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

Percentage Accurate: 67.9% → 91.3%

Time: 19.1s

Alternatives: 22

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: 67.9% 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: 91.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-293} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t z) (- x y)) (- a t)))))
   (if (or (<= t_1 -1e-293) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - z) * Float64(x - y)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.0000000000000001e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 92.1%

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

      3. fma-define 92.2%

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

   3. Simplified 92.2%

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

   if -1.0000000000000001e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. clear-num 4.5%

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

      2. inv-pow 4.5%

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

      3. *-commutative 4.5%

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

      4. associate-/r* 4.6%

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

   4. Applied egg-rr 4.6%

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

      1. div-inv 4.6%

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

   6. Applied egg-rr 4.6%

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

   7. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in y around 0 99.6%

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

       1. mul-1-neg 99.6%

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

       2. associate-/l* 99.7%

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

       3. distribute-rgt-neg-in 99.7%

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

       4. distribute-neg-frac2 99.7%

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

   12. Simplified 99.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t} \leq -1 \cdot 10^{-293} \lor \neg \left(x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-293} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- t z) (- x y)) (- a t)))))
   (if (or (<= t_1 -1e-293) (not (<= t_1 0.0)))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (+ y (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (((t - z) * (x - y)) / (a - t))
    if ((t_1 <= (-1d-293)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - z) * (x - y)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - z) * (x - y)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-293) or not (t_1 <= 0.0):
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - z) * Float64(x - y)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-293) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - z) * (x - y)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-293) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.0000000000000001e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 69.8%

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

      1. clear-num 69.7%

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

      2. inv-pow 69.7%

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

      3. *-commutative 69.7%

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

      4. associate-/r* 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. div-inv 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. *-un-lft-identity 92.0%

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

      2. +-commutative 92.0%

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

      3. unpow-prod-down 92.0%

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

      4. fma-define 92.0%

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

      5. unpow-1 92.0%

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

      6. inv-pow 92.0%

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

      7. pow-pow 92.1%

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

      8. metadata-eval 92.1%

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

      9. pow1 92.1%

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

   8. Applied egg-rr 92.1%

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

      1. *-lft-identity 92.1%

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

      2. fma-undefine 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*r/ 92.1%

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

      5. *-rgt-identity 92.1%

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

   10. Simplified 92.1%

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

   if -1.0000000000000001e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.4%

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

      1. clear-num 4.5%

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

      2. inv-pow 4.5%

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

      3. *-commutative 4.5%

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

      4. associate-/r* 4.6%

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

   4. Applied egg-rr 4.6%

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

      1. div-inv 4.6%

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

   6. Applied egg-rr 4.6%

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

   7. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in y around 0 99.6%

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

       1. mul-1-neg 99.6%

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

       2. associate-/l* 99.7%

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

       3. distribute-rgt-neg-in 99.7%

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

       4. distribute-neg-frac2 99.7%

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

   12. Simplified 99.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t} \leq -1 \cdot 10^{-293} \lor \neg \left(x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z - a}{t}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+240}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ (- z a) t)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= a -2.1e+240)
     (+ x (* (- y x) (/ z a)))
     (if (<= a -6.5e+125)
       (+ x (* y (/ t (- t a))))
       (if (<= a -1.06e-10)
         t_2
         (if (<= a -4.3e-67)
           t_1
           (if (<= a -2.2e-85)
             t_2
             (if (<= a 1.5e-277)
               t_1
               (if (<= a 3.6e+73)
                 (* y (/ (- z t) (- a t)))
                 (+ x (* y (/ (- z t) a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * ((z - a) / t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -2.1e+240) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -6.5e+125) {
		tmp = x + (y * (t / (t - a)));
	} else if (a <= -1.06e-10) {
		tmp = t_2;
	} else if (a <= -4.3e-67) {
		tmp = t_1;
	} else if (a <= -2.2e-85) {
		tmp = t_2;
	} else if (a <= 1.5e-277) {
		tmp = t_1;
	} else if (a <= 3.6e+73) {
		tmp = y * ((z - t) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x * ((z - a) / t))
    t_2 = x + (z * ((y - x) / a))
    if (a <= (-2.1d+240)) then
        tmp = x + ((y - x) * (z / a))
    else if (a <= (-6.5d+125)) then
        tmp = x + (y * (t / (t - a)))
    else if (a <= (-1.06d-10)) then
        tmp = t_2
    else if (a <= (-4.3d-67)) then
        tmp = t_1
    else if (a <= (-2.2d-85)) then
        tmp = t_2
    else if (a <= 1.5d-277) then
        tmp = t_1
    else if (a <= 3.6d+73) then
        tmp = y * ((z - t) / (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 t_1 = y + (x * ((z - a) / t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -2.1e+240) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -6.5e+125) {
		tmp = x + (y * (t / (t - a)));
	} else if (a <= -1.06e-10) {
		tmp = t_2;
	} else if (a <= -4.3e-67) {
		tmp = t_1;
	} else if (a <= -2.2e-85) {
		tmp = t_2;
	} else if (a <= 1.5e-277) {
		tmp = t_1;
	} else if (a <= 3.6e+73) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * ((z - a) / t))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -2.1e+240:
		tmp = x + ((y - x) * (z / a))
	elif a <= -6.5e+125:
		tmp = x + (y * (t / (t - a)))
	elif a <= -1.06e-10:
		tmp = t_2
	elif a <= -4.3e-67:
		tmp = t_1
	elif a <= -2.2e-85:
		tmp = t_2
	elif a <= 1.5e-277:
		tmp = t_1
	elif a <= 3.6e+73:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -2.1e+240)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (a <= -6.5e+125)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (a <= -1.06e-10)
		tmp = t_2;
	elseif (a <= -4.3e-67)
		tmp = t_1;
	elseif (a <= -2.2e-85)
		tmp = t_2;
	elseif (a <= 1.5e-277)
		tmp = t_1;
	elseif (a <= 3.6e+73)
		tmp = Float64(y * Float64(Float64(z - t) / 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)
	t_1 = y + (x * ((z - a) / t));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -2.1e+240)
		tmp = x + ((y - x) * (z / a));
	elseif (a <= -6.5e+125)
		tmp = x + (y * (t / (t - a)));
	elseif (a <= -1.06e-10)
		tmp = t_2;
	elseif (a <= -4.3e-67)
		tmp = t_1;
	elseif (a <= -2.2e-85)
		tmp = t_2;
	elseif (a <= 1.5e-277)
		tmp = t_1;
	elseif (a <= 3.6e+73)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+240], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.5e+125], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.06e-10], t$95$2, If[LessEqual[a, -4.3e-67], t$95$1, If[LessEqual[a, -2.2e-85], t$95$2, If[LessEqual[a, 1.5e-277], t$95$1, If[LessEqual[a, 3.6e+73], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.0999999999999999e240

   1. Initial program 45.7%

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

      1. clear-num 45.7%

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

      2. inv-pow 45.7%

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

      3. *-commutative 45.7%

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

      4. associate-/r* 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. +-commutative 99.8%

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

      3. unpow-prod-down 99.8%

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

      4. fma-define 99.8%

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

      5. unpow-1 99.8%

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

      6. inv-pow 99.8%

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

      7. pow-pow 99.8%

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

      8. metadata-eval 99.8%

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

      9. pow1 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. *-lft-identity 99.8%

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

      2. fma-undefine 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r/ 99.9%

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

      5. *-rgt-identity 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in t around 0 60.5%

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

       1. *-commutative 60.5%

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

       2. *-lft-identity 60.5%

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

       3. times-frac 96.7%

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

       4. /-rgt-identity 96.7%

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

   13. Simplified 96.7%

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

   if -2.0999999999999999e240 < a < -6.4999999999999999e125

   1. Initial program 50.9%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 82.6%

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

      1. neg-mul-1 82.6%

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

      2. distribute-neg-frac2 82.6%

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

      3. neg-sub0 82.6%

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

      4. associate--r- 82.6%

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

      5. neg-sub0 82.6%

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

   8. Simplified 82.6%

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

   if -6.4999999999999999e125 < a < -1.06e-10 or -4.30000000000000027e-67 < a < -2.2e-85

   1. Initial program 80.8%

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

   3. Taylor expanded in t around 0 77.3%

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

      1. associate-/l* 80.3%

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

   5. Simplified 80.3%

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

   if -1.06e-10 < a < -4.30000000000000027e-67 or -2.2e-85 < a < 1.49999999999999989e-277

   1. Initial program 63.8%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. *-commutative 63.7%

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

      4. associate-/r* 78.4%

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

   4. Applied egg-rr 78.4%

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

      1. div-inv 78.3%

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

   6. Applied egg-rr 78.3%

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

   7. Taylor expanded in t around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. associate-*r/ 82.5%

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

      3. associate-*r/ 82.5%

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

      4. mul-1-neg 82.5%

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

      5. div-sub 82.5%

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

      6. mul-1-neg 82.5%

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

      7. distribute-lft-out-- 82.5%

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

      8. associate-*r/ 82.5%

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

      9. mul-1-neg 82.5%

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

      10. unsub-neg 82.5%

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

      11. distribute-rgt-out-- 82.5%

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

   9. Simplified 82.5%

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

   10. Taylor expanded in y around 0 75.1%

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

       1. mul-1-neg 75.1%

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

       2. associate-/l* 81.4%

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

       3. distribute-rgt-neg-in 81.4%

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

       4. distribute-neg-frac2 81.4%

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

   12. Simplified 81.4%

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

   if 1.49999999999999989e-277 < a < 3.5999999999999999e73

   1. Initial program 72.3%

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

      1. clear-num 72.1%

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

      2. inv-pow 72.1%

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

      3. *-commutative 72.1%

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

      4. associate-/r* 84.2%

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

   4. Applied egg-rr 84.2%

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

      1. div-inv 84.1%

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

   6. Applied egg-rr 84.1%

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

   7. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 73.6%

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

   9. Simplified 73.6%

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

   if 3.5999999999999999e73 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+240}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-85}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-277}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ y (/ (* z (- x y)) t))))
   (if (<= a -1.15e-10)
     (+ x (* (- y x) (/ z a)))
     (if (<= a -2.1e-62)
       t_2
       (if (<= a -3.1e-76)
         (+ x (* z (/ (- y x) a)))
         (if (<= a -1.6e-127)
           t_1
           (if (<= a 3e-151)
             t_2
             (if (<= a 7.5e+74) t_1 (+ x (* y (/ (- z t) a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = y + ((z * (x - y)) / t);
	double tmp;
	if (a <= -1.15e-10) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -2.1e-62) {
		tmp = t_2;
	} else if (a <= -3.1e-76) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= -1.6e-127) {
		tmp = t_1;
	} else if (a <= 3e-151) {
		tmp = t_2;
	} else if (a <= 7.5e+74) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = y + ((z * (x - y)) / t)
    if (a <= (-1.15d-10)) then
        tmp = x + ((y - x) * (z / a))
    else if (a <= (-2.1d-62)) then
        tmp = t_2
    else if (a <= (-3.1d-76)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= (-1.6d-127)) then
        tmp = t_1
    else if (a <= 3d-151) then
        tmp = t_2
    else if (a <= 7.5d+74) then
        tmp = t_1
    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 t_1 = y * ((z - t) / (a - t));
	double t_2 = y + ((z * (x - y)) / t);
	double tmp;
	if (a <= -1.15e-10) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -2.1e-62) {
		tmp = t_2;
	} else if (a <= -3.1e-76) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= -1.6e-127) {
		tmp = t_1;
	} else if (a <= 3e-151) {
		tmp = t_2;
	} else if (a <= 7.5e+74) {
		tmp = t_1;
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = y + ((z * (x - y)) / t)
	tmp = 0
	if a <= -1.15e-10:
		tmp = x + ((y - x) * (z / a))
	elif a <= -2.1e-62:
		tmp = t_2
	elif a <= -3.1e-76:
		tmp = x + (z * ((y - x) / a))
	elif a <= -1.6e-127:
		tmp = t_1
	elif a <= 3e-151:
		tmp = t_2
	elif a <= 7.5e+74:
		tmp = t_1
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(y + Float64(Float64(z * Float64(x - y)) / t))
	tmp = 0.0
	if (a <= -1.15e-10)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (a <= -2.1e-62)
		tmp = t_2;
	elseif (a <= -3.1e-76)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= -1.6e-127)
		tmp = t_1;
	elseif (a <= 3e-151)
		tmp = t_2;
	elseif (a <= 7.5e+74)
		tmp = t_1;
	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)
	t_1 = y * ((z - t) / (a - t));
	t_2 = y + ((z * (x - y)) / t);
	tmp = 0.0;
	if (a <= -1.15e-10)
		tmp = x + ((y - x) * (z / a));
	elseif (a <= -2.1e-62)
		tmp = t_2;
	elseif (a <= -3.1e-76)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= -1.6e-127)
		tmp = t_1;
	elseif (a <= 3e-151)
		tmp = t_2;
	elseif (a <= 7.5e+74)
		tmp = t_1;
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-10], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-62], t$95$2, If[LessEqual[a, -3.1e-76], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-127], t$95$1, If[LessEqual[a, 3e-151], t$95$2, If[LessEqual[a, 7.5e+74], t$95$1, N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.15000000000000004e-10

   1. Initial program 59.2%

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

      1. clear-num 59.2%

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

      2. inv-pow 59.2%

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

      3. *-commutative 59.2%

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

      4. associate-/r* 95.2%

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

   4. Applied egg-rr 95.2%

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

      1. div-inv 95.2%

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

   6. Applied egg-rr 95.2%

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

      1. *-un-lft-identity 95.2%

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

      2. +-commutative 95.2%

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

      3. unpow-prod-down 95.2%

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

      4. fma-define 95.2%

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

      5. unpow-1 95.2%

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

      6. inv-pow 95.2%

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

      7. pow-pow 95.3%

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

      8. metadata-eval 95.3%

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

      9. pow1 95.3%

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

   8. Applied egg-rr 95.3%

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

      1. *-lft-identity 95.3%

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

      2. fma-undefine 95.2%

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

      3. *-commutative 95.2%

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

      4. associate-*r/ 95.3%

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

      5. *-rgt-identity 95.3%

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

   10. Simplified 95.3%

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

   11. Taylor expanded in t around 0 60.7%

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

       1. *-commutative 60.7%

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

       2. *-lft-identity 60.7%

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

       3. times-frac 74.4%

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

       4. /-rgt-identity 74.4%

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

   13. Simplified 74.4%

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

   if -1.15000000000000004e-10 < a < -2.0999999999999999e-62 or -1.60000000000000009e-127 < a < 3e-151

   1. Initial program 71.0%

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

      1. clear-num 70.9%

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

      2. inv-pow 70.9%

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

      3. *-commutative 70.9%

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

      4. associate-/r* 79.6%

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

   4. Applied egg-rr 79.6%

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

      1. div-inv 79.5%

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

   6. Applied egg-rr 79.5%

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

   7. Taylor expanded in t around inf 85.6%

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

      1. associate--l+ 85.6%

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

      2. associate-*r/ 85.6%

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

      3. associate-*r/ 85.6%

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

      4. mul-1-neg 85.6%

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

      5. div-sub 85.6%

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

      6. mul-1-neg 85.6%

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

      7. distribute-lft-out-- 85.6%

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

      8. associate-*r/ 85.6%

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

      9. mul-1-neg 85.6%

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

      10. unsub-neg 85.6%

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

      11. distribute-rgt-out-- 85.6%

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

   9. Simplified 85.6%

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

   10. Taylor expanded in z around inf 80.8%

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

   if -2.0999999999999999e-62 < a < -3.0999999999999997e-76

   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 69.0%

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

      1. associate-/l* 69.3%

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

   5. Simplified 69.3%

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

   if -3.0999999999999997e-76 < a < -1.60000000000000009e-127 or 3e-151 < a < 7.5e74

   1. Initial program 65.5%

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

      1. clear-num 65.3%

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

      2. inv-pow 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/r* 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. div-inv 83.4%

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

   6. Applied egg-rr 83.4%

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

   7. Taylor expanded in x around 0 55.0%

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

      1. associate-/l* 73.2%

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

   9. Simplified 73.2%

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

   if 7.5e74 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-10}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-76}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-151}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+238}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+238)
   (+ x (* (- y x) (/ z a)))
   (if (<= a -2.6e+125)
     (+ x (* y (/ t (- t a))))
     (if (<= a -1.1e-10)
       (+ x (* z (/ (- y x) a)))
       (if (<= a 7e-151)
         (+ y (/ (* z (- x y)) t))
         (if (<= a 1.95e+74)
           (* y (/ (- z t) (- a t)))
           (+ x (* y (/ (- z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+238) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -2.6e+125) {
		tmp = x + (y * (t / (t - a)));
	} else if (a <= -1.1e-10) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 7e-151) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 1.95e+74) {
		tmp = y * ((z - t) / (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 <= (-5d+238)) then
        tmp = x + ((y - x) * (z / a))
    else if (a <= (-2.6d+125)) then
        tmp = x + (y * (t / (t - a)))
    else if (a <= (-1.1d-10)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= 7d-151) then
        tmp = y + ((z * (x - y)) / t)
    else if (a <= 1.95d+74) then
        tmp = y * ((z - t) / (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 <= -5e+238) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= -2.6e+125) {
		tmp = x + (y * (t / (t - a)));
	} else if (a <= -1.1e-10) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 7e-151) {
		tmp = y + ((z * (x - y)) / t);
	} else if (a <= 1.95e+74) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+238:
		tmp = x + ((y - x) * (z / a))
	elif a <= -2.6e+125:
		tmp = x + (y * (t / (t - a)))
	elif a <= -1.1e-10:
		tmp = x + (z * ((y - x) / a))
	elif a <= 7e-151:
		tmp = y + ((z * (x - y)) / t)
	elif a <= 1.95e+74:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+238)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (a <= -2.6e+125)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (a <= -1.1e-10)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= 7e-151)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (a <= 1.95e+74)
		tmp = Float64(y * Float64(Float64(z - t) / 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 <= -5e+238)
		tmp = x + ((y - x) * (z / a));
	elseif (a <= -2.6e+125)
		tmp = x + (y * (t / (t - a)));
	elseif (a <= -1.1e-10)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= 7e-151)
		tmp = y + ((z * (x - y)) / t);
	elseif (a <= 1.95e+74)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+238], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e+125], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-10], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-151], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+74], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.99999999999999995e238

   1. Initial program 45.7%

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

      1. clear-num 45.7%

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

      2. inv-pow 45.7%

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

      3. *-commutative 45.7%

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

      4. associate-/r* 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. +-commutative 99.8%

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

      3. unpow-prod-down 99.8%

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

      4. fma-define 99.8%

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

      5. unpow-1 99.8%

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

      6. inv-pow 99.8%

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

      7. pow-pow 99.8%

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

      8. metadata-eval 99.8%

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

      9. pow1 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. *-lft-identity 99.8%

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

      2. fma-undefine 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r/ 99.9%

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

      5. *-rgt-identity 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in t around 0 60.5%

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

       1. *-commutative 60.5%

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

       2. *-lft-identity 60.5%

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

       3. times-frac 96.7%

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

       4. /-rgt-identity 96.7%

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

   13. Simplified 96.7%

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

   if -4.99999999999999995e238 < a < -2.60000000000000003e125

   1. Initial program 50.9%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 82.6%

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

      1. neg-mul-1 82.6%

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

      2. distribute-neg-frac2 82.6%

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

      3. neg-sub0 82.6%

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

      4. associate--r- 82.6%

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

      5. neg-sub0 82.6%

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

   8. Simplified 82.6%

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

   if -2.60000000000000003e125 < a < -1.09999999999999995e-10

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0 75.5%

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

      1. associate-/l* 79.2%

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

   5. Simplified 79.2%

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

   if -1.09999999999999995e-10 < a < 6.99999999999999991e-151

   1. Initial program 71.5%

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

      1. clear-num 71.3%

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

      2. inv-pow 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-/r* 80.9%

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

   4. Applied egg-rr 80.9%

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

      1. div-inv 80.8%

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

   6. Applied egg-rr 80.8%

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

   7. Taylor expanded in t around inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. associate-*r/ 78.3%

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

      3. associate-*r/ 78.3%

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

      4. mul-1-neg 78.3%

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

      5. div-sub 79.2%

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

      6. mul-1-neg 79.2%

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

      7. distribute-lft-out-- 79.2%

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

      8. associate-*r/ 79.2%

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

      9. mul-1-neg 79.2%

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

      10. unsub-neg 79.2%

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

      11. distribute-rgt-out-- 79.2%

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

   9. Simplified 79.2%

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

   10. Taylor expanded in z around inf 74.5%

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

   if 6.99999999999999991e-151 < a < 1.95000000000000004e74

   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 64.1%

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

      2. inv-pow 64.1%

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

      3. *-commutative 64.1%

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

      4. associate-/r* 82.5%

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

   4. Applied egg-rr 82.5%

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

      1. div-inv 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in x around 0 53.8%

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

      1. associate-/l* 72.1%

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

   9. Simplified 72.1%

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

   if 1.95000000000000004e74 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+238}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+199}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+176)
   (* x (/ z (- a)))
   (if (<= z -2.05e+49)
     (* y (/ z a))
     (if (<= z 4.4e+71)
       (+ x y)
       (if (<= z 5e+135)
         (* y (/ (- z) t))
         (if (<= z 2.5e+199) (+ x y) (* z (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+176) {
		tmp = x * (z / -a);
	} else if (z <= -2.05e+49) {
		tmp = y * (z / a);
	} else if (z <= 4.4e+71) {
		tmp = x + y;
	} else if (z <= 5e+135) {
		tmp = y * (-z / t);
	} else if (z <= 2.5e+199) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= (-3.2d+176)) then
        tmp = x * (z / -a)
    else if (z <= (-2.05d+49)) then
        tmp = y * (z / a)
    else if (z <= 4.4d+71) then
        tmp = x + y
    else if (z <= 5d+135) then
        tmp = y * (-z / t)
    else if (z <= 2.5d+199) then
        tmp = x + y
    else
        tmp = 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 (z <= -3.2e+176) {
		tmp = x * (z / -a);
	} else if (z <= -2.05e+49) {
		tmp = y * (z / a);
	} else if (z <= 4.4e+71) {
		tmp = x + y;
	} else if (z <= 5e+135) {
		tmp = y * (-z / t);
	} else if (z <= 2.5e+199) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+176:
		tmp = x * (z / -a)
	elif z <= -2.05e+49:
		tmp = y * (z / a)
	elif z <= 4.4e+71:
		tmp = x + y
	elif z <= 5e+135:
		tmp = y * (-z / t)
	elif z <= 2.5e+199:
		tmp = x + y
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+176)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (z <= -2.05e+49)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 4.4e+71)
		tmp = Float64(x + y);
	elseif (z <= 5e+135)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 2.5e+199)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+176)
		tmp = x * (z / -a);
	elseif (z <= -2.05e+49)
		tmp = y * (z / a);
	elseif (z <= 4.4e+71)
		tmp = x + y;
	elseif (z <= 5e+135)
		tmp = y * (-z / t);
	elseif (z <= 2.5e+199)
		tmp = x + y;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+176], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e+49], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+71], N[(x + y), $MachinePrecision], If[LessEqual[z, 5e+135], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+199], N[(x + y), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1999999999999998e176

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 42.9%

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

   5. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/l* 42.4%

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

      3. distribute-rgt-neg-in 42.4%

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

      4. distribute-neg-frac2 42.4%

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

   7. Simplified 42.4%

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

   if -3.1999999999999998e176 < z < -2.05e49

   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 z around inf 73.8%

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

   4. Taylor expanded in t around 0 57.0%

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

   5. Taylor expanded in y around inf 40.7%

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

      1. associate-/l* 51.7%

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

   7. Simplified 51.7%

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

   if -2.05e49 < z < 4.39999999999999989e71 or 5.00000000000000029e135 < z < 2.4999999999999999e199

   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 y around inf 64.3%

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

      1. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in t around inf 49.2%

      \[\leadsto x + y \cdot \color{blue}{1} \]

   if 4.39999999999999989e71 < z < 5.00000000000000029e135

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf 62.6%

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

   4. Taylor expanded in a around 0 43.5%

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

      1. distribute-lft-out-- 43.5%

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

      2. div-sub 43.5%

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

      3. associate-*r/ 43.5%

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

      4. neg-mul-1 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in y around inf 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 44.2%

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

      3. distribute-rgt-neg-in 44.2%

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

      4. distribute-neg-frac2 44.2%

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

   9. Simplified 44.2%

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

   if 2.4999999999999999e199 < z

   1. Initial program 60.0%

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

   3. Taylor expanded in z around inf 90.6%

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

   4. Taylor expanded in t around 0 60.9%

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

   5. Taylor expanded in y around inf 33.4%

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

      1. *-commutative 33.4%

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

      2. *-lft-identity 33.4%

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

      3. times-frac 45.3%

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

      4. /-rgt-identity 45.3%

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

   7. Simplified 45.3%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+199}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.15 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= a -3.15e+174)
     t_2
     (if (<= a -1.1e+148)
       t_1
       (if (<= a -6.5e-12) (+ x (/ (* y z) a)) (if (<= a 4.2e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -3.15e+174) {
		tmp = t_2;
	} else if (a <= -1.1e+148) {
		tmp = t_1;
	} else if (a <= -6.5e-12) {
		tmp = x + ((y * z) / a);
	} else if (a <= 4.2e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y * (z / a))
    if (a <= (-3.15d+174)) then
        tmp = t_2
    else if (a <= (-1.1d+148)) then
        tmp = t_1
    else if (a <= (-6.5d-12)) then
        tmp = x + ((y * z) / a)
    else if (a <= 4.2d+75) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (a <= -3.15e+174) {
		tmp = t_2;
	} else if (a <= -1.1e+148) {
		tmp = t_1;
	} else if (a <= -6.5e-12) {
		tmp = x + ((y * z) / a);
	} else if (a <= 4.2e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * (z / a))
	tmp = 0
	if a <= -3.15e+174:
		tmp = t_2
	elif a <= -1.1e+148:
		tmp = t_1
	elif a <= -6.5e-12:
		tmp = x + ((y * z) / a)
	elif a <= 4.2e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.15e+174)
		tmp = t_2;
	elseif (a <= -1.1e+148)
		tmp = t_1;
	elseif (a <= -6.5e-12)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 4.2e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -3.15e+174)
		tmp = t_2;
	elseif (a <= -1.1e+148)
		tmp = t_1;
	elseif (a <= -6.5e-12)
		tmp = x + ((y * z) / a);
	elseif (a <= 4.2e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.15e+174], t$95$2, If[LessEqual[a, -1.1e+148], t$95$1, If[LessEqual[a, -6.5e-12], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.15e174 or 4.19999999999999997e75 < a

   1. Initial program 58.5%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around 0 62.3%

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

      1. associate-/l* 74.4%

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

   8. Simplified 74.4%

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

   if -3.15e174 < a < -1.0999999999999999e148 or -6.5000000000000002e-12 < a < 4.19999999999999997e75

   1. Initial program 67.3%

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

      1. clear-num 67.1%

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

      2. inv-pow 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-/r* 81.7%

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

   4. Applied egg-rr 81.7%

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

      1. div-inv 81.7%

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

   6. Applied egg-rr 81.7%

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

   7. Taylor expanded in x around 0 53.4%

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

      1. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -1.0999999999999999e148 < a < -6.5000000000000002e-12

   1. Initial program 77.0%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. associate-/l* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around 0 61.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+174}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+196}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) a))))
   (if (<= z -5.3e+48)
     t_1
     (if (<= z 1.75e+70)
       (+ x y)
       (if (<= z 6.2e+156)
         (* z (/ y (- a t)))
         (if (<= z 2.35e+196) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / a);
	double tmp;
	if (z <= -5.3e+48) {
		tmp = t_1;
	} else if (z <= 1.75e+70) {
		tmp = x + y;
	} else if (z <= 6.2e+156) {
		tmp = z * (y / (a - t));
	} else if (z <= 2.35e+196) {
		tmp = x + y;
	} 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 = z * ((y - x) / a)
    if (z <= (-5.3d+48)) then
        tmp = t_1
    else if (z <= 1.75d+70) then
        tmp = x + y
    else if (z <= 6.2d+156) then
        tmp = z * (y / (a - t))
    else if (z <= 2.35d+196) then
        tmp = x + y
    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 = z * ((y - x) / a);
	double tmp;
	if (z <= -5.3e+48) {
		tmp = t_1;
	} else if (z <= 1.75e+70) {
		tmp = x + y;
	} else if (z <= 6.2e+156) {
		tmp = z * (y / (a - t));
	} else if (z <= 2.35e+196) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / a)
	tmp = 0
	if z <= -5.3e+48:
		tmp = t_1
	elif z <= 1.75e+70:
		tmp = x + y
	elif z <= 6.2e+156:
		tmp = z * (y / (a - t))
	elif z <= 2.35e+196:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / a))
	tmp = 0.0
	if (z <= -5.3e+48)
		tmp = t_1;
	elseif (z <= 1.75e+70)
		tmp = Float64(x + y);
	elseif (z <= 6.2e+156)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (z <= 2.35e+196)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / a);
	tmp = 0.0;
	if (z <= -5.3e+48)
		tmp = t_1;
	elseif (z <= 1.75e+70)
		tmp = x + y;
	elseif (z <= 6.2e+156)
		tmp = z * (y / (a - t));
	elseif (z <= 2.35e+196)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+48], t$95$1, If[LessEqual[z, 1.75e+70], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.2e+156], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+196], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3e48 or 2.3500000000000001e196 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in z around inf 76.2%

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

   4. Taylor expanded in a around inf 54.7%

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

   if -5.3e48 < z < 1.75000000000000001e70 or 6.2000000000000004e156 < z < 2.3500000000000001e196

   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 y around inf 65.3%

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

      1. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around inf 50.0%

      \[\leadsto x + y \cdot \color{blue}{1} \]

   if 1.75000000000000001e70 < z < 6.2000000000000004e156

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf 65.3%

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

   4. Taylor expanded in y around inf 49.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+196}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e+218)
   y
   (if (<= t -2.45e+146)
     (* x (/ (- z a) t))
     (if (<= t -9.4e+33) y (if (<= t 5.2e-26) (+ x (* y (/ z a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+218) {
		tmp = y;
	} else if (t <= -2.45e+146) {
		tmp = x * ((z - a) / t);
	} else if (t <= -9.4e+33) {
		tmp = y;
	} else if (t <= 5.2e-26) {
		tmp = x + (y * (z / a));
	} else {
		tmp = 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 <= (-5.8d+218)) then
        tmp = y
    else if (t <= (-2.45d+146)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-9.4d+33)) then
        tmp = y
    else if (t <= 5.2d-26) then
        tmp = x + (y * (z / a))
    else
        tmp = 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 <= -5.8e+218) {
		tmp = y;
	} else if (t <= -2.45e+146) {
		tmp = x * ((z - a) / t);
	} else if (t <= -9.4e+33) {
		tmp = y;
	} else if (t <= 5.2e-26) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e+218:
		tmp = y
	elif t <= -2.45e+146:
		tmp = x * ((z - a) / t)
	elif t <= -9.4e+33:
		tmp = y
	elif t <= 5.2e-26:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e+218)
		tmp = y;
	elseif (t <= -2.45e+146)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -9.4e+33)
		tmp = y;
	elseif (t <= 5.2e-26)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e+218)
		tmp = y;
	elseif (t <= -2.45e+146)
		tmp = x * ((z - a) / t);
	elseif (t <= -9.4e+33)
		tmp = y;
	elseif (t <= 5.2e-26)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e+218], y, If[LessEqual[t, -2.45e+146], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.4e+33], y, If[LessEqual[t, 5.2e-26], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.7999999999999999e218 or -2.4500000000000001e146 < t < -9.3999999999999996e33

   1. Initial program 34.8%

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

   3. Taylor expanded in t around inf 56.6%

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

   if -5.7999999999999999e218 < t < -2.4500000000000001e146

   1. Initial program 28.2%

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

      1. clear-num 28.2%

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

      2. inv-pow 28.2%

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

      3. *-commutative 28.2%

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

      4. associate-/r* 67.4%

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

   4. Applied egg-rr 67.4%

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

      1. div-inv 67.1%

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

   6. Applied egg-rr 67.1%

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

   7. Taylor expanded in t around inf 59.9%

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

      1. associate--l+ 59.9%

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

      2. associate-*r/ 59.9%

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

      3. associate-*r/ 59.9%

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

      4. mul-1-neg 59.9%

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

      5. div-sub 59.9%

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

      6. mul-1-neg 59.9%

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

      7. distribute-lft-out-- 59.9%

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

      8. associate-*r/ 59.9%

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

      9. mul-1-neg 59.9%

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

      10. unsub-neg 59.9%

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

      11. distribute-rgt-out-- 59.9%

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

   9. Simplified 59.9%

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

   10. Taylor expanded in y around 0 43.2%

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

       1. associate-/l* 51.5%

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

   12. Simplified 51.5%

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

   if -9.3999999999999996e33 < t < 5.2000000000000002e-26

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around 0 57.7%

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

      1. associate-/l* 60.4%

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

   8. Simplified 60.4%

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

   if 5.2000000000000002e-26 < t

   1. Initial program 47.6%

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

   3. Taylor expanded in y around inf 50.2%

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

      1. associate-/l* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in t around inf 51.6%

      \[\leadsto x + y \cdot \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{+33}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+80}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.16e+80)
   (+ y (* (- z a) (/ (- x y) t)))
   (if (<= t 3.5e+23)
     (+ x (/ (* (- t z) (- x y)) (- a t)))
     (+ x (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+80) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 3.5e+23) {
		tmp = x + (((t - z) * (x - y)) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.16d+80)) then
        tmp = y + ((z - a) * ((x - y) / t))
    else if (t <= 3.5d+23) then
        tmp = x + (((t - z) * (x - y)) / (a - t))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+80) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else if (t <= 3.5e+23) {
		tmp = x + (((t - z) * (x - y)) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.16e+80:
		tmp = y + ((z - a) * ((x - y) / t))
	elif t <= 3.5e+23:
		tmp = x + (((t - z) * (x - y)) / (a - t))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.16e+80)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	elseif (t <= 3.5e+23)
		tmp = Float64(x + Float64(Float64(Float64(t - z) * Float64(x - y)) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.16e+80)
		tmp = y + ((z - a) * ((x - y) / t));
	elseif (t <= 3.5e+23)
		tmp = x + (((t - z) * (x - y)) / (a - t));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.16e+80], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+23], N[(x + N[(N[(N[(t - z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15999999999999997e80

   1. Initial program 24.0%

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

   3. Taylor expanded in t around inf 58.2%

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

      1. associate--l+ 58.2%

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

      2. distribute-lft-out-- 58.2%

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

      3. div-sub 58.2%

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

      4. mul-1-neg 58.2%

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

      5. unsub-neg 58.2%

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

      6. div-sub 58.2%

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

      7. associate-/l* 66.4%

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

      8. associate-/l* 73.6%

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

      9. distribute-rgt-out-- 73.8%

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

   5. Simplified 73.8%

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

   if -1.15999999999999997e80 < t < 3.5000000000000002e23

   1. Initial program 86.7%

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

   if 3.5000000000000002e23 < t

   1. Initial program 42.1%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. associate-/l* 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+80}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{\left(t - z\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+48} \lor \neg \left(z \leq 2.46 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.62e+177)
   (* x (/ z (- a)))
   (if (or (<= z -3.9e+48) (not (<= z 2.46e+70)))
     (* z (/ y (- a t)))
     (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.62e+177) {
		tmp = x * (z / -a);
	} else if ((z <= -3.9e+48) || !(z <= 2.46e+70)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = 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 (z <= (-1.62d+177)) then
        tmp = x * (z / -a)
    else if ((z <= (-3.9d+48)) .or. (.not. (z <= 2.46d+70))) then
        tmp = z * (y / (a - t))
    else
        tmp = 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 (z <= -1.62e+177) {
		tmp = x * (z / -a);
	} else if ((z <= -3.9e+48) || !(z <= 2.46e+70)) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.62e+177:
		tmp = x * (z / -a)
	elif (z <= -3.9e+48) or not (z <= 2.46e+70):
		tmp = z * (y / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.62e+177)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif ((z <= -3.9e+48) || !(z <= 2.46e+70))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.62e+177)
		tmp = x * (z / -a);
	elseif ((z <= -3.9e+48) || ~((z <= 2.46e+70)))
		tmp = z * (y / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.62e+177], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.9e+48], N[Not[LessEqual[z, 2.46e+70]], $MachinePrecision]], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.61999999999999999e177

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 42.9%

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

   5. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/l* 42.4%

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

      3. distribute-rgt-neg-in 42.4%

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

      4. distribute-neg-frac2 42.4%

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

   7. Simplified 42.4%

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

   if -1.61999999999999999e177 < z < -3.9000000000000001e48 or 2.45999999999999995e70 < z

   1. Initial program 63.2%

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

   3. Taylor expanded in z around inf 74.2%

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

   4. Taylor expanded in y around inf 46.8%

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

   if -3.9000000000000001e48 < z < 2.45999999999999995e70

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. associate-/l* 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around inf 50.1%

      \[\leadsto x + y \cdot \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+48} \lor \neg \left(z \leq 2.46 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+169} \lor \neg \left(x \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.15e+169) (not (<= x 2e+67)))
   (* x (+ (/ (- z t) (- t a)) 1.0))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.15e+169) || !(x <= 2e+67)) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.15d+169)) .or. (.not. (x <= 2d+67))) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.15e+169) || !(x <= 2e+67)) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.15e+169) or not (x <= 2e+67):
		tmp = x * (((z - t) / (t - a)) + 1.0)
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.15e+169) || !(x <= 2e+67))
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.15e+169) || ~((x <= 2e+67)))
		tmp = x * (((z - t) / (t - a)) + 1.0);
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.15e+169], N[Not[LessEqual[x, 2e+67]], $MachinePrecision]], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e169 or 1.99999999999999997e67 < x

   1. Initial program 47.4%

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

   3. Taylor expanded in x around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

   5. Simplified 71.8%

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

   if -1.15e169 < x < 1.99999999999999997e67

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+169} \lor \neg \left(x \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+198}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+176)
   (* x (/ z (- a)))
   (if (<= z -1.12e+49)
     (* y (/ z a))
     (if (<= z 5.5e+198) (+ x y) (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+176) {
		tmp = x * (z / -a);
	} else if (z <= -1.12e+49) {
		tmp = y * (z / a);
	} else if (z <= 5.5e+198) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= (-1.95d+176)) then
        tmp = x * (z / -a)
    else if (z <= (-1.12d+49)) then
        tmp = y * (z / a)
    else if (z <= 5.5d+198) then
        tmp = x + y
    else
        tmp = 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 (z <= -1.95e+176) {
		tmp = x * (z / -a);
	} else if (z <= -1.12e+49) {
		tmp = y * (z / a);
	} else if (z <= 5.5e+198) {
		tmp = x + y;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+176:
		tmp = x * (z / -a)
	elif z <= -1.12e+49:
		tmp = y * (z / a)
	elif z <= 5.5e+198:
		tmp = x + y
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+176)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (z <= -1.12e+49)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 5.5e+198)
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.95e+176)
		tmp = x * (z / -a);
	elseif (z <= -1.12e+49)
		tmp = y * (z / a);
	elseif (z <= 5.5e+198)
		tmp = x + y;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+176], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e+49], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+198], N[(x + y), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9500000000000001e176

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 42.9%

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

   5. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/l* 42.4%

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

      3. distribute-rgt-neg-in 42.4%

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

      4. distribute-neg-frac2 42.4%

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

   7. Simplified 42.4%

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

   if -1.9500000000000001e176 < z < -1.12000000000000005e49

   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 z around inf 73.8%

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

   4. Taylor expanded in t around 0 57.0%

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

   5. Taylor expanded in y around inf 40.7%

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

      1. associate-/l* 51.7%

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

   7. Simplified 51.7%

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

   if -1.12000000000000005e49 < z < 5.5000000000000004e198

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around inf 46.6%

      \[\leadsto x + y \cdot \color{blue}{1} \]

   if 5.5000000000000004e198 < z

   1. Initial program 60.0%

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

   3. Taylor expanded in z around inf 90.6%

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

   4. Taylor expanded in t around 0 60.9%

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

   5. Taylor expanded in y around inf 33.4%

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

      1. *-commutative 33.4%

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

      2. *-lft-identity 33.4%

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

      3. times-frac 45.3%

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

      4. /-rgt-identity 45.3%

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

   7. Simplified 45.3%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+198}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-12} \lor \neg \left(a \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.2e-12) (not (<= a 1.9e+73)))
   (+ x (* y (/ (- z t) a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.2e-12) || !(a <= 1.9e+73)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.2d-12)) .or. (.not. (a <= 1.9d+73))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.2e-12) || !(a <= 1.9e+73)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.2e-12) or not (a <= 1.9e+73):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.2e-12) || !(a <= 1.9e+73))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.2e-12) || ~((a <= 1.9e+73)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.2e-12], N[Not[LessEqual[a, 1.9e+73]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.19999999999999979e-12 or 1.90000000000000011e73 < a

   1. Initial program 62.1%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

   if -8.19999999999999979e-12 < a < 1.90000000000000011e73

   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 68.7%

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

      2. inv-pow 68.7%

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

      3. *-commutative 68.7%

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

      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. Step-by-step derivation

      1. div-inv 81.1%

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

   6. Applied egg-rr 81.1%

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

   7. Taylor expanded in x around 0 55.4%

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

      1. associate-/l* 68.6%

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

   9. Simplified 68.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-12} \lor \neg \left(a \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e-8)
   (+ x (* z (/ (- y x) a)))
   (if (<= a 3.2e+75) (* y (/ (- z t) (- 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-8) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 3.2e+75) {
		tmp = y * ((z - t) / (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-8)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= 3.2d+75) then
        tmp = y * ((z - t) / (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-8) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= 3.2e+75) {
		tmp = y * ((z - t) / (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-8:
		tmp = x + (z * ((y - x) / a))
	elif a <= 3.2e+75:
		tmp = y * ((z - t) / (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-8)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= 3.2e+75)
		tmp = Float64(y * Float64(Float64(z - t) / 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-8)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= 3.2e+75)
		tmp = y * ((z - t) / (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-8], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+75], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.19999999999999989e-8

   1. Initial program 58.5%

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

   3. Taylor expanded in t around 0 60.1%

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

      1. associate-/l* 73.9%

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

   5. Simplified 73.9%

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

   if -4.19999999999999989e-8 < a < 3.19999999999999985e75

   1. Initial program 69.5%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. *-commutative 69.4%

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

      4. associate-/r* 81.5%

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

   4. Applied egg-rr 81.5%

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

      1. div-inv 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in x around 0 55.0%

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

      1. associate-/l* 68.0%

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

   9. Simplified 68.0%

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

   if 3.19999999999999985e75 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.8e-9)
   (+ x (* (- y x) (/ z a)))
   (if (<= a 3.1e+74) (* y (/ (- z t) (- a t))) (+ x (* y (/ (- z t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e-9) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= 3.1e+74) {
		tmp = y * ((z - t) / (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 <= (-9.8d-9)) then
        tmp = x + ((y - x) * (z / a))
    else if (a <= 3.1d+74) then
        tmp = y * ((z - t) / (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 <= -9.8e-9) {
		tmp = x + ((y - x) * (z / a));
	} else if (a <= 3.1e+74) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.8e-9:
		tmp = x + ((y - x) * (z / a))
	elif a <= 3.1e+74:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.8e-9)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (a <= 3.1e+74)
		tmp = Float64(y * Float64(Float64(z - t) / 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 <= -9.8e-9)
		tmp = x + ((y - x) * (z / a));
	elseif (a <= 3.1e+74)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.8e-9], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+74], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.80000000000000007e-9

   1. Initial program 58.5%

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

      1. clear-num 58.5%

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

      2. inv-pow 58.5%

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

      3. *-commutative 58.5%

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

      4. associate-/r* 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. div-inv 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. *-un-lft-identity 95.1%

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

      2. +-commutative 95.1%

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

      3. unpow-prod-down 95.1%

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

      4. fma-define 95.2%

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

      5. unpow-1 95.2%

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

      6. inv-pow 95.2%

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

      7. pow-pow 95.2%

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

      8. metadata-eval 95.2%

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

      9. pow1 95.2%

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

   8. Applied egg-rr 95.2%

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

      1. *-lft-identity 95.2%

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

      2. fma-undefine 95.2%

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

      3. *-commutative 95.2%

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

      4. associate-*r/ 95.2%

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

      5. *-rgt-identity 95.2%

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

   10. Simplified 95.2%

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

   11. Taylor expanded in t around 0 60.1%

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

       1. *-commutative 60.1%

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

       2. *-lft-identity 60.1%

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

       3. times-frac 74.0%

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

       4. /-rgt-identity 74.0%

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

   13. Simplified 74.0%

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

   if -9.80000000000000007e-9 < a < 3.10000000000000021e74

   1. Initial program 69.5%

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

      1. clear-num 69.4%

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

      2. inv-pow 69.4%

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

      3. *-commutative 69.4%

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

      4. associate-/r* 81.5%

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

   4. Applied egg-rr 81.5%

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

      1. div-inv 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in x around 0 55.0%

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

      1. associate-/l* 68.0%

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

   9. Simplified 68.0%

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

   if 3.10000000000000021e74 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 66.3%

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

      1. associate-/l* 81.1%

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

   8. Simplified 81.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e+62)
   x
   (if (<= a -4.9e-90) (* y (/ z a)) (if (<= a 8.6e+75) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+62) {
		tmp = x;
	} else if (a <= -4.9e-90) {
		tmp = y * (z / a);
	} else if (a <= 8.6e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.95d+62)) then
        tmp = x
    else if (a <= (-4.9d-90)) then
        tmp = y * (z / a)
    else if (a <= 8.6d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+62) {
		tmp = x;
	} else if (a <= -4.9e-90) {
		tmp = y * (z / a);
	} else if (a <= 8.6e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e+62:
		tmp = x
	elif a <= -4.9e-90:
		tmp = y * (z / a)
	elif a <= 8.6e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e+62)
		tmp = x;
	elseif (a <= -4.9e-90)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= 8.6e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e+62)
		tmp = x;
	elseif (a <= -4.9e-90)
		tmp = y * (z / a);
	elseif (a <= 8.6e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e+62], x, If[LessEqual[a, -4.9e-90], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+75], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.95e62 or 8.6000000000000002e75 < a

   1. Initial program 57.6%

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

   3. Taylor expanded in a around inf 49.6%

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

   if -1.95e62 < a < -4.89999999999999982e-90

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 67.4%

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

   4. Taylor expanded in t around 0 45.3%

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

   5. Taylor expanded in y around inf 38.9%

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

      1. associate-/l* 38.9%

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

   7. Simplified 38.9%

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

   if -4.89999999999999982e-90 < a < 8.6000000000000002e75

   1. Initial program 68.5%

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

   3. Taylor expanded in t around inf 40.0%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+62)
   x
   (if (<= a -3.15e-88) (* z (/ y a)) (if (<= a 8.5e+75) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+62) {
		tmp = x;
	} else if (a <= -3.15e-88) {
		tmp = z * (y / a);
	} else if (a <= 8.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+62)) then
        tmp = x
    else if (a <= (-3.15d-88)) then
        tmp = z * (y / a)
    else if (a <= 8.5d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+62) {
		tmp = x;
	} else if (a <= -3.15e-88) {
		tmp = z * (y / a);
	} else if (a <= 8.5e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+62:
		tmp = x
	elif a <= -3.15e-88:
		tmp = z * (y / a)
	elif a <= 8.5e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+62)
		tmp = x;
	elseif (a <= -3.15e-88)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 8.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+62)
		tmp = x;
	elseif (a <= -3.15e-88)
		tmp = z * (y / a);
	elseif (a <= 8.5e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+62], x, If[LessEqual[a, -3.15e-88], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+75], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.89999999999999992e62 or 8.4999999999999993e75 < a

   1. Initial program 57.6%

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

   3. Taylor expanded in a around inf 49.6%

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

   if -1.89999999999999992e62 < a < -3.15000000000000022e-88

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 67.4%

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

   4. Taylor expanded in t around 0 45.3%

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

   5. Taylor expanded in y around inf 38.9%

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

      1. *-commutative 38.9%

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

      2. *-lft-identity 38.9%

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

      3. times-frac 38.9%

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

      4. /-rgt-identity 38.9%

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

   7. Simplified 38.9%

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

   if -3.15000000000000022e-88 < a < 8.4999999999999993e75

   1. Initial program 68.5%

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

   3. Taylor expanded in t around inf 40.0%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+49} \lor \neg \left(z \leq 6.2 \cdot 10^{+198}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+49) (not (<= z 6.2e+198))) (* z (/ y a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+49) || !(z <= 6.2e+198)) {
		tmp = z * (y / a);
	} else {
		tmp = 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 ((z <= (-1d+49)) .or. (.not. (z <= 6.2d+198))) then
        tmp = z * (y / a)
    else
        tmp = 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 ((z <= -1e+49) || !(z <= 6.2e+198)) {
		tmp = z * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+49) or not (z <= 6.2e+198):
		tmp = z * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+49) || !(z <= 6.2e+198))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e+49) || ~((z <= 6.2e+198)))
		tmp = z * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+49], N[Not[LessEqual[z, 6.2e+198]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999946e48 or 6.1999999999999995e198 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf 75.6%

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

   4. Taylor expanded in t around 0 53.6%

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

   5. Taylor expanded in y around inf 30.5%

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

      1. *-commutative 30.5%

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

      2. *-lft-identity 30.5%

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

      3. times-frac 40.6%

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

      4. /-rgt-identity 40.6%

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

   7. Simplified 40.6%

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

   if -9.99999999999999946e48 < z < 6.1999999999999995e198

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around inf 46.6%

      \[\leadsto x + y \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+49} \lor \neg \left(z \leq 6.2 \cdot 10^{+198}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-13) x (if (<= a 8.6e+75) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-13) {
		tmp = x;
	} else if (a <= 8.6e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-13)) then
        tmp = x
    else if (a <= 8.6d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-13) {
		tmp = x;
	} else if (a <= 8.6e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-13:
		tmp = x
	elif a <= 8.6e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-13)
		tmp = x;
	elseif (a <= 8.6e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-13)
		tmp = x;
	elseif (a <= 8.6e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-13], x, If[LessEqual[a, 8.6e+75], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-13 or 8.6000000000000002e75 < a

   1. Initial program 62.1%

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

   3. Taylor expanded in a around inf 44.7%

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

   if -1.6e-13 < a < 8.6000000000000002e75

   1. Initial program 68.9%

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

   3. Taylor expanded in t around inf 39.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 66.0%

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

3. Taylor expanded in y around -inf 71.0%

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

   1. mul-1-neg 71.0%

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

   2. *-commutative 71.0%

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

   3. distribute-rgt-neg-in 71.0%

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

   4. +-commutative 71.0%

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

   5. times-frac 76.4%

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

   6. distribute-rgt-out 78.8%

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

5. Simplified 78.8%

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

6. Taylor expanded in t around inf 23.8%

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

7. Taylor expanded in y around 0 2.7%

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

   1. distribute-rgt1-in 2.7%

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

   2. metadata-eval 2.7%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.7%

      \[\leadsto \color{blue}{0} \]

9. Simplified 2.7%

   \[\leadsto \color{blue}{0} \]

10. Final simplification 2.7%

    \[\leadsto 0 \]
11. Add Preprocessing

Alternative 22: 25.4% 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 66.0%

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

3. Taylor expanded in a around inf 22.8%

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

4. Final simplification 22.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 87.4% 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 2024067 
(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))))