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

Percentage Accurate: 68.3% → 90.3%

Time: 17.6s

Alternatives: 19

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-260} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-260) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (- y (/ (* (- y x) (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-260) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - (((y - x) * (z - a)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-260) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-260], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000003e-260 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.6%

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

      1. +-commutative 69.6%

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

      2. associate-/l* 90.6%

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

      3. fma-define 90.6%

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

   3. Simplified 90.6%

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

   if -5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.5%

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

      1. +-commutative 9.5%

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

      2. associate-/l* 9.4%

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

      3. fma-define 9.5%

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

   3. Simplified 9.5%

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

      1. clear-num 9.5%

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

      2. inv-pow 9.5%

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

   6. Applied egg-rr 9.5%

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

      1. unpow-1 9.5%

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

   8. Simplified 9.5%

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

   9. Taylor expanded in t around inf 99.8%

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

       1. associate--l+ 99.8%

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

       2. associate-*r/ 99.8%

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

       3. associate-*r/ 99.8%

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

       4. mul-1-neg 99.8%

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

       5. div-sub 99.9%

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

       6. mul-1-neg 99.9%

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

       7. distribute-lft-out-- 99.9%

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

       8. associate-*r/ 99.9%

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

       9. mul-1-neg 99.9%

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

       10. distribute-rgt-out-- 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-260} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-260)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= t_2 4e+295)
           (+ x (/ -1.0 (/ (- a t) (* (- y x) (- t z)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-260) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 4e+295) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-260) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 4e+295) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-260:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	elif t_2 <= 4e+295:
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-260)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (t_2 <= 4e+295)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / Float64(Float64(y - x) * Float64(t - z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-260)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (t_2 <= 4e+295)
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-260], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+295], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 3.9999999999999999e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 37.3%

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

   3. Taylor expanded in t around inf 46.1%

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

      1. associate--l+ 46.1%

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

      2. distribute-lft-out-- 46.1%

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

      3. div-sub 50.8%

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

      4. mul-1-neg 50.8%

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

      5. unsub-neg 50.8%

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

      6. div-sub 46.1%

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

      7. associate-/l* 59.6%

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

      8. associate-/l* 60.6%

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

      9. distribute-rgt-out-- 69.4%

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

   5. Simplified 69.4%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000003e-260

   1. Initial program 95.9%

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

   if -5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.5%

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

      1. +-commutative 9.5%

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

      2. associate-/l* 9.4%

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

      3. fma-define 9.5%

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

   3. Simplified 9.5%

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

      1. clear-num 9.5%

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

      2. inv-pow 9.5%

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

   6. Applied egg-rr 9.5%

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

      1. unpow-1 9.5%

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

   8. Simplified 9.5%

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

   9. Taylor expanded in t around inf 99.8%

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

       1. associate--l+ 99.8%

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

       2. associate-*r/ 99.8%

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

       3. associate-*r/ 99.8%

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

       4. mul-1-neg 99.8%

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

       5. div-sub 99.9%

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

       6. mul-1-neg 99.9%

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

       7. distribute-lft-out-- 99.9%

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

       8. associate-*r/ 99.9%

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

       9. mul-1-neg 99.9%

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

       10. distribute-rgt-out-- 100.0%

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

   11. Simplified 100.0%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999999e295

   1. Initial program 94.4%

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

      1. clear-num 94.4%

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

      2. inv-pow 94.4%

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

      3. *-commutative 94.4%

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

      4. associate-/r* 93.5%

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

   4. Applied egg-rr 93.5%

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

      1. unpow-1 93.5%

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

      2. associate-/l/ 94.4%

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

      3. *-commutative 94.4%

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

   6. Simplified 94.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (* x (* (/ (- z t) (- a t)) (+ -1.0 (/ y x)))))
     (if (<= t_1 -5e-260)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= t_1 4e+295)
           (+ x (/ -1.0 (/ (- a t) (* (- y x) (- t z)))))
           (+ y (* (- z a) (/ (- x y) t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t_1 <= -5e-260) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_1 <= 4e+295) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	} else if (t_1 <= -5e-260) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_1 <= 4e+295) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))))
	elif t_1 <= -5e-260:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	elif t_1 <= 4e+295:
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))))
	else:
		tmp = y + ((z - a) * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(x * Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(-1.0 + Float64(y / x)))));
	elseif (t_1 <= -5e-260)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (t_1 <= 4e+295)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / Float64(Float64(y - x) * Float64(t - z)))));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (x * (((z - t) / (a - t)) * (-1.0 + (y / x))));
	elseif (t_1 <= -5e-260)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (t_1 <= 4e+295)
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	else
		tmp = y + ((z - a) * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-260], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+295], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 37.7%

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

   3. Taylor expanded in x around inf 41.0%

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

      1. times-frac 68.3%

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

      2. distribute-rgt-out 74.9%

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

   5. Simplified 74.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000003e-260

   1. Initial program 95.9%

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

   if -5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.5%

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

      1. +-commutative 9.5%

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

      2. associate-/l* 9.4%

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

      3. fma-define 9.5%

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

   3. Simplified 9.5%

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

      1. clear-num 9.5%

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

      2. inv-pow 9.5%

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

   6. Applied egg-rr 9.5%

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

      1. unpow-1 9.5%

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

   8. Simplified 9.5%

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

   9. Taylor expanded in t around inf 99.8%

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

       1. associate--l+ 99.8%

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

       2. associate-*r/ 99.8%

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

       3. associate-*r/ 99.8%

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

       4. mul-1-neg 99.8%

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

       5. div-sub 99.9%

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

       6. mul-1-neg 99.9%

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

       7. distribute-lft-out-- 99.9%

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

       8. associate-*r/ 99.9%

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

       9. mul-1-neg 99.9%

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

       10. distribute-rgt-out-- 100.0%

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

   11. Simplified 100.0%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999999e295

   1. Initial program 94.4%

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

      1. clear-num 94.4%

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

      2. inv-pow 94.4%

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

      3. *-commutative 94.4%

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

      4. associate-/r* 93.5%

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

   4. Applied egg-rr 93.5%

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

      1. unpow-1 93.5%

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

      2. associate-/l/ 94.4%

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

      3. *-commutative 94.4%

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

   6. Simplified 94.4%

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

   if 3.9999999999999999e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 37.0%

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

   3. Taylor expanded in t around inf 52.1%

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

      1. associate--l+ 52.1%

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

      2. distribute-lft-out-- 52.1%

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

      3. div-sub 55.5%

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

      4. mul-1-neg 55.5%

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

      5. unsub-neg 55.5%

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

      6. div-sub 52.1%

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

      7. associate-/l* 68.3%

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

      8. associate-/l* 68.2%

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

      9. distribute-rgt-out-- 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + x \cdot \left(\frac{z - t}{a - t} \cdot \left(-1 + \frac{y}{x}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-260)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= t_2 4e+295) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-260) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 4e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-260) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (t_2 <= 4e+295) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-260:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((y - x) * (z - a)) / t)
	elif t_2 <= 4e+295:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-260)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (t_2 <= 4e+295)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-260)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (t_2 <= 4e+295)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-260], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+295], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 3.9999999999999999e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 37.3%

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

   3. Taylor expanded in t around inf 46.1%

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

      1. associate--l+ 46.1%

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

      2. distribute-lft-out-- 46.1%

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

      3. div-sub 50.8%

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

      4. mul-1-neg 50.8%

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

      5. unsub-neg 50.8%

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

      6. div-sub 46.1%

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

      7. associate-/l* 59.6%

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

      8. associate-/l* 60.6%

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

      9. distribute-rgt-out-- 69.4%

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

   5. Simplified 69.4%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.0000000000000003e-260 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999999e295

   1. Initial program 95.0%

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

   if -5.0000000000000003e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 9.5%

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

      1. +-commutative 9.5%

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

      2. associate-/l* 9.4%

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

      3. fma-define 9.5%

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

   3. Simplified 9.5%

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

      1. clear-num 9.5%

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

      2. inv-pow 9.5%

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

   6. Applied egg-rr 9.5%

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

      1. unpow-1 9.5%

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

   8. Simplified 9.5%

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

   9. Taylor expanded in t around inf 99.8%

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

       1. associate--l+ 99.8%

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

       2. associate-*r/ 99.8%

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

       3. associate-*r/ 99.8%

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

       4. mul-1-neg 99.8%

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

       5. div-sub 99.9%

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

       6. mul-1-neg 99.9%

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

       7. distribute-lft-out-- 99.9%

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

       8. associate-*r/ 99.9%

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

       9. mul-1-neg 99.9%

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

       10. distribute-rgt-out-- 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+153}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y a)))))
   (if (<= t -2.3e+153)
     y
     (if (<= t -8.6e+53)
       t_1
       (if (<= t -2.95e+51)
         (+ x y)
         (if (<= t -1.6e-187)
           (+ x (* y (/ z a)))
           (if (<= t -1.22e-299)
             (* z (/ (- y x) a))
             (if (<= t 1.66e+24)
               (* x (- 1.0 (/ z a)))
               (if (<= t 7.5e+113) t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double tmp;
	if (t <= -2.3e+153) {
		tmp = y;
	} else if (t <= -8.6e+53) {
		tmp = t_1;
	} else if (t <= -2.95e+51) {
		tmp = x + y;
	} else if (t <= -1.6e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.22e-299) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.66e+24) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 7.5e+113) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / a))
    if (t <= (-2.3d+153)) then
        tmp = y
    else if (t <= (-8.6d+53)) then
        tmp = t_1
    else if (t <= (-2.95d+51)) then
        tmp = x + y
    else if (t <= (-1.6d-187)) then
        tmp = x + (y * (z / a))
    else if (t <= (-1.22d-299)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.66d+24) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 7.5d+113) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double tmp;
	if (t <= -2.3e+153) {
		tmp = y;
	} else if (t <= -8.6e+53) {
		tmp = t_1;
	} else if (t <= -2.95e+51) {
		tmp = x + y;
	} else if (t <= -1.6e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.22e-299) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.66e+24) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 7.5e+113) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / a))
	tmp = 0
	if t <= -2.3e+153:
		tmp = y
	elif t <= -8.6e+53:
		tmp = t_1
	elif t <= -2.95e+51:
		tmp = x + y
	elif t <= -1.6e-187:
		tmp = x + (y * (z / a))
	elif t <= -1.22e-299:
		tmp = z * ((y - x) / a)
	elif t <= 1.66e+24:
		tmp = x * (1.0 - (z / a))
	elif t <= 7.5e+113:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -2.3e+153)
		tmp = y;
	elseif (t <= -8.6e+53)
		tmp = t_1;
	elseif (t <= -2.95e+51)
		tmp = Float64(x + y);
	elseif (t <= -1.6e-187)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -1.22e-299)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.66e+24)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 7.5e+113)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / a));
	tmp = 0.0;
	if (t <= -2.3e+153)
		tmp = y;
	elseif (t <= -8.6e+53)
		tmp = t_1;
	elseif (t <= -2.95e+51)
		tmp = x + y;
	elseif (t <= -1.6e-187)
		tmp = x + (y * (z / a));
	elseif (t <= -1.22e-299)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.66e+24)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 7.5e+113)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+153], y, If[LessEqual[t, -8.6e+53], t$95$1, If[LessEqual[t, -2.95e+51], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.6e-187], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.22e-299], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.66e+24], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+113], t$95$1, y]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.3000000000000001e153 or 7.5000000000000001e113 < t

   1. Initial program 34.8%

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

   3. Taylor expanded in t around inf 62.2%

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

   if -2.3000000000000001e153 < t < -8.5999999999999995e53 or 1.65999999999999991e24 < t < 7.5000000000000001e113

   1. Initial program 58.3%

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

   3. Taylor expanded in z around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. unsub-neg 41.6%

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

      3. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around inf 45.0%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

   9. Taylor expanded in t around 0 37.5%

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

       1. mul-1-neg 37.5%

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

       2. unsub-neg 37.5%

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

       3. associate-/l* 49.7%

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

   11. Simplified 49.7%

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

   if -8.5999999999999995e53 < t < -2.94999999999999991e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in t around inf 54.7%

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

       1. sub-neg 54.7%

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

       2. mul-1-neg 54.7%

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

       3. remove-double-neg 54.7%

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

       4. +-commutative 54.7%

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

   11. Simplified 54.7%

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

   if -2.94999999999999991e51 < t < -1.5999999999999999e-187

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 64.8%

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

   4. Taylor expanded in y around inf 62.0%

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

      1. associate-/l* 64.6%

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

   6. Simplified 64.6%

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

   if -1.5999999999999999e-187 < t < -1.22e-299

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 87.0%

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

   4. Taylor expanded in z around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if -1.22e-299 < t < 1.65999999999999991e24

   1. Initial program 88.5%

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

   3. Taylor expanded in t around 0 66.3%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in x around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

   8. Simplified 58.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+153}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+53}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 15000:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.8e+39)
     t_2
     (if (<= t 1.95e-90)
       t_1
       (if (<= t 1.3e-54)
         t_2
         (if (<= t 1.22e-27)
           t_1
           (if (<= t 15000.0)
             (* z (/ (- y x) (- a t)))
             (if (<= t 3.6e+26) (* x (- 1.0 (/ z a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.8e+39) {
		tmp = t_2;
	} else if (t <= 1.95e-90) {
		tmp = t_1;
	} else if (t <= 1.3e-54) {
		tmp = t_2;
	} else if (t <= 1.22e-27) {
		tmp = t_1;
	} else if (t <= 15000.0) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 3.6e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-2.8d+39)) then
        tmp = t_2
    else if (t <= 1.95d-90) then
        tmp = t_1
    else if (t <= 1.3d-54) then
        tmp = t_2
    else if (t <= 1.22d-27) then
        tmp = t_1
    else if (t <= 15000.0d0) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 3.6d+26) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.8e+39) {
		tmp = t_2;
	} else if (t <= 1.95e-90) {
		tmp = t_1;
	} else if (t <= 1.3e-54) {
		tmp = t_2;
	} else if (t <= 1.22e-27) {
		tmp = t_1;
	} else if (t <= 15000.0) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 3.6e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.8e+39:
		tmp = t_2
	elif t <= 1.95e-90:
		tmp = t_1
	elif t <= 1.3e-54:
		tmp = t_2
	elif t <= 1.22e-27:
		tmp = t_1
	elif t <= 15000.0:
		tmp = z * ((y - x) / (a - t))
	elif t <= 3.6e+26:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.8e+39)
		tmp = t_2;
	elseif (t <= 1.95e-90)
		tmp = t_1;
	elseif (t <= 1.3e-54)
		tmp = t_2;
	elseif (t <= 1.22e-27)
		tmp = t_1;
	elseif (t <= 15000.0)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 3.6e+26)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.8e+39)
		tmp = t_2;
	elseif (t <= 1.95e-90)
		tmp = t_1;
	elseif (t <= 1.3e-54)
		tmp = t_2;
	elseif (t <= 1.22e-27)
		tmp = t_1;
	elseif (t <= 15000.0)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 3.6e+26)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+39], t$95$2, If[LessEqual[t, 1.95e-90], t$95$1, If[LessEqual[t, 1.3e-54], t$95$2, If[LessEqual[t, 1.22e-27], t$95$1, If[LessEqual[t, 15000.0], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000001e39 or 1.95000000000000002e-90 < t < 1.30000000000000001e-54 or 3.60000000000000024e26 < t

   1. Initial program 44.5%

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

      1. +-commutative 44.5%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. unpow-1 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in y around inf 70.1%

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

       1. div-sub 70.1%

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

   11. Simplified 70.1%

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

   if -2.80000000000000001e39 < t < 1.95000000000000002e-90 or 1.30000000000000001e-54 < t < 1.22e-27

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 79.6%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if 1.22e-27 < t < 15000

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 79.4%

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

      3. fma-define 79.6%

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

   3. Simplified 79.6%

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

      1. clear-num 79.6%

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

      2. inv-pow 79.6%

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

   6. Applied egg-rr 79.6%

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

      1. unpow-1 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in z around inf 74.0%

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

       1. div-sub 74.2%

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

   11. Simplified 74.2%

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

   if 15000 < t < 3.60000000000000024e26

   1. Initial program 63.0%

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

   3. Taylor expanded in t around 0 44.3%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   8. Simplified 81.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-27}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 15000:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 15500:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.55e+39)
     t_2
     (if (<= t 1.3e-90)
       t_1
       (if (<= t 1.5e-54)
         t_2
         (if (<= t 4.6e-26)
           t_1
           (if (<= t 15500.0)
             (/ (* (- y x) z) (- a t))
             (if (<= t 3.4e+26) (* x (- 1.0 (/ z a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.55e+39) {
		tmp = t_2;
	} else if (t <= 1.3e-90) {
		tmp = t_1;
	} else if (t <= 1.5e-54) {
		tmp = t_2;
	} else if (t <= 4.6e-26) {
		tmp = t_1;
	} else if (t <= 15500.0) {
		tmp = ((y - x) * z) / (a - t);
	} else if (t <= 3.4e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-1.55d+39)) then
        tmp = t_2
    else if (t <= 1.3d-90) then
        tmp = t_1
    else if (t <= 1.5d-54) then
        tmp = t_2
    else if (t <= 4.6d-26) then
        tmp = t_1
    else if (t <= 15500.0d0) then
        tmp = ((y - x) * z) / (a - t)
    else if (t <= 3.4d+26) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.55e+39) {
		tmp = t_2;
	} else if (t <= 1.3e-90) {
		tmp = t_1;
	} else if (t <= 1.5e-54) {
		tmp = t_2;
	} else if (t <= 4.6e-26) {
		tmp = t_1;
	} else if (t <= 15500.0) {
		tmp = ((y - x) * z) / (a - t);
	} else if (t <= 3.4e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.55e+39:
		tmp = t_2
	elif t <= 1.3e-90:
		tmp = t_1
	elif t <= 1.5e-54:
		tmp = t_2
	elif t <= 4.6e-26:
		tmp = t_1
	elif t <= 15500.0:
		tmp = ((y - x) * z) / (a - t)
	elif t <= 3.4e+26:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.55e+39)
		tmp = t_2;
	elseif (t <= 1.3e-90)
		tmp = t_1;
	elseif (t <= 1.5e-54)
		tmp = t_2;
	elseif (t <= 4.6e-26)
		tmp = t_1;
	elseif (t <= 15500.0)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (t <= 3.4e+26)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.55e+39)
		tmp = t_2;
	elseif (t <= 1.3e-90)
		tmp = t_1;
	elseif (t <= 1.5e-54)
		tmp = t_2;
	elseif (t <= 4.6e-26)
		tmp = t_1;
	elseif (t <= 15500.0)
		tmp = ((y - x) * z) / (a - t);
	elseif (t <= 3.4e+26)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+39], t$95$2, If[LessEqual[t, 1.3e-90], t$95$1, If[LessEqual[t, 1.5e-54], t$95$2, If[LessEqual[t, 4.6e-26], t$95$1, If[LessEqual[t, 15500.0], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5500000000000001e39 or 1.3e-90 < t < 1.50000000000000005e-54 or 3.4000000000000003e26 < t

   1. Initial program 44.5%

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

      1. +-commutative 44.5%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. unpow-1 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in y around inf 70.1%

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

       1. div-sub 70.1%

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

   11. Simplified 70.1%

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

   if -1.5500000000000001e39 < t < 1.3e-90 or 1.50000000000000005e-54 < t < 4.60000000000000018e-26

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 79.6%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   if 4.60000000000000018e-26 < t < 15500

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 79.4%

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

      3. fma-define 79.6%

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

   3. Simplified 79.6%

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

      1. clear-num 79.6%

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

      2. inv-pow 79.6%

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

   6. Applied egg-rr 79.6%

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

      1. unpow-1 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in z around -inf 74.4%

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

   if 15500 < t < 3.4000000000000003e26

   1. Initial program 63.0%

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

   3. Taylor expanded in t around 0 44.3%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   8. Simplified 81.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 15500:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- t a)))))
   (if (<= t -1.9e+161)
     y
     (if (<= t -1.55e+52)
       t_1
       (if (<= t -1.6e-187)
         (+ x (* y (/ z a)))
         (if (<= t -8e-300)
           (* z (/ (- y x) a))
           (if (<= t 3.5e+26)
             (* x (- 1.0 (/ z a)))
             (if (<= t 1.65e+119) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (t - a));
	double tmp;
	if (t <= -1.9e+161) {
		tmp = y;
	} else if (t <= -1.55e+52) {
		tmp = t_1;
	} else if (t <= -1.6e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -8e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.5e+26) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.65e+119) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (t - a))
    if (t <= (-1.9d+161)) then
        tmp = y
    else if (t <= (-1.55d+52)) then
        tmp = t_1
    else if (t <= (-1.6d-187)) then
        tmp = x + (y * (z / a))
    else if (t <= (-8d-300)) then
        tmp = z * ((y - x) / a)
    else if (t <= 3.5d+26) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.65d+119) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (t - a));
	double tmp;
	if (t <= -1.9e+161) {
		tmp = y;
	} else if (t <= -1.55e+52) {
		tmp = t_1;
	} else if (t <= -1.6e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -8e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 3.5e+26) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.65e+119) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (t - a))
	tmp = 0
	if t <= -1.9e+161:
		tmp = y
	elif t <= -1.55e+52:
		tmp = t_1
	elif t <= -1.6e-187:
		tmp = x + (y * (z / a))
	elif t <= -8e-300:
		tmp = z * ((y - x) / a)
	elif t <= 3.5e+26:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.65e+119:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (t <= -1.9e+161)
		tmp = y;
	elseif (t <= -1.55e+52)
		tmp = t_1;
	elseif (t <= -1.6e-187)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -8e-300)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 3.5e+26)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.65e+119)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (t - a));
	tmp = 0.0;
	if (t <= -1.9e+161)
		tmp = y;
	elseif (t <= -1.55e+52)
		tmp = t_1;
	elseif (t <= -1.6e-187)
		tmp = x + (y * (z / a));
	elseif (t <= -8e-300)
		tmp = z * ((y - x) / a);
	elseif (t <= 3.5e+26)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.65e+119)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+161], y, If[LessEqual[t, -1.55e+52], t$95$1, If[LessEqual[t, -1.6e-187], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-300], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+119], t$95$1, y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.9000000000000001e161 or 1.6500000000000001e119 < t

   1. Initial program 34.3%

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

   3. Taylor expanded in t around inf 61.8%

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

   if -1.9000000000000001e161 < t < -1.55e52 or 3.4999999999999999e26 < t < 1.6500000000000001e119

   1. Initial program 57.5%

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

   3. Taylor expanded in z around 0 40.8%

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

      1. mul-1-neg 40.8%

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

      2. unsub-neg 40.8%

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

      3. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in x around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. associate-/l* 55.4%

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

   8. Simplified 55.4%

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

   if -1.55e52 < t < -1.5999999999999999e-187

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 64.8%

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

   4. Taylor expanded in y around inf 62.0%

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

      1. associate-/l* 64.6%

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

   6. Simplified 64.6%

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

   if -1.5999999999999999e-187 < t < -8.0000000000000002e-300

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 87.0%

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

   4. Taylor expanded in z around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if -8.0000000000000002e-300 < t < 3.4999999999999999e26

   1. Initial program 88.7%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   8. Simplified 58.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+161}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-54} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.4e+39)
     t_1
     (if (<= t 2.2e-90)
       (+ x (* z (/ (- y x) a)))
       (if (or (<= t 3.1e-54) (not (<= t 3.8e+26)))
         t_1
         (* x (+ (/ (- z t) (- t a)) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.4e+39) {
		tmp = t_1;
	} else if (t <= 2.2e-90) {
		tmp = x + (z * ((y - x) / a));
	} else if ((t <= 3.1e-54) || !(t <= 3.8e+26)) {
		tmp = t_1;
	} else {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-1.4d+39)) then
        tmp = t_1
    else if (t <= 2.2d-90) then
        tmp = x + (z * ((y - x) / a))
    else if ((t <= 3.1d-54) .or. (.not. (t <= 3.8d+26))) then
        tmp = t_1
    else
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.4e+39) {
		tmp = t_1;
	} else if (t <= 2.2e-90) {
		tmp = x + (z * ((y - x) / a));
	} else if ((t <= 3.1e-54) || !(t <= 3.8e+26)) {
		tmp = t_1;
	} else {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.4e+39:
		tmp = t_1
	elif t <= 2.2e-90:
		tmp = x + (z * ((y - x) / a))
	elif (t <= 3.1e-54) or not (t <= 3.8e+26):
		tmp = t_1
	else:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.4e+39)
		tmp = t_1;
	elseif (t <= 2.2e-90)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif ((t <= 3.1e-54) || !(t <= 3.8e+26))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.4e+39)
		tmp = t_1;
	elseif (t <= 2.2e-90)
		tmp = x + (z * ((y - x) / a));
	elseif ((t <= 3.1e-54) || ~((t <= 3.8e+26)))
		tmp = t_1;
	else
		tmp = x * (((z - t) / (t - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+39], t$95$1, If[LessEqual[t, 2.2e-90], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.1e-54], N[Not[LessEqual[t, 3.8e+26]], $MachinePrecision]], t$95$1, N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000001e39 or 2.19999999999999986e-90 < t < 3.10000000000000004e-54 or 3.8000000000000002e26 < t

   1. Initial program 44.5%

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

      1. +-commutative 44.5%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. unpow-1 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in y around inf 70.1%

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

       1. div-sub 70.1%

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

   11. Simplified 70.1%

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

   if -1.40000000000000001e39 < t < 2.19999999999999986e-90

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

   if 3.10000000000000004e-54 < t < 3.8000000000000002e26

   1. Initial program 74.2%

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

   3. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   5. Simplified 67.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-54} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))) (t_2 (* z (/ (- y x) (- a t)))))
   (if (<= z -6.1e+187)
     t_2
     (if (<= z -1.7e+143)
       t_1
       (if (<= z -1.96e+108)
         (/ (* (- y x) z) (- a t))
         (if (<= z 4.2e+79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -6.1e+187) {
		tmp = t_2;
	} else if (z <= -1.7e+143) {
		tmp = t_1;
	} else if (z <= -1.96e+108) {
		tmp = ((y - x) * z) / (a - t);
	} else if (z <= 4.2e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    t_2 = z * ((y - x) / (a - t))
    if (z <= (-6.1d+187)) then
        tmp = t_2
    else if (z <= (-1.7d+143)) then
        tmp = t_1
    else if (z <= (-1.96d+108)) then
        tmp = ((y - x) * z) / (a - t)
    else if (z <= 4.2d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -6.1e+187) {
		tmp = t_2;
	} else if (z <= -1.7e+143) {
		tmp = t_1;
	} else if (z <= -1.96e+108) {
		tmp = ((y - x) * z) / (a - t);
	} else if (z <= 4.2e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	t_2 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -6.1e+187:
		tmp = t_2
	elif z <= -1.7e+143:
		tmp = t_1
	elif z <= -1.96e+108:
		tmp = ((y - x) * z) / (a - t)
	elif z <= 4.2e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -6.1e+187)
		tmp = t_2;
	elseif (z <= -1.7e+143)
		tmp = t_1;
	elseif (z <= -1.96e+108)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (z <= 4.2e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	t_2 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -6.1e+187)
		tmp = t_2;
	elseif (z <= -1.7e+143)
		tmp = t_1;
	elseif (z <= -1.96e+108)
		tmp = ((y - x) * z) / (a - t);
	elseif (z <= 4.2e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.1e+187], t$95$2, If[LessEqual[z, -1.7e+143], t$95$1, If[LessEqual[z, -1.96e+108], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0999999999999996e187 or 4.20000000000000016e79 < z

   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* 94.3%

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

      3. fma-define 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. inv-pow 94.3%

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

   6. Applied egg-rr 94.3%

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

      1. unpow-1 94.3%

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

   8. Simplified 94.3%

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

   9. Taylor expanded in z around inf 80.3%

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

       1. div-sub 83.2%

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

   11. Simplified 83.2%

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

   if -6.0999999999999996e187 < z < -1.69999999999999991e143 or -1.9600000000000001e108 < z < 4.20000000000000016e79

   1. Initial program 64.4%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

   if -1.69999999999999991e143 < z < -1.9600000000000001e108

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-/l* 71.6%

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

      3. fma-define 71.6%

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

   3. Simplified 71.6%

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

      1. clear-num 71.4%

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

      2. inv-pow 71.4%

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

   6. Applied egg-rr 71.4%

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

      1. unpow-1 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in z around -inf 89.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+143}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+189} \lor \neg \left(x \leq 5.5 \cdot 10^{-44}\right) \land \left(x \leq 1.08 \cdot 10^{+14} \lor \neg \left(x \leq 2.05 \cdot 10^{+90}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.5e+189)
         (and (not (<= x 5.5e-44)) (or (<= x 1.08e+14) (not (<= x 2.05e+90)))))
   (* x (- 1.0 (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+189) || (!(x <= 5.5e-44) && ((x <= 1.08e+14) || !(x <= 2.05e+90)))) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.5d+189)) .or. (.not. (x <= 5.5d-44)) .and. (x <= 1.08d+14) .or. (.not. (x <= 2.05d+90))) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.5e+189) || (!(x <= 5.5e-44) && ((x <= 1.08e+14) || !(x <= 2.05e+90)))) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.5e+189) or (not (x <= 5.5e-44) and ((x <= 1.08e+14) or not (x <= 2.05e+90))):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.5e+189) || (!(x <= 5.5e-44) && ((x <= 1.08e+14) || !(x <= 2.05e+90))))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.5e+189) || (~((x <= 5.5e-44)) && ((x <= 1.08e+14) || ~((x <= 2.05e+90)))))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.5e+189], And[N[Not[LessEqual[x, 5.5e-44]], $MachinePrecision], Or[LessEqual[x, 1.08e+14], N[Not[LessEqual[x, 2.05e+90]], $MachinePrecision]]]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999973e189 or 5.49999999999999993e-44 < x < 1.08e14 or 2.05000000000000021e90 < x

   1. Initial program 63.8%

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

   3. Taylor expanded in t around 0 56.0%

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

      1. associate-/l* 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

   8. Simplified 59.7%

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

   if -4.49999999999999973e189 < x < 5.49999999999999993e-44 or 1.08e14 < x < 2.05000000000000021e90

   1. Initial program 66.0%

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

      1. +-commutative 66.0%

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

      2. associate-/l* 84.9%

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

      3. fma-define 85.0%

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

   3. Simplified 85.0%

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

      1. clear-num 84.9%

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

      2. inv-pow 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. unpow-1 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in y around inf 71.4%

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

       1. div-sub 71.4%

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

   11. Simplified 71.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+189} \lor \neg \left(x \leq 5.5 \cdot 10^{-44}\right) \land \left(x \leq 1.08 \cdot 10^{+14} \lor \neg \left(x \leq 2.05 \cdot 10^{+90}\right)\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ (- z t) a)))))
   (if (<= a -4.6e+104)
     t_2
     (if (<= a -7e-278)
       t_1
       (if (<= a 5.7e-269)
         (* z (/ (- y x) (- a t)))
         (if (<= a 1.4e+95) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -4.6e+104) {
		tmp = t_2;
	} else if (a <= -7e-278) {
		tmp = t_1;
	} else if (a <= 5.7e-269) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.4e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y * ((z - t) / a))
    if (a <= (-4.6d+104)) then
        tmp = t_2
    else if (a <= (-7d-278)) then
        tmp = t_1
    else if (a <= 5.7d-269) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.4d+95) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -4.6e+104) {
		tmp = t_2;
	} else if (a <= -7e-278) {
		tmp = t_1;
	} else if (a <= 5.7e-269) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.4e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * ((z - t) / a))
	tmp = 0
	if a <= -4.6e+104:
		tmp = t_2
	elif a <= -7e-278:
		tmp = t_1
	elif a <= 5.7e-269:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.4e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -4.6e+104)
		tmp = t_2;
	elseif (a <= -7e-278)
		tmp = t_1;
	elseif (a <= 5.7e-269)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.4e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -4.6e+104)
		tmp = t_2;
	elseif (a <= -7e-278)
		tmp = t_1;
	elseif (a <= 5.7e-269)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.4e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+104], t$95$2, If[LessEqual[a, -7e-278], t$95$1, If[LessEqual[a, 5.7e-269], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+95], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.59999999999999969e104 or 1.3999999999999999e95 < a

   1. Initial program 72.8%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in a around inf 67.6%

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

      1. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

   if -4.59999999999999969e104 < a < -6.99999999999999941e-278 or 5.69999999999999969e-269 < a < 1.3999999999999999e95

   1. Initial program 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-/l* 79.3%

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

      3. fma-define 79.3%

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

   3. Simplified 79.3%

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

      1. clear-num 79.3%

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

      2. inv-pow 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. unpow-1 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in y around inf 64.0%

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

       1. div-sub 64.0%

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

   11. Simplified 64.0%

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

   if -6.99999999999999941e-278 < a < 5.69999999999999969e-269

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-/l* 83.4%

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

      3. fma-define 83.7%

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

   3. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

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

   6. Applied egg-rr 83.7%

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

      1. unpow-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around inf 71.1%

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

       1. div-sub 71.1%

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

   11. Simplified 71.1%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.8e+51)
   y
   (if (<= t -2e-187)
     (+ x (* y (/ z a)))
     (if (<= t -2.4e-300)
       (* z (/ (- y x) a))
       (if (<= t 6.8e+26) (* x (- 1.0 (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.8e+51) {
		tmp = y;
	} else if (t <= -2e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.4e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.8e+26) {
		tmp = x * (1.0 - (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 <= (-9.8d+51)) then
        tmp = y
    else if (t <= (-2d-187)) then
        tmp = x + (y * (z / a))
    else if (t <= (-2.4d-300)) then
        tmp = z * ((y - x) / a)
    else if (t <= 6.8d+26) then
        tmp = x * (1.0d0 - (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 <= -9.8e+51) {
		tmp = y;
	} else if (t <= -2e-187) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.4e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.8e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.8e+51:
		tmp = y
	elif t <= -2e-187:
		tmp = x + (y * (z / a))
	elif t <= -2.4e-300:
		tmp = z * ((y - x) / a)
	elif t <= 6.8e+26:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.8e+51)
		tmp = y;
	elseif (t <= -2e-187)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -2.4e-300)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 6.8e+26)
		tmp = Float64(x * Float64(1.0 - 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 <= -9.8e+51)
		tmp = y;
	elseif (t <= -2e-187)
		tmp = x + (y * (z / a));
	elseif (t <= -2.4e-300)
		tmp = z * ((y - x) / a);
	elseif (t <= 6.8e+26)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.8e+51], y, If[LessEqual[t, -2e-187], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-300], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.79999999999999967e51 or 6.8000000000000005e26 < t

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 51.9%

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

   if -9.79999999999999967e51 < t < -2e-187

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 64.8%

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

   4. Taylor expanded in y around inf 62.0%

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

      1. associate-/l* 64.6%

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

   6. Simplified 64.6%

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

   if -2e-187 < t < -2.39999999999999999e-300

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0 87.0%

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

   4. Taylor expanded in z around inf 72.6%

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

      1. div-sub 72.6%

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

   6. Simplified 72.6%

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

   if -2.39999999999999999e-300 < t < 6.8000000000000005e26

   1. Initial program 88.7%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+93}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+93)
   y
   (if (<= t -1.75e-300)
     (* z (/ (- y x) a))
     (if (<= t 6.5e+26) (* x (- 1.0 (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+93) {
		tmp = y;
	} else if (t <= -1.75e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.5e+26) {
		tmp = x * (1.0 - (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 <= (-7.6d+93)) then
        tmp = y
    else if (t <= (-1.75d-300)) then
        tmp = z * ((y - x) / a)
    else if (t <= 6.5d+26) then
        tmp = x * (1.0d0 - (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 <= -7.6e+93) {
		tmp = y;
	} else if (t <= -1.75e-300) {
		tmp = z * ((y - x) / a);
	} else if (t <= 6.5e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.6e+93:
		tmp = y
	elif t <= -1.75e-300:
		tmp = z * ((y - x) / a)
	elif t <= 6.5e+26:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+93)
		tmp = y;
	elseif (t <= -1.75e-300)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 6.5e+26)
		tmp = Float64(x * Float64(1.0 - 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 <= -7.6e+93)
		tmp = y;
	elseif (t <= -1.75e-300)
		tmp = z * ((y - x) / a);
	elseif (t <= 6.5e+26)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+93], y, If[LessEqual[t, -1.75e-300], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999996e93 or 6.50000000000000022e26 < t

   1. Initial program 39.2%

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

   3. Taylor expanded in t around inf 53.9%

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

   if -7.5999999999999996e93 < t < -1.7500000000000001e-300

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 68.8%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. div-sub 51.9%

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

   6. Simplified 51.9%

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

   if -1.7500000000000001e-300 < t < 6.50000000000000022e26

   1. Initial program 88.7%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+93}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-149} \lor \neg \left(a \leq 5.6 \cdot 10^{+66}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.45e-149) (not (<= a 5.6e+66)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (* (- z a) (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e-149) || !(a <= 5.6e+66)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.45d-149)) .or. (.not. (a <= 5.6d+66))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((z - a) * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e-149) || !(a <= 5.6e+66)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.45e-149) or not (a <= 5.6e+66):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((z - a) * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.45e-149) || !(a <= 5.6e+66))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.45e-149) || ~((a <= 5.6e+66)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((z - a) * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.45e-149], N[Not[LessEqual[a, 5.6e+66]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e-149 or 5.6000000000000001e66 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 67.4%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   if -1.45e-149 < a < 5.6000000000000001e66

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. distribute-lft-out-- 69.0%

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

      3. div-sub 72.2%

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

      4. mul-1-neg 72.2%

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

      5. unsub-neg 72.2%

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

      6. div-sub 69.0%

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

      7. associate-/l* 74.3%

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

      8. associate-/l* 72.6%

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

      9. distribute-rgt-out-- 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-149} \lor \neg \left(a \leq 5.6 \cdot 10^{+66}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+83) y (if (<= t 7e+26) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+83) {
		tmp = y;
	} else if (t <= 7e+26) {
		tmp = x * (1.0 - (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 <= (-8d+83)) then
        tmp = y
    else if (t <= 7d+26) then
        tmp = x * (1.0d0 - (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 <= -8e+83) {
		tmp = y;
	} else if (t <= 7e+26) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e+83:
		tmp = y
	elif t <= 7e+26:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+83)
		tmp = y;
	elseif (t <= 7e+26)
		tmp = Float64(x * Float64(1.0 - 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 <= -8e+83)
		tmp = y;
	elseif (t <= 7e+26)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+83], y, If[LessEqual[t, 7e+26], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000025e83 or 6.9999999999999998e26 < t

   1. Initial program 39.7%

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

   3. Taylor expanded in t around inf 53.5%

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

   if -8.00000000000000025e83 < t < 6.9999999999999998e26

   1. Initial program 88.0%

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

   3. Taylor expanded in t around 0 68.3%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in x around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. unsub-neg 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e+105) x (if (<= a 3.6e+99) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e+105) {
		tmp = x;
	} else if (a <= 3.6e+99) {
		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 <= (-6.8d+105)) then
        tmp = x
    else if (a <= 3.6d+99) 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 <= -6.8e+105) {
		tmp = x;
	} else if (a <= 3.6e+99) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e+105:
		tmp = x
	elif a <= 3.6e+99:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e+105)
		tmp = x;
	elseif (a <= 3.6e+99)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e+105)
		tmp = x;
	elseif (a <= 3.6e+99)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e+105], x, If[LessEqual[a, 3.6e+99], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.7999999999999999e105 or 3.6000000000000002e99 < a

   1. Initial program 72.4%

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

   3. Taylor expanded in a around inf 48.4%

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

   if -6.7999999999999999e105 < a < 3.6000000000000002e99

   1. Initial program 62.3%

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

   3. Taylor expanded in t around inf 39.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e-93) (+ x y) (if (<= a 1.45e+100) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e-93) {
		tmp = x + y;
	} else if (a <= 1.45e+100) {
		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 <= (-1.7d-93)) then
        tmp = x + y
    else if (a <= 1.45d+100) 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 <= -1.7e-93) {
		tmp = x + y;
	} else if (a <= 1.45e+100) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e-93:
		tmp = x + y
	elif a <= 1.45e+100:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e-93)
		tmp = Float64(x + y);
	elseif (a <= 1.45e+100)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e-93)
		tmp = x + y;
	elseif (a <= 1.45e+100)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e-93], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.45e+100], y, x]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000001e-93

   1. Initial program 66.1%

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

   3. Taylor expanded in z around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. unsub-neg 46.5%

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

      3. associate-/l* 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in y around inf 46.3%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in t around inf 40.1%

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

       1. sub-neg 40.1%

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

       2. mul-1-neg 40.1%

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

       3. remove-double-neg 40.1%

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

       4. +-commutative 40.1%

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

   11. Simplified 40.1%

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

   if -1.70000000000000001e-93 < a < 1.45e100

   1. Initial program 62.2%

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

   3. Taylor expanded in t around inf 41.7%

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

   if 1.45e100 < a

   1. Initial program 74.7%

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

   3. Taylor expanded in a around inf 52.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.7% 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 65.3%

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

3. Taylor expanded in a around inf 21.3%

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

4. Final simplification 21.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.5% 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 2024071 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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