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

Percentage Accurate: 68.3% → 86.9%

Time: 16.1s

Alternatives: 17

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: 68.3% 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: 86.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+171} \lor \neg \left(t \leq 1.35 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \left(\left(\mathsf{fma}\left(-1, \frac{z}{t}, \mathsf{fma}\left(-1, a \cdot \frac{x}{t \cdot y}, \frac{a}{t}\right)\right) + x \cdot \frac{z}{t \cdot y}\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.95e+171) (not (<= t 1.35e+64)))
   (*
    y
    (+
     (+
      (fma -1.0 (/ z t) (fma -1.0 (* a (/ x (* t y))) (/ a t)))
      (* x (/ z (* t y))))
     1.0))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.95e+171) || !(t <= 1.35e+64)) {
		tmp = y * ((fma(-1.0, (z / t), fma(-1.0, (a * (x / (t * y))), (a / t))) + (x * (z / (t * y)))) + 1.0);
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.95e+171) || !(t <= 1.35e+64))
		tmp = Float64(y * Float64(Float64(fma(-1.0, Float64(z / t), fma(-1.0, Float64(a * Float64(x / Float64(t * y))), Float64(a / t))) + Float64(x * Float64(z / Float64(t * y)))) + 1.0));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.95e+171], N[Not[LessEqual[t, 1.35e+64]], $MachinePrecision]], N[(y * N[(N[(N[(-1.0 * N[(z / t), $MachinePrecision] + N[(-1.0 * N[(a * N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.95e171 or 1.35e64 < t

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. associate-/l* 56.8%

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

      3. fma-define 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. +-commutative 51.8%

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

      5. associate-/r* 50.1%

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

      6. associate-/l* 41.8%

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

      7. *-lft-identity 41.8%

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

      8. times-frac 44.8%

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

      9. /-rgt-identity 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in t around inf 85.4%

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

      1. associate--l+ 85.4%

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

      2. fma-define 85.4%

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

      3. fma-define 85.4%

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

      4. associate-/l* 92.2%

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

      5. mul-1-neg 92.2%

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

      6. associate-/l* 90.7%

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

   10. Simplified 90.7%

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

   if -1.95e171 < t < 1.35e64

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+171} \lor \neg \left(t \leq 1.35 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \left(\left(\mathsf{fma}\left(-1, \frac{z}{t}, \mathsf{fma}\left(-1, a \cdot \frac{x}{t \cdot y}, \frac{a}{t}\right)\right) + x \cdot \frac{z}{t \cdot y}\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+178} \lor \neg \left(t \leq 7.5 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot \left(\left(\left(\left(\frac{a}{t} - \frac{a \cdot x}{t \cdot y}\right) - \frac{z}{t}\right) + 1\right) + \frac{z \cdot x}{t \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+178) (not (<= t 7.5e+63)))
   (*
    y
    (+
     (+ (- (- (/ a t) (/ (* a x) (* t y))) (/ z t)) 1.0)
     (/ (* z x) (* t y))))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+178) || !(t <= 7.5e+63)) {
		tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0) + ((z * x) / (t * y)));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+178) || !(t <= 7.5e+63))
		tmp = Float64(y * Float64(Float64(Float64(Float64(Float64(a / t) - Float64(Float64(a * x) / Float64(t * y))) - Float64(z / t)) + 1.0) + Float64(Float64(z * x) / Float64(t * y))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+178], N[Not[LessEqual[t, 7.5e+63]], $MachinePrecision]], N[(y * N[(N[(N[(N[(N[(a / t), $MachinePrecision] - N[(N[(a * x), $MachinePrecision] / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e178 or 7.5000000000000005e63 < t

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. associate-/l* 56.8%

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

      3. fma-define 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. +-commutative 51.8%

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

      5. associate-/r* 50.1%

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

      6. associate-/l* 41.8%

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

      7. *-lft-identity 41.8%

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

      8. times-frac 44.8%

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

      9. /-rgt-identity 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in t around inf 85.4%

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

   if -1.2e178 < t < 7.5000000000000005e63

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+178} \lor \neg \left(t \leq 7.5 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot \left(\left(\left(\left(\frac{a}{t} - \frac{a \cdot x}{t \cdot y}\right) - \frac{z}{t}\right) + 1\right) + \frac{z \cdot x}{t \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+172} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot \left(\left(\left(\left(\frac{a}{t} - \frac{a \cdot x}{t \cdot y}\right) - \frac{z}{t}\right) + 1\right) + \frac{z \cdot x}{t \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+172) (not (<= t 3.8e+26)))
   (*
    y
    (+
     (+ (- (- (/ a t) (/ (* a x) (* t y))) (/ z t)) 1.0)
     (/ (* z x) (* t y))))
   (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+172) || !(t <= 3.8e+26)) {
		tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0) + ((z * x) / (t * y)));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (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 ((t <= (-2.8d+172)) .or. (.not. (t <= 3.8d+26))) then
        tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0d0) + ((z * x) / (t * y)))
    else
        tmp = x + ((z - t) * ((y - x) * ((-1.0d0) / (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 ((t <= -2.8e+172) || !(t <= 3.8e+26)) {
		tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0) + ((z * x) / (t * y)));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+172) or not (t <= 3.8e+26):
		tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0) + ((z * x) / (t * y)))
	else:
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+172) || !(t <= 3.8e+26))
		tmp = Float64(y * Float64(Float64(Float64(Float64(Float64(a / t) - Float64(Float64(a * x) / Float64(t * y))) - Float64(z / t)) + 1.0) + Float64(Float64(z * x) / Float64(t * y))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+172) || ~((t <= 3.8e+26)))
		tmp = y * (((((a / t) - ((a * x) / (t * y))) - (z / t)) + 1.0) + ((z * x) / (t * y)));
	else
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+172], N[Not[LessEqual[t, 3.8e+26]], $MachinePrecision]], N[(y * N[(N[(N[(N[(N[(a / t), $MachinePrecision] - N[(N[(a * x), $MachinePrecision] / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] / N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e172 or 3.8000000000000002e26 < t

   1. Initial program 34.4%

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

      1. +-commutative 34.4%

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

      2. associate-/l* 59.2%

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

      3. fma-define 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in y around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. +-commutative 54.7%

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

      5. associate-/r* 53.3%

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

      6. associate-/l* 45.9%

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

      7. *-lft-identity 45.9%

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

      8. times-frac 48.6%

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

      9. /-rgt-identity 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in t around inf 84.6%

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

   if -2.8e172 < t < 3.8000000000000002e26

   1. Initial program 81.8%

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

      1. div-inv 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*l* 93.6%

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

   4. Applied egg-rr 93.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+172} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot \left(\left(\left(\left(\frac{a}{t} - \frac{a \cdot x}{t \cdot y}\right) - \frac{z}{t}\right) + 1\right) + \frac{z \cdot x}{t \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+174}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+174)
   (+ y (* a (/ (- y x) t)))
   (if (<= t -5e+46)
     (+ x (* (- t z) (/ y (- t a))))
     (if (<= t 3e+18)
       (+ x (/ (* (- y x) (- z t)) (- a t)))
       (- y (/ (* (- x y) (- a z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+174) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -5e+46) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 3e+18) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = y - (((x - y) * (a - z)) / 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 (t <= (-6d+174)) then
        tmp = y + (a * ((y - x) / t))
    else if (t <= (-5d+46)) then
        tmp = x + ((t - z) * (y / (t - a)))
    else if (t <= 3d+18) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = y - (((x - y) * (a - z)) / 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 (t <= -6e+174) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -5e+46) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 3e+18) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+174:
		tmp = y + (a * ((y - x) / t))
	elif t <= -5e+46:
		tmp = x + ((t - z) * (y / (t - a)))
	elif t <= 3e+18:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+174)
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	elseif (t <= -5e+46)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	elseif (t <= 3e+18)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e+174)
		tmp = y + (a * ((y - x) / t));
	elseif (t <= -5e+46)
		tmp = x + ((t - z) * (y / (t - a)));
	elseif (t <= 3e+18)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+174], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e+46], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+18], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e174

   1. Initial program 29.4%

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

      1. +-commutative 29.4%

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

      2. associate-/l* 61.0%

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

      3. fma-define 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-*r/ 75.3%

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

      3. associate-*r/ 75.3%

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

      4. mul-1-neg 75.3%

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

      5. div-sub 75.3%

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

      6. mul-1-neg 75.3%

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

      7. distribute-lft-out-- 75.3%

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

      8. associate-*r/ 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

      11. distribute-rgt-out-- 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. sub-neg 66.9%

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

      2. mul-1-neg 66.9%

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

      3. remove-double-neg 66.9%

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

      4. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -6e174 < t < -5.0000000000000002e46

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf 61.5%

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

      1. *-commutative 61.5%

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

      2. *-lft-identity 61.5%

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

      3. times-frac 81.8%

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

      4. /-rgt-identity 81.8%

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

   5. Simplified 81.8%

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

   if -5.0000000000000002e46 < t < 3e18

   1. Initial program 88.7%

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

   if 3e18 < t

   1. Initial program 36.3%

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

      1. +-commutative 36.3%

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

      2. associate-/l* 59.1%

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

      3. fma-define 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in t around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-*r/ 77.1%

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

      3. associate-*r/ 77.1%

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

      4. mul-1-neg 77.1%

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

      5. div-sub 77.1%

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

      6. mul-1-neg 77.1%

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

      7. distribute-lft-out-- 77.1%

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

      8. associate-*r/ 77.1%

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

      9. mul-1-neg 77.1%

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

      10. unsub-neg 77.1%

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

      11. distribute-rgt-out-- 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+174}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+172}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.5e+172)
   (+ y (* a (/ (- y x) t)))
   (if (<= t -6.2e+72)
     (+ x (* (- t z) (/ y (- t a))))
     (if (<= t 3.6e+26)
       (+ x (* z (/ (- y x) (- a t))))
       (- y (/ (* (- x y) (- a z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+172) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -6.2e+72) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 3.6e+26) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / 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 (t <= (-3.5d+172)) then
        tmp = y + (a * ((y - x) / t))
    else if (t <= (-6.2d+72)) then
        tmp = x + ((t - z) * (y / (t - a)))
    else if (t <= 3.6d+26) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = y - (((x - y) * (a - z)) / 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 (t <= -3.5e+172) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -6.2e+72) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 3.6e+26) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.5e+172:
		tmp = y + (a * ((y - x) / t))
	elif t <= -6.2e+72:
		tmp = x + ((t - z) * (y / (t - a)))
	elif t <= 3.6e+26:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.5e+172)
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	elseif (t <= -6.2e+72)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	elseif (t <= 3.6e+26)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.5e+172)
		tmp = y + (a * ((y - x) / t));
	elseif (t <= -6.2e+72)
		tmp = x + ((t - z) * (y / (t - a)));
	elseif (t <= 3.6e+26)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.5e+172], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e+72], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+26], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.49999999999999977e172

   1. Initial program 29.4%

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

      1. +-commutative 29.4%

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

      2. associate-/l* 61.0%

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

      3. fma-define 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-*r/ 75.3%

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

      3. associate-*r/ 75.3%

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

      4. mul-1-neg 75.3%

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

      5. div-sub 75.3%

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

      6. mul-1-neg 75.3%

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

      7. distribute-lft-out-- 75.3%

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

      8. associate-*r/ 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

      11. distribute-rgt-out-- 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. sub-neg 66.9%

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

      2. mul-1-neg 66.9%

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

      3. remove-double-neg 66.9%

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

      4. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -3.49999999999999977e172 < t < -6.19999999999999977e72

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-lft-identity 59.7%

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

      3. times-frac 81.3%

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

      4. /-rgt-identity 81.3%

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

   5. Simplified 81.3%

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

   if -6.19999999999999977e72 < t < 3.60000000000000024e26

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

   if 3.60000000000000024e26 < t

   1. Initial program 37.0%

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

      1. +-commutative 37.0%

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

      2. associate-/l* 58.3%

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

      3. fma-define 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in t around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. associate-*r/ 78.5%

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

      4. mul-1-neg 78.5%

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

      5. div-sub 78.5%

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

      6. mul-1-neg 78.5%

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

      7. distribute-lft-out-- 78.5%

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

      8. associate-*r/ 78.5%

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

      9. mul-1-neg 78.5%

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

      10. unsub-neg 78.5%

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

      11. distribute-rgt-out-- 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+172}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+171)
   (+ y (* a (/ (- y x) t)))
   (if (<= t -1.12e+73)
     (+ x (* (- t z) (/ y (- t a))))
     (if (<= t 2.9e+22)
       (+ x (* z (/ (- y x) (- a t))))
       (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+171) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -1.12e+73) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 2.9e+22) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d+171)) then
        tmp = y + (a * ((y - x) / t))
    else if (t <= (-1.12d+73)) then
        tmp = x + ((t - z) * (y / (t - a)))
    else if (t <= 2.9d+22) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+171) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= -1.12e+73) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else if (t <= 2.9e+22) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+171:
		tmp = y + (a * ((y - x) / t))
	elif t <= -1.12e+73:
		tmp = x + ((t - z) * (y / (t - a)))
	elif t <= 2.9e+22:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+171)
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	elseif (t <= -1.12e+73)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	elseif (t <= 2.9e+22)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+171)
		tmp = y + (a * ((y - x) / t));
	elseif (t <= -1.12e+73)
		tmp = x + ((t - z) * (y / (t - a)));
	elseif (t <= 2.9e+22)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+171], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e+73], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+22], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2500000000000001e171

   1. Initial program 29.4%

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

      1. +-commutative 29.4%

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

      2. associate-/l* 61.0%

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

      3. fma-define 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-*r/ 75.3%

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

      3. associate-*r/ 75.3%

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

      4. mul-1-neg 75.3%

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

      5. div-sub 75.3%

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

      6. mul-1-neg 75.3%

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

      7. distribute-lft-out-- 75.3%

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

      8. associate-*r/ 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

      11. distribute-rgt-out-- 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. sub-neg 66.9%

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

      2. mul-1-neg 66.9%

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

      3. remove-double-neg 66.9%

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

      4. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -1.2500000000000001e171 < t < -1.12e73

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-lft-identity 59.7%

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

      3. times-frac 81.3%

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

      4. /-rgt-identity 81.3%

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

   5. Simplified 81.3%

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

   if -1.12e73 < t < 2.9e22

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

   if 2.9e22 < t

   1. Initial program 37.0%

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

      1. +-commutative 37.0%

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

      2. associate-/l* 58.3%

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

      3. fma-define 58.3%

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

   3. Simplified 58.3%

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

      1. clear-num 58.2%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   7. Taylor expanded in y around inf 70.9%

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

      1. div-sub 70.9%

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

   9. Simplified 70.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+171}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+22}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+177}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+177)
   (+ y (* a (/ (- y x) t)))
   (if (<= t 3.8e+26)
     (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a)))))
     (- y (/ (* (- x y) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+177) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= 3.8e+26) {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	} else {
		tmp = y - (((x - y) * (a - z)) / 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 (t <= (-5.6d+177)) then
        tmp = y + (a * ((y - x) / t))
    else if (t <= 3.8d+26) then
        tmp = x + ((z - t) * ((y - x) * ((-1.0d0) / (t - a))))
    else
        tmp = y - (((x - y) * (a - z)) / 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 (t <= -5.6e+177) {
		tmp = y + (a * ((y - x) / t));
	} else if (t <= 3.8e+26) {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+177:
		tmp = y + (a * ((y - x) / t))
	elif t <= 3.8e+26:
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+177)
		tmp = Float64(y + Float64(a * Float64(Float64(y - x) / t)));
	elseif (t <= 3.8e+26)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+177)
		tmp = y + (a * ((y - x) / t));
	elseif (t <= 3.8e+26)
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+177], N[(y + N[(a * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+26], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000004e177

   1. Initial program 29.4%

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

      1. +-commutative 29.4%

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

      2. associate-/l* 61.0%

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

      3. fma-define 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-*r/ 75.3%

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

      3. associate-*r/ 75.3%

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

      4. mul-1-neg 75.3%

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

      5. div-sub 75.3%

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

      6. mul-1-neg 75.3%

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

      7. distribute-lft-out-- 75.3%

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

      8. associate-*r/ 75.3%

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

      9. mul-1-neg 75.3%

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

      10. unsub-neg 75.3%

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

      11. distribute-rgt-out-- 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around 0 66.9%

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

      1. sub-neg 66.9%

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

      2. mul-1-neg 66.9%

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

      3. remove-double-neg 66.9%

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

      4. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -5.60000000000000004e177 < t < 3.8000000000000002e26

   1. Initial program 81.8%

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

      1. div-inv 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*l* 93.6%

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

   4. Applied egg-rr 93.6%

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

   if 3.8000000000000002e26 < t

   1. Initial program 37.0%

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

      1. +-commutative 37.0%

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

      2. associate-/l* 58.3%

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

      3. fma-define 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in t around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. associate-*r/ 78.5%

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

      4. mul-1-neg 78.5%

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

      5. div-sub 78.5%

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

      6. mul-1-neg 78.5%

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

      7. distribute-lft-out-- 78.5%

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

      8. associate-*r/ 78.5%

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

      9. mul-1-neg 78.5%

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

      10. unsub-neg 78.5%

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

      11. distribute-rgt-out-- 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+177}:\\ \;\;\;\;y + a \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+88}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4800000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e+88)
   y
   (if (<= t -4800000000000.0)
     x
     (if (<= t 4e-98) (* z (/ (- y x) a)) (if (<= t 4.5e+23) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+88) {
		tmp = y;
	} else if (t <= -4800000000000.0) {
		tmp = x;
	} else if (t <= 4e-98) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.5e+23) {
		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 <= (-9.8d+88)) then
        tmp = y
    else if (t <= (-4800000000000.0d0)) then
        tmp = x
    else if (t <= 4d-98) then
        tmp = z * ((y - x) / a)
    else if (t <= 4.5d+23) 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 <= -9.8e+88) {
		tmp = y;
	} else if (t <= -4800000000000.0) {
		tmp = x;
	} else if (t <= 4e-98) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.5e+23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e+88:
		tmp = y
	elif t <= -4800000000000.0:
		tmp = x
	elif t <= 4e-98:
		tmp = z * ((y - x) / a)
	elif t <= 4.5e+23:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e+88)
		tmp = y;
	elseif (t <= -4800000000000.0)
		tmp = x;
	elseif (t <= 4e-98)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4.5e+23)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.8e+88)
		tmp = y;
	elseif (t <= -4800000000000.0)
		tmp = x;
	elseif (t <= 4e-98)
		tmp = z * ((y - x) / a);
	elseif (t <= 4.5e+23)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e+88], y, If[LessEqual[t, -4800000000000.0], x, If[LessEqual[t, 4e-98], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+23], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.8000000000000005e88 or 4.49999999999999979e23 < t

   1. Initial program 38.1%

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

      1. +-commutative 38.1%

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

      2. associate-/l* 66.0%

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

      3. fma-define 66.0%

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

   3. Simplified 66.0%

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

      1. clear-num 66.0%

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

      2. associate-/r/ 66.0%

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

   6. Applied egg-rr 66.0%

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

   7. Taylor expanded in t around inf 52.7%

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

   if -9.8000000000000005e88 < t < -4.8e12 or 3.99999999999999976e-98 < t < 4.49999999999999979e23

   1. Initial program 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 93.2%

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

      3. fma-define 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 44.9%

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

   if -4.8e12 < t < 3.99999999999999976e-98

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-/l* 94.8%

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

      3. fma-define 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 61.3%

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

   6. Taylor expanded in a around inf 50.1%

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

Alternative 9: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-174}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.38e+112)
   x
   (if (<= a -1.7e-100)
     (* z (/ y (- a t)))
     (if (<= a 6.5e-174) (* z (/ x (- t a))) (if (<= a 9.2e+86) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.38e+112) {
		tmp = x;
	} else if (a <= -1.7e-100) {
		tmp = z * (y / (a - t));
	} else if (a <= 6.5e-174) {
		tmp = z * (x / (t - a));
	} else if (a <= 9.2e+86) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.38d+112)) then
        tmp = x
    else if (a <= (-1.7d-100)) then
        tmp = z * (y / (a - t))
    else if (a <= 6.5d-174) then
        tmp = z * (x / (t - a))
    else if (a <= 9.2d+86) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.38e+112) {
		tmp = x;
	} else if (a <= -1.7e-100) {
		tmp = z * (y / (a - t));
	} else if (a <= 6.5e-174) {
		tmp = z * (x / (t - a));
	} else if (a <= 9.2e+86) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.38e+112:
		tmp = x
	elif a <= -1.7e-100:
		tmp = z * (y / (a - t))
	elif a <= 6.5e-174:
		tmp = z * (x / (t - a))
	elif a <= 9.2e+86:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.38e+112)
		tmp = x;
	elseif (a <= -1.7e-100)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (a <= 6.5e-174)
		tmp = Float64(z * Float64(x / Float64(t - a)));
	elseif (a <= 9.2e+86)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.38e+112)
		tmp = x;
	elseif (a <= -1.7e-100)
		tmp = z * (y / (a - t));
	elseif (a <= 6.5e-174)
		tmp = z * (x / (t - a));
	elseif (a <= 9.2e+86)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.38e+112], x, If[LessEqual[a, -1.7e-100], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-174], N[(z * N[(x / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+86], y, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3800000000000001e112 or 9.19999999999999958e86 < a

   1. Initial program 63.7%

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

      1. +-commutative 63.7%

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

      2. associate-/l* 92.0%

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

      3. fma-define 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in a around inf 57.8%

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

   if -1.3800000000000001e112 < a < -1.69999999999999988e-100

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 84.9%

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

      3. fma-define 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in z around inf 55.4%

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

   6. Taylor expanded in y around inf 41.9%

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

   if -1.69999999999999988e-100 < a < 6.50000000000000009e-174

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-/l* 75.2%

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

      3. fma-define 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in z around inf 57.8%

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

   6. Taylor expanded in y around 0 43.7%

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

      1. neg-mul-1 43.7%

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

      2. distribute-neg-frac2 43.7%

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

   8. Simplified 43.7%

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

   9. Taylor expanded in a around 0 43.7%

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

       1. neg-mul-1 43.7%

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

       2. sub-neg 43.7%

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

   11. Simplified 43.7%

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

   if 6.50000000000000009e-174 < a < 9.19999999999999958e86

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-/l* 78.2%

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

      3. fma-define 78.2%

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

   3. Simplified 78.2%

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

      1. clear-num 78.1%

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

      2. associate-/r/ 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in t around inf 36.4%

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

Alternative 10: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \frac{x}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+89)
   y
   (if (<= t 8.2e-261) x (if (<= t 1.05e+71) (* z (/ x (- t a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+89) {
		tmp = y;
	} else if (t <= 8.2e-261) {
		tmp = x;
	} else if (t <= 1.05e+71) {
		tmp = z * (x / (t - 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 <= (-1.15d+89)) then
        tmp = y
    else if (t <= 8.2d-261) then
        tmp = x
    else if (t <= 1.05d+71) then
        tmp = z * (x / (t - 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 <= -1.15e+89) {
		tmp = y;
	} else if (t <= 8.2e-261) {
		tmp = x;
	} else if (t <= 1.05e+71) {
		tmp = z * (x / (t - a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+89:
		tmp = y
	elif t <= 8.2e-261:
		tmp = x
	elif t <= 1.05e+71:
		tmp = z * (x / (t - a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+89)
		tmp = y;
	elseif (t <= 8.2e-261)
		tmp = x;
	elseif (t <= 1.05e+71)
		tmp = Float64(z * Float64(x / Float64(t - a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+89)
		tmp = y;
	elseif (t <= 8.2e-261)
		tmp = x;
	elseif (t <= 1.05e+71)
		tmp = z * (x / (t - a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+89], y, If[LessEqual[t, 8.2e-261], x, If[LessEqual[t, 1.05e+71], N[(z * N[(x / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1499999999999999e89 or 1.04999999999999995e71 < t

   1. Initial program 34.8%

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

      1. +-commutative 34.8%

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

      2. associate-/l* 65.1%

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

      3. fma-define 65.1%

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

   3. Simplified 65.1%

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

      1. clear-num 65.0%

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

      2. associate-/r/ 65.1%

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

   6. Applied egg-rr 65.1%

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

   7. Taylor expanded in t around inf 55.4%

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

   if -1.1499999999999999e89 < t < 8.2000000000000003e-261

   1. Initial program 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 38.2%

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

   if 8.2000000000000003e-261 < t < 1.04999999999999995e71

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 92.5%

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

      3. fma-define 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf 64.3%

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

   6. Taylor expanded in y around 0 39.3%

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

      1. neg-mul-1 39.3%

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

      2. distribute-neg-frac2 39.3%

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

   8. Simplified 39.3%

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

   9. Taylor expanded in a around 0 39.3%

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

       1. neg-mul-1 39.3%

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

       2. sub-neg 39.3%

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

   11. Simplified 39.3%

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

Alternative 11: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+101} \lor \neg \left(t \leq 3.1 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.9e+101) (not (<= t 3.1e+25)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.9e+101) || !(t <= 3.1e+25)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (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 ((t <= (-1.9d+101)) .or. (.not. (t <= 3.1d+25))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((y - x) / (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 ((t <= -1.9e+101) || !(t <= 3.1e+25)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.9e+101) or not (t <= 3.1e+25):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.9e+101) || !(t <= 3.1e+25))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.9e+101) || ~((t <= 3.1e+25)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.9e+101], N[Not[LessEqual[t, 3.1e+25]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8999999999999999e101 or 3.0999999999999998e25 < t

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-/l* 65.0%

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

      3. fma-define 65.0%

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

   3. Simplified 65.0%

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

      1. clear-num 64.9%

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

      2. associate-/r/ 64.9%

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

   6. Applied egg-rr 64.9%

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

   7. Taylor expanded in y around inf 71.3%

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

      1. div-sub 71.3%

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

   9. Simplified 71.3%

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

   if -1.8999999999999999e101 < t < 3.0999999999999998e25

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+101} \lor \neg \left(t \leq 3.1 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+67} \lor \neg \left(t \leq 3.1 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e+67) (not (<= t 3.1e+18)))
   (* 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 <= -3e+67) || !(t <= 3.1e+18)) {
		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 <= (-3d+67)) .or. (.not. (t <= 3.1d+18))) 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 <= -3e+67) || !(t <= 3.1e+18)) {
		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 <= -3e+67) or not (t <= 3.1e+18):
		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 <= -3e+67) || !(t <= 3.1e+18))
		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 <= -3e+67) || ~((t <= 3.1e+18)))
		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, -3e+67], N[Not[LessEqual[t, 3.1e+18]], $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 < -3.0000000000000001e67 or 3.1e18 < t

   1. Initial program 38.6%

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

      1. +-commutative 38.6%

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

      2. associate-/l* 66.5%

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

      3. fma-define 66.5%

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

   3. Simplified 66.5%

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

      1. clear-num 66.4%

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

      2. associate-/r/ 66.4%

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

   6. Applied egg-rr 66.4%

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

   7. Taylor expanded in y around inf 69.5%

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

      1. div-sub 69.5%

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

   9. Simplified 69.5%

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

   if -3.0000000000000001e67 < t < 3.1e18

   1. Initial program 87.8%

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

   3. Taylor expanded in t around 0 66.2%

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

      1. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+67} \lor \neg \left(t \leq 3.1 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{+112} \lor \neg \left(a \leq 8.2 \cdot 10^{+91}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.38e+112) (not (<= a 8.2e+91)))
   (+ x (* y (/ (- z t) a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.38e+112) || !(a <= 8.2e+91)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.38d+112)) .or. (.not. (a <= 8.2d+91))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.38e+112) || !(a <= 8.2e+91)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.38e+112) or not (a <= 8.2e+91):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.38e+112) || !(a <= 8.2e+91))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.38e+112) || ~((a <= 8.2e+91)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.38e+112], N[Not[LessEqual[a, 8.2e+91]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3800000000000001e112 or 8.2000000000000005e91 < a

   1. Initial program 63.7%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around inf 65.6%

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

      1. associate-/l* 75.2%

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

   8. Simplified 75.2%

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

   if -1.3800000000000001e112 < a < 8.2000000000000005e91

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-/l* 78.7%

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

      3. fma-define 78.7%

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

   3. Simplified 78.7%

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

      1. clear-num 78.6%

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

      2. associate-/r/ 78.5%

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

   6. Applied egg-rr 78.5%

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

   7. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   9. Simplified 65.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{+112} \lor \neg \left(a \leq 8.2 \cdot 10^{+91}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+112} \lor \neg \left(a \leq 4.1 \cdot 10^{+92}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9e+112) (not (<= a 4.1e+92)))
   (+ x (* y (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9e+112) || !(a <= 4.1e+92)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9d+112)) .or. (.not. (a <= 4.1d+92))) then
        tmp = x + (y * (z / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9e+112) || !(a <= 4.1e+92)) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9e+112) or not (a <= 4.1e+92):
		tmp = x + (y * (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9e+112) || !(a <= 4.1e+92))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9e+112) || ~((a <= 4.1e+92)))
		tmp = x + (y * (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9e+112], N[Not[LessEqual[a, 4.1e+92]], $MachinePrecision]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.9999999999999998e112 or 4.10000000000000024e92 < a

   1. Initial program 63.7%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around inf 65.6%

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

      1. associate-/l* 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in z around inf 63.1%

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

       1. associate-/l* 71.0%

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

   11. Simplified 71.0%

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

   if -8.9999999999999998e112 < a < 4.10000000000000024e92

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-/l* 78.7%

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

      3. fma-define 78.7%

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

   3. Simplified 78.7%

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

      1. clear-num 78.6%

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

      2. associate-/r/ 78.5%

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

   6. Applied egg-rr 78.5%

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

   7. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   9. Simplified 65.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+112} \lor \neg \left(a \leq 4.1 \cdot 10^{+92}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+89) y (if (<= t 3.2e+26) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+89) {
		tmp = y;
	} else if (t <= 3.2e+26) {
		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 <= (-6.2d+89)) then
        tmp = y
    else if (t <= 3.2d+26) 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 <= -6.2e+89) {
		tmp = y;
	} else if (t <= 3.2e+26) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+89:
		tmp = y
	elif t <= 3.2e+26:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+89)
		tmp = y;
	elseif (t <= 3.2e+26)
		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 <= -6.2e+89)
		tmp = y;
	elseif (t <= 3.2e+26)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+89], y, If[LessEqual[t, 3.2e+26], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e89 or 3.20000000000000029e26 < t

   1. Initial program 38.1%

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

      1. +-commutative 38.1%

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

      2. associate-/l* 66.0%

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

      3. fma-define 66.0%

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

   3. Simplified 66.0%

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

      1. clear-num 66.0%

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

      2. associate-/r/ 66.0%

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

   6. Applied egg-rr 66.0%

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

   7. Taylor expanded in t around inf 52.7%

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

   if -6.2e89 < t < 3.20000000000000029e26

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around inf 55.4%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in z around inf 51.6%

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

       1. associate-/l* 56.7%

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

   11. Simplified 56.7%

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

Alternative 16: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{+89}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e+101) x (if (<= a 3.85e+89) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+101) {
		tmp = x;
	} else if (a <= 3.85e+89) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.1d+101)) then
        tmp = x
    else if (a <= 3.85d+89) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+101) {
		tmp = x;
	} else if (a <= 3.85e+89) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e+101:
		tmp = x
	elif a <= 3.85e+89:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e+101)
		tmp = x;
	elseif (a <= 3.85e+89)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e+101)
		tmp = x;
	elseif (a <= 3.85e+89)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e+101], x, If[LessEqual[a, 3.85e+89], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999999e101 or 3.8500000000000002e89 < a

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 56.0%

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

   if -3.09999999999999999e101 < a < 3.8500000000000002e89

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-/l* 78.3%

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

      3. fma-define 78.3%

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

   3. Simplified 78.3%

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

      1. clear-num 78.2%

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

      2. associate-/r/ 78.1%

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

   6. Applied egg-rr 78.1%

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

   7. Taylor expanded in t around inf 34.8%

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

Alternative 17: 24.1% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

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

   1. +-commutative 67.0%

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

   2. associate-/l* 83.2%

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

   3. fma-define 83.2%

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

3. Simplified 83.2%

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

5. Taylor expanded in a around inf 23.4%

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

Developer Target 1: 87.1% 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 2024141 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

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