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

Percentage Accurate: 68.3% → 88.7%

Time: 23.0s

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: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+182} \lor \neg \left(t \leq 1.2 \cdot 10^{+133}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.12e+182) (not (<= t 1.2e+133)))
   (+ y (* (/ (- y x) t) (- a z)))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.12e+182) || !(t <= 1.2e+133)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.12e+182) || !(t <= 1.2e+133))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.12e+182], N[Not[LessEqual[t, 1.2e+133]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.11999999999999994e182 or 1.1999999999999999e133 < t

   1. Initial program 30.8%

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

      1. clear-num 30.8%

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

      2. inv-pow 30.8%

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

      3. *-commutative 30.8%

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

      4. associate-/r* 55.7%

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

   4. Applied egg-rr 55.7%

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

      1. unpow-1 55.7%

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

   6. Applied egg-rr 55.7%

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

   7. Taylor expanded in t around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. distribute-lft-out-- 63.0%

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

      3. div-sub 63.0%

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

      4. mul-1-neg 63.0%

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

      5. unsub-neg 63.0%

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

      6. div-sub 63.0%

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

      7. associate-/l* 76.2%

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

      8. associate-/l* 91.5%

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

      9. distribute-rgt-out-- 91.5%

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

   9. Simplified 91.5%

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

   if -1.11999999999999994e182 < t < 1.1999999999999999e133

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-/l* 91.9%

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

      3. fma-define 91.9%

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

   3. Simplified 91.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+182} \lor \neg \left(t \leq 1.2 \cdot 10^{+133}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-252}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e-252)
       t_2
       (if (<= t_2 0.0)
         (+ y (* (- y x) (/ (- a z) t)))
         (if (<= t_2 2e+301) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e-252) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 2e+301) {
		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 + (((y - x) / t) * (a - z));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e-252) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 2e+301) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e-252:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t_2 <= 2e+301:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e-252)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t_2 <= 2e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) / t) * (a - z));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e-252)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t_2 <= 2e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e-252], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+301], 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 2.00000000000000011e301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.3%

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

      1. clear-num 41.3%

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

      2. inv-pow 41.3%

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

      3. *-commutative 41.3%

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

      4. associate-/r* 76.5%

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

   4. Applied egg-rr 76.5%

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

      1. unpow-1 76.5%

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

   6. Applied egg-rr 76.5%

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

   7. Taylor expanded in t around inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. distribute-lft-out-- 49.7%

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

      3. div-sub 50.9%

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

      4. mul-1-neg 50.9%

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

      5. unsub-neg 50.9%

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

      6. div-sub 49.7%

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

      7. associate-/l* 59.5%

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

      8. associate-/l* 72.4%

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

      9. distribute-rgt-out-- 75.7%

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

   9. Simplified 75.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.00000000000000008e-252 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000011e301

   1. Initial program 99.8%

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

   if -5.00000000000000008e-252 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.3%

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

   3. Taylor expanded in t around inf 95.3%

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

      1. associate--l+ 95.3%

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

      2. associate-*r/ 95.3%

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

      3. associate-*r/ 95.3%

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

      4. div-sub 95.4%

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

      5. distribute-lft-out-- 95.4%

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

      6. associate-*r/ 95.4%

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

      7. mul-1-neg 95.4%

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

      8. unsub-neg 95.4%

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

      9. distribute-rgt-out-- 95.3%

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

      10. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-252}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.7e+52)
   (- x (* x (/ z a)))
   (if (<= a 7.5e-209)
     (* y (/ (- t z) t))
     (if (<= a 4.3e-39)
       (/ z (/ t (- x y)))
       (if (<= a 5.7e+51)
         (+ x (/ (* y z) a))
         (if (<= a 1.7e+95) (* t (/ y (- t a))) (+ x (* z (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+52) {
		tmp = x - (x * (z / a));
	} else if (a <= 7.5e-209) {
		tmp = y * ((t - z) / t);
	} else if (a <= 4.3e-39) {
		tmp = z / (t / (x - y));
	} else if (a <= 5.7e+51) {
		tmp = x + ((y * z) / a);
	} else if (a <= 1.7e+95) {
		tmp = t * (y / (t - a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.7d+52)) then
        tmp = x - (x * (z / a))
    else if (a <= 7.5d-209) then
        tmp = y * ((t - z) / t)
    else if (a <= 4.3d-39) then
        tmp = z / (t / (x - y))
    else if (a <= 5.7d+51) then
        tmp = x + ((y * z) / a)
    else if (a <= 1.7d+95) then
        tmp = t * (y / (t - a))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+52) {
		tmp = x - (x * (z / a));
	} else if (a <= 7.5e-209) {
		tmp = y * ((t - z) / t);
	} else if (a <= 4.3e-39) {
		tmp = z / (t / (x - y));
	} else if (a <= 5.7e+51) {
		tmp = x + ((y * z) / a);
	} else if (a <= 1.7e+95) {
		tmp = t * (y / (t - a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e+52:
		tmp = x - (x * (z / a))
	elif a <= 7.5e-209:
		tmp = y * ((t - z) / t)
	elif a <= 4.3e-39:
		tmp = z / (t / (x - y))
	elif a <= 5.7e+51:
		tmp = x + ((y * z) / a)
	elif a <= 1.7e+95:
		tmp = t * (y / (t - a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e+52)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (a <= 7.5e-209)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 4.3e-39)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 5.7e+51)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 1.7e+95)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e+52)
		tmp = x - (x * (z / a));
	elseif (a <= 7.5e-209)
		tmp = y * ((t - z) / t);
	elseif (a <= 4.3e-39)
		tmp = z / (t / (x - y));
	elseif (a <= 5.7e+51)
		tmp = x + ((y * z) / a);
	elseif (a <= 1.7e+95)
		tmp = t * (y / (t - a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e+52], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-209], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-39], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e+51], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+95], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.7e52

   1. Initial program 65.0%

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

   3. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in y around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

      3. associate-/l* 61.8%

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

   8. Simplified 61.8%

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

   if -4.7e52 < a < 7.49999999999999965e-209

   1. Initial program 72.7%

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

      1. clear-num 72.6%

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

      2. inv-pow 72.6%

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

      3. *-commutative 72.6%

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

      4. associate-/r* 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in x around 0 60.7%

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

      1. associate-/l* 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around 0 63.2%

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

      1. associate-*r/ 63.2%

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

      2. neg-mul-1 63.2%

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

   10. Simplified 63.2%

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

   if 7.49999999999999965e-209 < a < 4.2999999999999999e-39

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 73.3%

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

      1. sub-div 73.3%

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

      2. div-inv 73.2%

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

   5. Applied egg-rr 73.2%

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

   6. Taylor expanded in a around 0 47.1%

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

      1. mul-1-neg 47.1%

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

      2. associate-/l* 55.6%

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

      3. distribute-rgt-neg-in 55.6%

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

      4. distribute-neg-frac2 55.6%

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

   8. Simplified 55.6%

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

      1. associate-*r/ 47.1%

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

      2. distribute-frac-neg2 47.1%

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

      3. add-sqr-sqrt 27.7%

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

      4. sqrt-unprod 25.6%

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

      5. sqr-neg 25.6%

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

      6. sqrt-unprod 1.1%

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

      7. add-sqr-sqrt 10.7%

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

      8. associate-*r/ 10.8%

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

      9. clear-num 10.8%

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

      10. un-div-inv 10.8%

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

      11. add-sqr-sqrt 1.1%

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

      12. sqrt-unprod 25.8%

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

      13. sqr-neg 25.8%

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

      14. sqrt-unprod 30.5%

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

      15. add-sqr-sqrt 55.8%

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

   10. Applied egg-rr 55.8%

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

   if 4.2999999999999999e-39 < a < 5.7000000000000002e51

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 53.0%

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

      1. associate-/l* 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 53.2%

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

   if 5.7000000000000002e51 < a < 1.70000000000000011e95

   1. Initial program 68.9%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-/r* 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in z around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-/l* 75.1%

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

      3. distribute-rgt-neg-in 75.1%

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

      4. distribute-frac-neg2 75.1%

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

      5. neg-sub0 75.1%

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

      6. associate--r- 75.1%

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

      7. neg-sub0 75.1%

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

   10. Simplified 75.1%

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

   if 1.70000000000000011e95 < a

   1. Initial program 66.6%

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

   3. Taylor expanded in t around 0 53.4%

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

      1. associate-/l* 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 59.7%

      \[\leadsto x + z \cdot \color{blue}{\frac{y}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+52}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 0.00065:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+52)
   x
   (if (<= a -6e-193)
     y
     (if (<= a 0.00065)
       (* x (/ z t))
       (if (<= a 9e+108) (* y (/ (- z t) a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+52) {
		tmp = x;
	} else if (a <= -6e-193) {
		tmp = y;
	} else if (a <= 0.00065) {
		tmp = x * (z / t);
	} else if (a <= 9e+108) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d+52)) then
        tmp = x
    else if (a <= (-6d-193)) then
        tmp = y
    else if (a <= 0.00065d0) then
        tmp = x * (z / t)
    else if (a <= 9d+108) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+52) {
		tmp = x;
	} else if (a <= -6e-193) {
		tmp = y;
	} else if (a <= 0.00065) {
		tmp = x * (z / t);
	} else if (a <= 9e+108) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+52:
		tmp = x
	elif a <= -6e-193:
		tmp = y
	elif a <= 0.00065:
		tmp = x * (z / t)
	elif a <= 9e+108:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+52)
		tmp = x;
	elseif (a <= -6e-193)
		tmp = y;
	elseif (a <= 0.00065)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 9e+108)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+52)
		tmp = x;
	elseif (a <= -6e-193)
		tmp = y;
	elseif (a <= 0.00065)
		tmp = x * (z / t);
	elseif (a <= 9e+108)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+52], x, If[LessEqual[a, -6e-193], y, If[LessEqual[a, 0.00065], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+108], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2e52 or 9e108 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 50.3%

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

   if -3.2e52 < a < -5.9999999999999998e-193

   1. Initial program 74.9%

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

   3. Taylor expanded in t around inf 41.3%

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

   if -5.9999999999999998e-193 < a < 6.4999999999999997e-4

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 62.4%

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

      1. sub-div 62.4%

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

      2. div-inv 62.3%

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

   5. Applied egg-rr 62.3%

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

   6. Taylor expanded in a around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. associate-/l* 54.0%

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

      3. distribute-rgt-neg-in 54.0%

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

      4. distribute-neg-frac2 54.0%

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

   8. Simplified 54.0%

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

   9. Taylor expanded in y around 0 36.2%

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

       1. associate-/l* 42.0%

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

   11. Simplified 42.0%

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

   if 6.4999999999999997e-4 < a < 9e108

   1. Initial program 72.9%

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

      1. clear-num 72.8%

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

      2. inv-pow 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/r* 90.3%

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

   4. Applied egg-rr 90.3%

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

   5. Taylor expanded in x around 0 50.9%

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

      1. associate-/l* 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in a around inf 35.6%

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

      1. associate-/l* 42.8%

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

   10. Simplified 42.8%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-193}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 0.00065:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-39}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= a -3.2e-49)
     t_1
     (if (<= a 2.75e-39)
       (/ z (/ t (- x y)))
       (if (<= a 2.6e+51)
         (+ x (/ (* y z) a))
         (if (<= a 1.75e+95) (* t (/ y (- t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -3.2e-49) {
		tmp = t_1;
	} else if (a <= 2.75e-39) {
		tmp = z / (t / (x - y));
	} else if (a <= 2.6e+51) {
		tmp = x + ((y * z) / a);
	} else if (a <= 1.75e+95) {
		tmp = t * (y / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (a <= (-3.2d-49)) then
        tmp = t_1
    else if (a <= 2.75d-39) then
        tmp = z / (t / (x - y))
    else if (a <= 2.6d+51) then
        tmp = x + ((y * z) / a)
    else if (a <= 1.75d+95) then
        tmp = t * (y / (t - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (a <= -3.2e-49) {
		tmp = t_1;
	} else if (a <= 2.75e-39) {
		tmp = z / (t / (x - y));
	} else if (a <= 2.6e+51) {
		tmp = x + ((y * z) / a);
	} else if (a <= 1.75e+95) {
		tmp = t * (y / (t - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if a <= -3.2e-49:
		tmp = t_1
	elif a <= 2.75e-39:
		tmp = z / (t / (x - y))
	elif a <= 2.6e+51:
		tmp = x + ((y * z) / a)
	elif a <= 1.75e+95:
		tmp = t * (y / (t - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.2e-49)
		tmp = t_1;
	elseif (a <= 2.75e-39)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 2.6e+51)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 1.75e+95)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (a <= -3.2e-49)
		tmp = t_1;
	elseif (a <= 2.75e-39)
		tmp = z / (t / (x - y));
	elseif (a <= 2.6e+51)
		tmp = x + ((y * z) / a);
	elseif (a <= 1.75e+95)
		tmp = t * (y / (t - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-49], t$95$1, If[LessEqual[a, 2.75e-39], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+51], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e+95], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.20000000000000002e-49 or 1.75e95 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in t around 0 55.3%

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

      1. associate-/l* 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around inf 55.6%

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

   if -3.20000000000000002e-49 < a < 2.75000000000000009e-39

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. sub-div 61.4%

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

      2. div-inv 61.3%

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

   5. Applied egg-rr 61.3%

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

   6. Taylor expanded in a around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. associate-/l* 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

      4. distribute-neg-frac2 54.2%

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

   8. Simplified 54.2%

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

      1. associate-*r/ 50.7%

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

      2. distribute-frac-neg2 50.7%

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

      3. add-sqr-sqrt 28.1%

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

      4. sqrt-unprod 21.6%

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

      5. sqr-neg 21.6%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 5.1%

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

      8. associate-*r/ 5.2%

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

      9. clear-num 5.2%

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

      10. un-div-inv 5.2%

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

      11. add-sqr-sqrt 1.0%

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

      12. sqrt-unprod 21.7%

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

      13. sqr-neg 21.7%

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

      14. sqrt-unprod 30.6%

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

      15. add-sqr-sqrt 54.2%

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

   10. Applied egg-rr 54.2%

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

   if 2.75000000000000009e-39 < a < 2.6000000000000001e51

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 53.0%

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

      1. associate-/l* 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around inf 53.2%

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

   if 2.6000000000000001e51 < a < 1.75e95

   1. Initial program 68.9%

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

      1. clear-num 68.9%

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

      2. inv-pow 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-/r* 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in z around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-/l* 75.1%

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

      3. distribute-rgt-neg-in 75.1%

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

      4. distribute-frac-neg2 75.1%

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

      5. neg-sub0 75.1%

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

      6. associate--r- 75.1%

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

      7. neg-sub0 75.1%

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

   10. Simplified 75.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-39}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+105}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-46} \lor \neg \left(a \leq 2.3 \cdot 10^{-41}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+105)
   (+ x (* z (/ (- y x) (- a t))))
   (if (or (<= a -1.2e-46) (not (<= a 2.3e-41)))
     (+ x (* (- z t) (/ y (- a t))))
     (+ y (* (- y x) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+105) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if ((a <= -1.2e-46) || !(a <= 2.3e-41)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.8d+105)) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if ((a <= (-1.2d-46)) .or. (.not. (a <= 2.3d-41))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+105) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if ((a <= -1.2e-46) || !(a <= 2.3e-41)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+105:
		tmp = x + (z * ((y - x) / (a - t)))
	elif (a <= -1.2e-46) or not (a <= 2.3e-41):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+105)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif ((a <= -1.2e-46) || !(a <= 2.3e-41))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+105)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif ((a <= -1.2e-46) || ~((a <= 2.3e-41)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+105], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.2e-46], N[Not[LessEqual[a, 2.3e-41]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8e105

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate-/l* 89.9%

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

   5. Simplified 89.9%

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

   if -3.8e105 < a < -1.20000000000000007e-46 or 2.3000000000000001e-41 < a

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-/l* 79.2%

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

   5. Simplified 79.2%

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

   if -1.20000000000000007e-46 < a < 2.3000000000000001e-41

   1. Initial program 66.7%

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

   3. Taylor expanded in t around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. associate-*r/ 82.6%

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

      3. associate-*r/ 82.6%

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

      4. div-sub 83.6%

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

      5. distribute-lft-out-- 83.6%

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

      6. associate-*r/ 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. distribute-rgt-out-- 83.6%

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

      10. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+105}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-46} \lor \neg \left(a \leq 2.3 \cdot 10^{-41}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e+52)
   (+ x (* z (/ (- y x) a)))
   (if (<= a 8.2e-238)
     (/ y (/ (- a t) (- z t)))
     (if (<= a 2.5e-30)
       (* z (* (- y x) (/ -1.0 (- t a))))
       (+ x (* y (/ (- z t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e+52) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 8.2e-238) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e-30) {
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3d+52)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= 8.2d-238) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 2.5d-30) then
        tmp = z * ((y - x) * ((-1.0d0) / (t - a)))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e+52) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 8.2e-238) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 2.5e-30) {
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e+52:
		tmp = x + (z * ((y - x) / a))
	elif a <= 8.2e-238:
		tmp = y / ((a - t) / (z - t))
	elif a <= 2.5e-30:
		tmp = z * ((y - x) * (-1.0 / (t - a)))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e+52)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= 8.2e-238)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 2.5e-30)
		tmp = Float64(z * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e+52)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= 8.2e-238)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 2.5e-30)
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e+52], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e-238], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-30], N[(z * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3e52

   1. Initial program 65.0%

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

   3. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   if -3e52 < a < 8.2000000000000002e-238

   1. Initial program 73.0%

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

      1. clear-num 72.9%

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

      2. inv-pow 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

      1. clear-num 69.5%

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

      2. un-div-inv 69.5%

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

   9. Applied egg-rr 69.5%

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

   if 8.2000000000000002e-238 < a < 2.49999999999999986e-30

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 71.5%

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

      1. sub-div 71.5%

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

      2. div-inv 71.4%

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

   5. Applied egg-rr 71.4%

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

   if 2.49999999999999986e-30 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around inf 59.6%

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

      1. associate-/l* 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+157} \lor \neg \left(t \leq 2.1 \cdot 10^{+127}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - t}{z - t}}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+157) (not (<= t 2.1e+127)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (/ -1.0 (/ (/ (- a t) (- z t)) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+157) || !(t <= 2.1e+127)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + (-1.0 / (((a - t) / (z - t)) / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.6d+157)) .or. (.not. (t <= 2.1d+127))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x + ((-1.0d0) / (((a - t) / (z - t)) / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+157) || !(t <= 2.1e+127)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + (-1.0 / (((a - t) / (z - t)) / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+157) or not (t <= 2.1e+127):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + (-1.0 / (((a - t) / (z - t)) / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+157) || !(t <= 2.1e+127))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - t) / Float64(z - t)) / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e+157) || ~((t <= 2.1e+127)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x + (-1.0 / (((a - t) / (z - t)) / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e+157], N[Not[LessEqual[t, 2.1e+127]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.60000000000000011e157 or 2.09999999999999992e127 < t

   1. Initial program 30.2%

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

      1. clear-num 30.3%

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

      2. inv-pow 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-/r* 57.0%

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

   4. Applied egg-rr 57.0%

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

      1. unpow-1 57.0%

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

   6. Applied egg-rr 57.0%

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

   7. Taylor expanded in t around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. distribute-lft-out-- 62.6%

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

      3. div-sub 62.6%

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

      4. mul-1-neg 62.6%

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

      5. unsub-neg 62.6%

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

      6. div-sub 62.6%

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

      7. associate-/l* 75.4%

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

      8. associate-/l* 91.8%

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

      9. distribute-rgt-out-- 91.8%

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

   9. Simplified 91.8%

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

   if -2.60000000000000011e157 < t < 2.09999999999999992e127

   1. Initial program 83.8%

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

      1. clear-num 83.8%

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

      2. inv-pow 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-/r* 91.8%

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

   4. Applied egg-rr 91.8%

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

      1. unpow-1 91.8%

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

   6. Applied egg-rr 91.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+157} \lor \neg \left(t \leq 2.1 \cdot 10^{+127}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - t}{z - t}}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 76:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.6e+108)
   (* x (/ z (- t a)))
   (if (<= x -1.65e-51)
     (+ x (* z (/ y a)))
     (if (<= x 76.0) (* y (/ (- z t) (- a t))) (- x (* x (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.6e+108) {
		tmp = x * (z / (t - a));
	} else if (x <= -1.65e-51) {
		tmp = x + (z * (y / a));
	} else if (x <= 76.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4.6d+108)) then
        tmp = x * (z / (t - a))
    else if (x <= (-1.65d-51)) then
        tmp = x + (z * (y / a))
    else if (x <= 76.0d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.6e+108) {
		tmp = x * (z / (t - a));
	} else if (x <= -1.65e-51) {
		tmp = x + (z * (y / a));
	} else if (x <= 76.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.6e+108:
		tmp = x * (z / (t - a))
	elif x <= -1.65e-51:
		tmp = x + (z * (y / a))
	elif x <= 76.0:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.6e+108)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (x <= -1.65e-51)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (x <= 76.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.6e+108)
		tmp = x * (z / (t - a));
	elseif (x <= -1.65e-51)
		tmp = x + (z * (y / a));
	elseif (x <= 76.0)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.6e+108], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e-51], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 76.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.5999999999999998e108

   1. Initial program 44.7%

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

   3. Taylor expanded in z around inf 48.5%

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

   4. Taylor expanded in y around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-/l* 48.5%

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

      3. distribute-lft-neg-in 48.5%

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

   6. Simplified 48.5%

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

   if -4.5999999999999998e108 < x < -1.64999999999999986e-51

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 49.0%

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

      1. associate-/l* 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in y around inf 51.6%

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

   if -1.64999999999999986e-51 < x < 76

   1. Initial program 79.6%

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

      1. clear-num 79.5%

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

      2. inv-pow 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-/r* 91.0%

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

   4. Applied egg-rr 91.0%

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

   5. Taylor expanded in x around 0 67.4%

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

      1. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

   if 76 < x

   1. Initial program 64.6%

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

   3. Taylor expanded in t around 0 59.7%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 76:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 47:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.2e+108)
   (* x (/ z (- t a)))
   (if (<= x -8.8e-54)
     (+ x (* y (/ (- z t) a)))
     (if (<= x 47.0) (* y (/ (- z t) (- a t))) (- x (* x (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.2e+108) {
		tmp = x * (z / (t - a));
	} else if (x <= -8.8e-54) {
		tmp = x + (y * ((z - t) / a));
	} else if (x <= 47.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.2d+108)) then
        tmp = x * (z / (t - a))
    else if (x <= (-8.8d-54)) then
        tmp = x + (y * ((z - t) / a))
    else if (x <= 47.0d0) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.2e+108) {
		tmp = x * (z / (t - a));
	} else if (x <= -8.8e-54) {
		tmp = x + (y * ((z - t) / a));
	} else if (x <= 47.0) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.2e+108:
		tmp = x * (z / (t - a))
	elif x <= -8.8e-54:
		tmp = x + (y * ((z - t) / a))
	elif x <= 47.0:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.2e+108)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (x <= -8.8e-54)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (x <= 47.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.2e+108)
		tmp = x * (z / (t - a));
	elseif (x <= -8.8e-54)
		tmp = x + (y * ((z - t) / a));
	elseif (x <= 47.0)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.2e+108], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.8e-54], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 47.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2000000000000005e108

   1. Initial program 44.7%

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

   3. Taylor expanded in z around inf 48.5%

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

   4. Taylor expanded in y around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-/l* 48.5%

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

      3. distribute-lft-neg-in 48.5%

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

   6. Simplified 48.5%

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

   if -5.2000000000000005e108 < x < -8.7999999999999998e-54

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 52.6%

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

      1. associate-/l* 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 52.5%

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

      1. associate-/l* 55.4%

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

   8. Simplified 55.4%

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

   if -8.7999999999999998e-54 < x < 47

   1. Initial program 79.6%

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

      1. clear-num 79.5%

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

      2. inv-pow 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-/r* 91.0%

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

   4. Applied egg-rr 91.0%

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

   5. Taylor expanded in x around 0 67.4%

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

      1. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

   if 47 < x

   1. Initial program 64.6%

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

   3. Taylor expanded in t around 0 59.7%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 47:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e+52)
   (+ x (* z (/ (- y x) a)))
   (if (<= a 4.8e-240)
     (/ y (/ (- a t) (- z t)))
     (if (<= a 1.6e-32) (/ (* (- y x) z) (- a t)) (+ x (* y (/ (- z t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+52) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 4.8e-240) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 1.6e-32) {
		tmp = ((y - x) * z) / (a - t);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.2d+52)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= 4.8d-240) then
        tmp = y / ((a - t) / (z - t))
    else if (a <= 1.6d-32) then
        tmp = ((y - x) * z) / (a - t)
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+52) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 4.8e-240) {
		tmp = y / ((a - t) / (z - t));
	} else if (a <= 1.6e-32) {
		tmp = ((y - x) * z) / (a - t);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e+52:
		tmp = x + (z * ((y - x) / a))
	elif a <= 4.8e-240:
		tmp = y / ((a - t) / (z - t))
	elif a <= 1.6e-32:
		tmp = ((y - x) * z) / (a - t)
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e+52)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= 4.8e-240)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (a <= 1.6e-32)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.2e+52)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= 4.8e-240)
		tmp = y / ((a - t) / (z - t));
	elseif (a <= 1.6e-32)
		tmp = ((y - x) * z) / (a - t);
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e+52], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-240], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-32], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2e52

   1. Initial program 65.0%

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

   3. Taylor expanded in t around 0 61.9%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   if -4.2e52 < a < 4.7999999999999999e-240

   1. Initial program 73.0%

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

      1. clear-num 72.9%

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

      2. inv-pow 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-/r* 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around 0 62.4%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

      1. clear-num 69.5%

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

      2. un-div-inv 69.5%

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

   9. Applied egg-rr 69.5%

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

   if 4.7999999999999999e-240 < a < 1.6000000000000001e-32

   1. Initial program 64.3%

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

      1. clear-num 64.4%

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

      2. inv-pow 64.4%

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

      3. *-commutative 64.4%

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

      4. associate-/r* 67.7%

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

   4. Applied egg-rr 67.7%

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

   5. Taylor expanded in z around -inf 64.6%

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

   if 1.6000000000000001e-32 < a

   1. Initial program 71.8%

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

   3. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around inf 59.6%

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

      1. associate-/l* 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-72} \lor \neg \left(z \leq 4.5 \cdot 10^{+172}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e-72) (not (<= z 4.5e+172)))
   (* z (* (- y x) (/ -1.0 (- t a))))
   (+ x (* (- z t) (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-72) || !(z <= 4.5e+172)) {
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.4d-72)) .or. (.not. (z <= 4.5d+172))) then
        tmp = z * ((y - x) * ((-1.0d0) / (t - a)))
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-72) || !(z <= 4.5e+172)) {
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e-72) or not (z <= 4.5e+172):
		tmp = z * ((y - x) * (-1.0 / (t - a)))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e-72) || !(z <= 4.5e+172))
		tmp = Float64(z * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e-72) || ~((z <= 4.5e+172)))
		tmp = z * ((y - x) * (-1.0 / (t - a)));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e-72], N[Not[LessEqual[z, 4.5e+172]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000005e-72 or 4.5000000000000002e172 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 79.6%

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

      1. sub-div 79.6%

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

      2. div-inv 79.6%

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

   5. Applied egg-rr 79.6%

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

   if -4.40000000000000005e-72 < z < 4.5000000000000002e172

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-72} \lor \neg \left(z \leq 4.5 \cdot 10^{+172}\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+155)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 1.52e+47)
     (+ x (* z (/ (- y x) (- a t))))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+155) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.52e+47) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d+155)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 1.52d+47) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+155) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.52e+47) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+155:
		tmp = y / ((a - t) / (z - t))
	elif t <= 1.52e+47:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+155)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 1.52e+47)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+155)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 1.52e+47)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+155], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.52e+47], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999973e155

   1. Initial program 30.7%

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

      1. clear-num 30.9%

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

      2. inv-pow 30.9%

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

      3. *-commutative 30.9%

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

      4. associate-/r* 56.1%

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

   4. Applied egg-rr 56.1%

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

   5. Taylor expanded in x around 0 38.9%

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

      1. associate-/l* 64.4%

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

   7. Simplified 64.4%

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

      1. clear-num 64.4%

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

      2. un-div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if -4.49999999999999973e155 < t < 1.52e47

   1. Initial program 83.9%

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

   3. Taylor expanded in z around inf 70.7%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   if 1.52e47 < t

   1. Initial program 44.6%

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

      1. clear-num 44.6%

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

      2. inv-pow 44.6%

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

      3. *-commutative 44.6%

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

      4. associate-/r* 67.5%

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

   4. Applied egg-rr 67.5%

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

   5. Taylor expanded in x around 0 34.7%

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

      1. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+52)
   x
   (if (<= a -7.5e-192) y (if (<= a 1.15e-31) (* x (/ z t)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+52) {
		tmp = x;
	} else if (a <= -7.5e-192) {
		tmp = y;
	} else if (a <= 1.15e-31) {
		tmp = x * (z / t);
	} 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 <= (-2.3d+52)) then
        tmp = x
    else if (a <= (-7.5d-192)) then
        tmp = y
    else if (a <= 1.15d-31) then
        tmp = x * (z / t)
    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 <= -2.3e+52) {
		tmp = x;
	} else if (a <= -7.5e-192) {
		tmp = y;
	} else if (a <= 1.15e-31) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+52:
		tmp = x
	elif a <= -7.5e-192:
		tmp = y
	elif a <= 1.15e-31:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+52)
		tmp = x;
	elseif (a <= -7.5e-192)
		tmp = y;
	elseif (a <= 1.15e-31)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+52)
		tmp = x;
	elseif (a <= -7.5e-192)
		tmp = y;
	elseif (a <= 1.15e-31)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+52], x, If[LessEqual[a, -7.5e-192], y, If[LessEqual[a, 1.15e-31], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3e52 or 1.1499999999999999e-31 < a

   1. Initial program 69.2%

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

   3. Taylor expanded in a around inf 43.3%

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

   if -2.3e52 < a < -7.5000000000000001e-192

   1. Initial program 74.9%

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

   3. Taylor expanded in t around inf 41.3%

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

   if -7.5000000000000001e-192 < a < 1.1499999999999999e-31

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. sub-div 65.7%

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

      2. div-inv 65.6%

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

   5. Applied egg-rr 65.6%

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

   6. Taylor expanded in a around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/l* 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

      4. distribute-neg-frac2 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in y around 0 38.7%

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

       1. associate-/l* 43.8%

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

   11. Simplified 43.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-5} \lor \neg \left(x \leq 0.0054\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8e-5) (not (<= x 0.0054)))
   (+ x (* z (/ (- y x) a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8e-5) || !(x <= 0.0054)) {
		tmp = x + (z * ((y - x) / 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 <= (-8d-5)) .or. (.not. (x <= 0.0054d0))) then
        tmp = x + (z * ((y - x) / 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 <= -8e-5) || !(x <= 0.0054)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8e-5) or not (x <= 0.0054):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8e-5) || !(x <= 0.0054))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / 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 <= -8e-5) || ~((x <= 0.0054)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8e-5], N[Not[LessEqual[x, 0.0054]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000065e-5 or 0.0054000000000000003 < x

   1. Initial program 60.4%

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

   3. Taylor expanded in t around 0 50.8%

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

      1. associate-/l* 54.9%

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

   5. Simplified 54.9%

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

   if -8.00000000000000065e-5 < x < 0.0054000000000000003

   1. Initial program 79.7%

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

      1. clear-num 79.6%

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

      2. inv-pow 79.6%

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

      3. *-commutative 79.6%

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

      4. associate-/r* 90.5%

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

   4. Applied egg-rr 90.5%

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

   5. Taylor expanded in x around 0 65.6%

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

      1. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-5} \lor \neg \left(x \leq 0.0054\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-49} \lor \neg \left(a \leq 1.5 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.7e-49) (not (<= a 1.5e-37)))
   (+ x (* z (/ y a)))
   (/ z (/ t (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e-49) || !(a <= 1.5e-37)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = z / (t / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.7d-49)) .or. (.not. (a <= 1.5d-37))) then
        tmp = x + (z * (y / a))
    else
        tmp = z / (t / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e-49) || !(a <= 1.5e-37)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = z / (t / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.7e-49) or not (a <= 1.5e-37):
		tmp = x + (z * (y / a))
	else:
		tmp = z / (t / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.7e-49) || !(a <= 1.5e-37))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(z / Float64(t / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.7e-49) || ~((a <= 1.5e-37)))
		tmp = x + (z * (y / a));
	else
		tmp = z / (t / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.7e-49], N[Not[LessEqual[a, 1.5e-37]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7000000000000001e-49 or 1.5e-37 < a

   1. Initial program 72.0%

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

   3. Taylor expanded in t around 0 52.1%

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

      1. associate-/l* 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around inf 52.4%

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

   if -3.7000000000000001e-49 < a < 1.5e-37

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. sub-div 61.4%

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

      2. div-inv 61.3%

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

   5. Applied egg-rr 61.3%

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

   6. Taylor expanded in a around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. associate-/l* 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

      4. distribute-neg-frac2 54.2%

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

   8. Simplified 54.2%

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

      1. associate-*r/ 50.7%

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

      2. distribute-frac-neg2 50.7%

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

      3. add-sqr-sqrt 28.1%

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

      4. sqrt-unprod 21.6%

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

      5. sqr-neg 21.6%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 5.1%

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

      8. associate-*r/ 5.2%

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

      9. clear-num 5.2%

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

      10. un-div-inv 5.2%

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

      11. add-sqr-sqrt 1.0%

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

      12. sqrt-unprod 21.7%

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

      13. sqr-neg 21.7%

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

      14. sqrt-unprod 30.6%

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

      15. add-sqr-sqrt 54.2%

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

   10. Applied egg-rr 54.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-49} \lor \neg \left(a \leq 1.5 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+139) y (if (<= t 6.2e+49) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+139) {
		tmp = y;
	} else if (t <= 6.2e+49) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d+139)) then
        tmp = y
    else if (t <= 6.2d+49) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+139) {
		tmp = y;
	} else if (t <= 6.2e+49) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+139:
		tmp = y
	elif t <= 6.2e+49:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+139)
		tmp = y;
	elseif (t <= 6.2e+49)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+139)
		tmp = y;
	elseif (t <= 6.2e+49)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+139], y, If[LessEqual[t, 6.2e+49], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999999e139 or 6.19999999999999985e49 < t

   1. Initial program 40.6%

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

   3. Taylor expanded in t around inf 50.8%

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

   if -4.4999999999999999e139 < t < 6.19999999999999985e49

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0 57.0%

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

      1. associate-/l* 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 49.2%

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

      1. associate-/l* 52.0%

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

   8. Simplified 52.0%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+96) y (if (<= t 1.9e+51) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+96) {
		tmp = y;
	} else if (t <= 1.9e+51) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.3d+96)) then
        tmp = y
    else if (t <= 1.9d+51) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+96) {
		tmp = y;
	} else if (t <= 1.9e+51) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+96:
		tmp = y
	elif t <= 1.9e+51:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+96)
		tmp = y;
	elseif (t <= 1.9e+51)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+96)
		tmp = y;
	elseif (t <= 1.9e+51)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+96], y, If[LessEqual[t, 1.9e+51], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e96 or 1.8999999999999999e51 < t

   1. Initial program 42.9%

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

   3. Taylor expanded in t around inf 46.0%

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

   if -1.3e96 < t < 1.8999999999999999e51

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 34.4%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.6% 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 69.8%

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

3. Taylor expanded in a around inf 24.7%

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

4. Final simplification 24.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024046 
(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))))