frac{x - y}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+93}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+33)
   y
   (if (<= t -2.05e-60)
     x
     (if (<= t 2.1e-167) (* y (/ z a)) (if (<= t 3.7e-19) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+33) {
		tmp = y;
	} else if (t <= -2.05e-60) {
		tmp = x;
	} else if (t <= 2.1e-167) {
		tmp = y * (z / a);
	} else if (t <= 3.7e-19) {
		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 <= (-3.6d+33)) then
        tmp = y
    else if (t <= (-2.05d-60)) then
        tmp = x
    else if (t <= 2.1d-167) then
        tmp = y * (z / a)
    else if (t <= 3.7d-19) 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 <= -3.6e+33) {
		tmp = y;
	} else if (t <= -2.05e-60) {
		tmp = x;
	} else if (t <= 2.1e-167) {
		tmp = y * (z / a);
	} else if (t <= 3.7e-19) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+33:
		tmp = y
	elif t <= -2.05e-60:
		tmp = x
	elif t <= 2.1e-167:
		tmp = y * (z / a)
	elif t <= 3.7e-19:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+33)
		tmp = y;
	elseif (t <= -2.05e-60)
		tmp = x;
	elseif (t <= 2.1e-167)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.7e-19)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+33)
		tmp = y;
	elseif (t <= -2.05e-60)
		tmp = x;
	elseif (t <= 2.1e-167)
		tmp = y * (z / a);
	elseif (t <= 3.7e-19)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+33], y, If[LessEqual[t, -2.05e-60], x, If[LessEqual[t, 2.1e-167], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-19], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6000000000000003e33 or 3.70000000000000005e-19 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in t around inf 48.0%

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

   if -3.6000000000000003e33 < t < -2.05000000000000006e-60 or 2.10000000000000017e-167 < t < 3.70000000000000005e-19

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 39.0%

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

   if -2.05000000000000006e-60 < t < 2.10000000000000017e-167

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.9%

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

   4. Taylor expanded in y around inf 60.4%

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

   5. Taylor expanded in x around 0 36.4%

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

      1. associate-*r/ 40.2%

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

   7. Simplified 40.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+59} \lor \neg \left(z \leq 1.15 \cdot 10^{+119}\right):\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+59) (not (<= z 1.15e+119)))
   (* z (/ (- x y) (- t a)))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+59) || !(z <= 1.15e+119)) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = x + (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 ((z <= (-1.85d+59)) .or. (.not. (z <= 1.15d+119))) then
        tmp = z * ((x - y) / (t - a))
    else
        tmp = x + (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 ((z <= -1.85e+59) || !(z <= 1.15e+119)) {
		tmp = z * ((x - y) / (t - a));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+59) or not (z <= 1.15e+119):
		tmp = z * ((x - y) / (t - a))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+59) || !(z <= 1.15e+119))
		tmp = Float64(z * Float64(Float64(x - y) / Float64(t - a)));
	else
		tmp = Float64(x + 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 ((z <= -1.85e+59) || ~((z <= 1.15e+119)))
		tmp = z * ((x - y) / (t - a));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+59], N[Not[LessEqual[z, 1.15e+119]], $MachinePrecision]], N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999999e59 or 1.15e119 < z

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. +-commutative 65.4%

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

      3. distribute-lft-in 65.4%

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

      4. mul-1-neg 65.4%

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

      5. distribute-rgt-neg-in 65.4%

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

      6. associate-/l* 65.5%

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

      7. mul-1-neg 65.5%

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

      8. *-rgt-identity 65.5%

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

      9. associate-+l+ 63.3%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around inf 77.0%

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

      1. div-sub 78.2%

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

   8. Simplified 78.2%

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

   if -1.84999999999999999e59 < z < 1.15e119

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+59} \lor \neg \left(z \leq 1.15 \cdot 10^{+119}\right):\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+35} \lor \neg \left(t \leq 4.05 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e+35) (not (<= t 4.05e-19)))
   (* 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 <= -1.75e+35) || !(t <= 4.05e-19)) {
		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 <= (-1.75d+35)) .or. (.not. (t <= 4.05d-19))) 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 <= -1.75e+35) || !(t <= 4.05e-19)) {
		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 <= -1.75e+35) or not (t <= 4.05e-19):
		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 <= -1.75e+35) || !(t <= 4.05e-19))
		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 <= -1.75e+35) || ~((t <= 4.05e-19)))
		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, -1.75e+35], N[Not[LessEqual[t, 4.05e-19]], $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 < -1.75e35 or 4.05000000000000012e-19 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in y around -inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. *-commutative 65.8%

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

      3. distribute-rgt-neg-in 65.8%

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

      4. +-commutative 65.8%

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

      5. times-frac 74.5%

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

      6. distribute-rgt-out 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in x around 0 43.7%

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

      1. associate-/l* 65.4%

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

   8. Simplified 65.4%

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

   if -1.75e35 < t < 4.05000000000000012e-19

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 70.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   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 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+35} \lor \neg \left(t \leq 4.05 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+56}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+56)
   (+ x (* y (/ z a)))
   (if (<= a 6.2e+139) (* y (/ (- z t) (- a t))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+56) {
		tmp = x + (y * (z / a));
	} else if (a <= 6.2e+139) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d+56)) then
        tmp = x + (y * (z / a))
    else if (a <= 6.2d+139) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+56) {
		tmp = x + (y * (z / a));
	} else if (a <= 6.2e+139) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+56:
		tmp = x + (y * (z / a))
	elif a <= 6.2e+139:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+56)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 6.2e+139)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e+56)
		tmp = x + (y * (z / a));
	elseif (a <= 6.2e+139)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+56], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+139], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.99999999999999999e56

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 67.3%

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

   4. Taylor expanded in y around inf 67.5%

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

      1. associate-/l* 69.6%

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

   6. Simplified 69.6%

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

   if -6.99999999999999999e56 < a < 6.2e139

   1. Initial program 70.2%

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

   3. Taylor expanded in y around -inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. *-commutative 69.4%

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

      3. distribute-rgt-neg-in 69.4%

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

      4. +-commutative 69.4%

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

      5. times-frac 70.5%

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

      6. distribute-rgt-out 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in x around 0 45.9%

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

      1. associate-/l* 59.3%

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

   8. Simplified 59.3%

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

   if 6.2e139 < a

   1. Initial program 59.5%

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

   3. Taylor expanded in t around 0 63.9%

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

      1. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in y around inf 75.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+56}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.4e+187) y (if (<= t 4.1e-19) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+187) {
		tmp = y;
	} else if (t <= 4.1e-19) {
		tmp = x + (y * (z / a));
	} 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 <= (-5.4d+187)) then
        tmp = y
    else if (t <= 4.1d-19) then
        tmp = x + (y * (z / a))
    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 <= -5.4e+187) {
		tmp = y;
	} else if (t <= 4.1e-19) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.4e+187:
		tmp = y
	elif t <= 4.1e-19:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4e+187)
		tmp = y;
	elseif (t <= 4.1e-19)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.4e+187)
		tmp = y;
	elseif (t <= 4.1e-19)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4e+187], y, If[LessEqual[t, 4.1e-19], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.40000000000000016e187 or 4.09999999999999985e-19 < t

   1. Initial program 48.9%

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

   3. Taylor expanded in t around inf 52.9%

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

   if -5.40000000000000016e187 < t < 4.09999999999999985e-19

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 63.5%

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

   4. Taylor expanded in y around inf 50.9%

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

      1. associate-/l* 56.3%

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

   6. Simplified 56.3%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+187}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.7e+29) y (if (<= t 1.12e-20) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.7e+29) {
		tmp = y;
	} else if (t <= 1.12e-20) {
		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 <= (-5.7d+29)) then
        tmp = y
    else if (t <= 1.12d-20) 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 <= -5.7e+29) {
		tmp = y;
	} else if (t <= 1.12e-20) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.7e+29:
		tmp = y
	elif t <= 1.12e-20:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.7e+29)
		tmp = y;
	elseif (t <= 1.12e-20)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.7e+29)
		tmp = y;
	elseif (t <= 1.12e-20)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.7e+29], y, If[LessEqual[t, 1.12e-20], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6999999999999999e29 or 1.12000000000000002e-20 < t

   1. Initial program 52.9%

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

   3. Taylor expanded in t around inf 48.0%

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

   if -5.6999999999999999e29 < t < 1.12000000000000002e-20

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 31.6%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% 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 70.5%

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

3. Taylor expanded in a around inf 24.3%

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

4. Final simplification 24.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.0% 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 2024082 
(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))))