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

Percentage Accurate: 67.2% → 89.8%

Time: 14.6s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.2% 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: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-227}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -4e-227)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (- y (/ (* (- x y) (- a z)) t))
       (fma (- y x) (/ (- z t) (- a t)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -4e-227) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -4e-227)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-227], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999978e-227

   1. Initial program 71.4%

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

      1. associate-/l* 95.1%

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

      2. *-commutative 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. clear-num 95.1%

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

      2. inv-pow 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

   8. Simplified 95.1%

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

      1. associate-*l/ 95.2%

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

      2. *-un-lft-identity 95.2%

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

   10. Applied egg-rr 95.2%

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

   if -3.99999999999999978e-227 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 7.3%

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

      1. +-commutative 7.3%

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

      2. associate-/l* 7.3%

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

      3. fma-define 7.3%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in t around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-*r/ 95.6%

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

      3. associate-*r/ 95.6%

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

      4. mul-1-neg 95.6%

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

      5. div-sub 95.5%

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

      6. mul-1-neg 95.5%

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

      7. distribute-lft-out-- 95.5%

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

      8. associate-*r/ 95.5%

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

      9. mul-1-neg 95.5%

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

      10. unsub-neg 95.5%

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

      11. distribute-rgt-out-- 95.6%

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

   7. Simplified 95.6%

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

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

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-/l* 90.6%

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

      3. fma-define 90.6%

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

   3. Simplified 90.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-227}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-227} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -4e-227) (not (<= t_1 0.0)))
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (- y (/ (* (- x y) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-227) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-4d-227)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y - (((x - y) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-227) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -4e-227) or not (t_1 <= 0.0):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -4e-227) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -4e-227) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-227], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999978e-227 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.6%

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

      1. associate-/l* 92.4%

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

      2. *-commutative 92.4%

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

   4. Applied egg-rr 92.4%

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

   if -3.99999999999999978e-227 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 7.3%

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

      1. +-commutative 7.3%

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

      2. associate-/l* 7.3%

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

      3. fma-define 7.3%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in t around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-*r/ 95.6%

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

      3. associate-*r/ 95.6%

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

      4. mul-1-neg 95.6%

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

      5. div-sub 95.5%

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

      6. mul-1-neg 95.5%

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

      7. distribute-lft-out-- 95.5%

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

      8. associate-*r/ 95.5%

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

      9. mul-1-neg 95.5%

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

      10. unsub-neg 95.5%

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

      11. distribute-rgt-out-- 95.6%

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

   7. Simplified 95.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-227} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-227}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -4e-227)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (- y (/ (* (- x y) (- a z)) t))
       (+ x (* (- y x) (/ (- z t) (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -4e-227) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) * ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if (t_1 <= (-4d-227)) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else if (t_1 <= 0.0d0) then
        tmp = y - (((x - y) * (a - z)) / t)
    else
        tmp = x + ((y - x) * ((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 t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -4e-227) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -4e-227:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	elif t_1 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -4e-227)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -4e-227)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	elseif (t_1 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-227], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -3.99999999999999978e-227

   1. Initial program 71.4%

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

      1. associate-/l* 95.1%

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

      2. *-commutative 95.1%

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

   4. Applied egg-rr 95.1%

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

      1. clear-num 95.1%

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

      2. inv-pow 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

   8. Simplified 95.1%

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

      1. associate-*l/ 95.2%

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

      2. *-un-lft-identity 95.2%

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

   10. Applied egg-rr 95.2%

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

   if -3.99999999999999978e-227 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 7.3%

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

      1. +-commutative 7.3%

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

      2. associate-/l* 7.3%

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

      3. fma-define 7.3%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in t around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. associate-*r/ 95.6%

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

      3. associate-*r/ 95.6%

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

      4. mul-1-neg 95.6%

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

      5. div-sub 95.5%

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

      6. mul-1-neg 95.5%

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

      7. distribute-lft-out-- 95.5%

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

      8. associate-*r/ 95.5%

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

      9. mul-1-neg 95.5%

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

      10. unsub-neg 95.5%

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

      11. distribute-rgt-out-- 95.6%

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

   7. Simplified 95.6%

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

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

   1. Initial program 75.2%

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

      1. associate-/l* 90.6%

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

      2. *-commutative 90.6%

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

   4. Applied egg-rr 90.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -4 \cdot 10^{-227}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-110}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- (- -1.0) (/ z t)))))
   (if (<= t -6e+90)
     t_1
     (if (<= t 2.25e-110)
       (+ x (* y (/ (- z t) a)))
       (if (<= t 1.02e+82) (* x (- 1.0 (/ z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-(-1.0) - (z / t));
	double tmp;
	if (t <= -6e+90) {
		tmp = t_1;
	} else if (t <= 2.25e-110) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 1.02e+82) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-(-1.0d0) - (z / t))
    if (t <= (-6d+90)) then
        tmp = t_1
    else if (t <= 2.25d-110) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 1.02d+82) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-(-1.0) - (z / t));
	double tmp;
	if (t <= -6e+90) {
		tmp = t_1;
	} else if (t <= 2.25e-110) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 1.02e+82) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-(-1.0) - (z / t))
	tmp = 0
	if t <= -6e+90:
		tmp = t_1
	elif t <= 2.25e-110:
		tmp = x + (y * ((z - t) / a))
	elif t <= 1.02e+82:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-(-1.0)) - Float64(z / t)))
	tmp = 0.0
	if (t <= -6e+90)
		tmp = t_1;
	elseif (t <= 2.25e-110)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 1.02e+82)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-(-1.0) - (z / t));
	tmp = 0.0;
	if (t <= -6e+90)
		tmp = t_1;
	elseif (t <= 2.25e-110)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 1.02e+82)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((--1.0) - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+90], t$95$1, If[LessEqual[t, 2.25e-110], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+82], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999957e90 or 1.0200000000000001e82 < t

   1. Initial program 41.4%

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

   3. Taylor expanded in y around inf 36.2%

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

      1. *-commutative 36.2%

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

      2. *-lft-identity 36.2%

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

      3. times-frac 57.8%

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

      4. /-rgt-identity 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in a around 0 51.7%

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

      1. associate-*r/ 51.7%

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

      2. neg-mul-1 51.7%

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

   8. Simplified 51.7%

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

   9. Taylor expanded in y around -inf 64.2%

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

   if -5.99999999999999957e90 < t < 2.25e-110

   1. Initial program 86.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. *-commutative 72.0%

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

      2. *-lft-identity 72.0%

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

      3. times-frac 70.1%

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

      4. /-rgt-identity 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in a around inf 62.9%

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

      1. associate-/l* 65.0%

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

   8. Simplified 65.0%

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

   if 2.25e-110 < t < 1.0200000000000001e82

   1. Initial program 78.6%

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

   3. Taylor expanded in t around 0 55.9%

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

   4. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-110}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -90000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-112}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- (- -1.0) (/ z t)))))
   (if (<= t -90000000.0)
     t_1
     (if (<= t 3.8e-112)
       (+ x (* y (/ z a)))
       (if (<= t 2.8e+82) (* x (- 1.0 (/ z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-(-1.0) - (z / t));
	double tmp;
	if (t <= -90000000.0) {
		tmp = t_1;
	} else if (t <= 3.8e-112) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.8e+82) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-(-1.0d0) - (z / t))
    if (t <= (-90000000.0d0)) then
        tmp = t_1
    else if (t <= 3.8d-112) then
        tmp = x + (y * (z / a))
    else if (t <= 2.8d+82) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-(-1.0) - (z / t));
	double tmp;
	if (t <= -90000000.0) {
		tmp = t_1;
	} else if (t <= 3.8e-112) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.8e+82) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-(-1.0) - (z / t))
	tmp = 0
	if t <= -90000000.0:
		tmp = t_1
	elif t <= 3.8e-112:
		tmp = x + (y * (z / a))
	elif t <= 2.8e+82:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-(-1.0)) - Float64(z / t)))
	tmp = 0.0
	if (t <= -90000000.0)
		tmp = t_1;
	elseif (t <= 3.8e-112)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.8e+82)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-(-1.0) - (z / t));
	tmp = 0.0;
	if (t <= -90000000.0)
		tmp = t_1;
	elseif (t <= 3.8e-112)
		tmp = x + (y * (z / a));
	elseif (t <= 2.8e+82)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((--1.0) - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -90000000.0], t$95$1, If[LessEqual[t, 3.8e-112], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+82], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9e7 or 2.8e82 < t

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

      2. *-lft-identity 38.1%

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

      3. times-frac 57.3%

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

      4. /-rgt-identity 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in a around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in y around -inf 60.2%

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

   if -9e7 < t < 3.79999999999999995e-112

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 75.9%

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

      1. *-commutative 75.9%

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

      2. *-lft-identity 75.9%

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

      3. times-frac 72.8%

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

      4. /-rgt-identity 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in t around 0 62.9%

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

      1. associate-/l* 64.8%

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

   8. Simplified 64.8%

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

   if 3.79999999999999995e-112 < t < 2.8e82

   1. Initial program 78.6%

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

   3. Taylor expanded in t around 0 55.9%

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

   4. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   6. Simplified 62.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -90000000:\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-112}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -0.0096:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+156}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+152)
   y
   (if (<= t -0.0096)
     (* z (/ (- x y) t))
     (if (<= t 3.2e+156) (+ x (* y (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+152) {
		tmp = y;
	} else if (t <= -0.0096) {
		tmp = z * ((x - y) / t);
	} else if (t <= 3.2e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+152)) then
        tmp = y
    else if (t <= (-0.0096d0)) then
        tmp = z * ((x - y) / t)
    else if (t <= 3.2d+156) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+152) {
		tmp = y;
	} else if (t <= -0.0096) {
		tmp = z * ((x - y) / t);
	} else if (t <= 3.2e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+152:
		tmp = y
	elif t <= -0.0096:
		tmp = z * ((x - y) / t)
	elif t <= 3.2e+156:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+152)
		tmp = y;
	elseif (t <= -0.0096)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 3.2e+156)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+152)
		tmp = y;
	elseif (t <= -0.0096)
		tmp = z * ((x - y) / t);
	elseif (t <= 3.2e+156)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+152], y, If[LessEqual[t, -0.0096], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+156], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000002e152 or 3.20000000000000002e156 < t

   1. Initial program 31.5%

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

   3. Taylor expanded in y around inf 29.6%

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

      1. *-commutative 29.6%

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

      2. *-lft-identity 29.6%

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

      3. times-frac 57.8%

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

      4. /-rgt-identity 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in t around inf 61.3%

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

      1. +-commutative 61.3%

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

   8. Simplified 61.3%

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

   9. Taylor expanded in y around inf 69.5%

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

   if -4.0000000000000002e152 < t < -0.00959999999999999916

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-/l* 76.8%

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

      3. fma-define 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 54.7%

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

   6. Taylor expanded in a around 0 48.2%

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

      1. distribute-lft-out-- 48.2%

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

      2. div-sub 48.2%

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

      3. associate-*r/ 48.2%

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

      4. neg-mul-1 48.2%

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

   8. Simplified 48.2%

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

   if -0.00959999999999999916 < t < 3.20000000000000002e156

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. *-lft-identity 68.2%

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

      3. times-frac 70.4%

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

      4. /-rgt-identity 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around 0 54.1%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -0.0096:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+156}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -0.0026:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+156}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+152)
   y
   (if (<= t -0.0026)
     (* x (/ z (- t a)))
     (if (<= t 3e+156) (+ x (* y (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+152) {
		tmp = y;
	} else if (t <= -0.0026) {
		tmp = x * (z / (t - a));
	} else if (t <= 3e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4d+152)) then
        tmp = y
    else if (t <= (-0.0026d0)) then
        tmp = x * (z / (t - a))
    else if (t <= 3d+156) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+152) {
		tmp = y;
	} else if (t <= -0.0026) {
		tmp = x * (z / (t - a));
	} else if (t <= 3e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+152:
		tmp = y
	elif t <= -0.0026:
		tmp = x * (z / (t - a))
	elif t <= 3e+156:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+152)
		tmp = y;
	elseif (t <= -0.0026)
		tmp = Float64(x * Float64(z / Float64(t - a)));
	elseif (t <= 3e+156)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e+152)
		tmp = y;
	elseif (t <= -0.0026)
		tmp = x * (z / (t - a));
	elseif (t <= 3e+156)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+152], y, If[LessEqual[t, -0.0026], N[(x * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+156], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000002e152 or 3e156 < t

   1. Initial program 31.5%

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

   3. Taylor expanded in y around inf 29.6%

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

      1. *-commutative 29.6%

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

      2. *-lft-identity 29.6%

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

      3. times-frac 57.8%

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

      4. /-rgt-identity 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in t around inf 61.3%

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

      1. +-commutative 61.3%

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

   8. Simplified 61.3%

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

   9. Taylor expanded in y around inf 69.5%

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

   if -4.0000000000000002e152 < t < -0.0025999999999999999

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. associate-/l* 76.8%

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

      3. fma-define 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around inf 54.7%

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

   6. Taylor expanded in y around 0 35.0%

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

      1. mul-1-neg 35.0%

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

      2. associate-/l* 38.2%

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

   8. Simplified 38.2%

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

   if -0.0025999999999999999 < t < 3e156

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. *-lft-identity 68.2%

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

      3. times-frac 70.4%

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

      4. /-rgt-identity 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around 0 54.1%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+152}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -0.0026:\\ \;\;\;\;x \cdot \frac{z}{t - a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+156}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-65} \lor \neg \left(y \leq 6.6 \cdot 10^{-159}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.5e-65) (not (<= y 6.6e-159)))
   (+ x (* y (/ (- z t) (- a t))))
   (* x (+ 1.0 (/ (- z t) (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.5e-65) || !(y <= 6.6e-159)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x * (1.0 + ((z - t) / (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 ((y <= (-6.5d-65)) .or. (.not. (y <= 6.6d-159))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = x * (1.0d0 + ((z - t) / (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 ((y <= -6.5e-65) || !(y <= 6.6e-159)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.5e-65) or not (y <= 6.6e-159):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x * (1.0 + ((z - t) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.5e-65) || !(y <= 6.6e-159))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.5e-65) || ~((y <= 6.6e-159)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x * (1.0 + ((z - t) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.5e-65], N[Not[LessEqual[y, 6.6e-159]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e-65 or 6.6000000000000003e-159 < y

   1. Initial program 68.3%

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

      1. associate-/l* 90.8%

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

      2. *-commutative 90.8%

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

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in y around inf 62.6%

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

      1. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

   if -6.5e-65 < y < 6.6000000000000003e-159

   1. Initial program 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 72.1%

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

      3. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-lft-identity 56.9%

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

      3. *-commutative 56.9%

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

      4. *-rgt-identity 56.9%

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

      5. times-frac 63.2%

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

      6. /-rgt-identity 63.2%

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

      7. distribute-lft-neg-out 63.2%

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

      8. mul-1-neg 63.2%

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

      9. distribute-rgt-in 63.2%

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

      10. mul-1-neg 63.2%

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

      11. unsub-neg 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-65} \lor \neg \left(y \leq 6.6 \cdot 10^{-159}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-77}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-46)
   (+ x (/ y (/ (- a t) (- z t))))
   (if (<= a 2e-77)
     (+ y (* (- z a) (/ (- x y) t)))
     (+ x (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-46) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (a <= 2e-77) {
		tmp = y + ((z - a) * ((x - y) / 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 (a <= (-4.5d-46)) then
        tmp = x + (y / ((a - t) / (z - t)))
    else if (a <= 2d-77) then
        tmp = y + ((z - a) * ((x - y) / 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 (a <= -4.5e-46) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (a <= 2e-77) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-46:
		tmp = x + (y / ((a - t) / (z - t)))
	elif a <= 2e-77:
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-46)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	elseif (a <= 2e-77)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / 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 (a <= -4.5e-46)
		tmp = x + (y / ((a - t) / (z - t)));
	elseif (a <= 2e-77)
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-46], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-77], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / 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 a < -4.50000000000000001e-46

   1. Initial program 72.8%

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

      1. associate-/l* 94.3%

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

      2. *-commutative 94.3%

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

   4. Applied egg-rr 94.3%

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

      1. clear-num 94.3%

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

      2. inv-pow 94.3%

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

   6. Applied egg-rr 94.3%

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

      1. unpow-1 94.3%

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

   8. Simplified 94.3%

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

      1. associate-*l/ 94.3%

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

      2. *-un-lft-identity 94.3%

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

   10. Applied egg-rr 94.3%

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

   11. Taylor expanded in y around inf 82.8%

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

   if -4.50000000000000001e-46 < a < 1.9999999999999999e-77

   1. Initial program 59.3%

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

      1. associate-/l* 72.8%

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

      2. *-commutative 72.8%

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

   4. Applied egg-rr 72.8%

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

      1. clear-num 72.8%

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

      2. inv-pow 72.8%

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

   6. Applied egg-rr 72.8%

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

      1. unpow-1 72.8%

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

   8. Simplified 72.8%

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

      1. associate-*l/ 72.9%

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

      2. *-un-lft-identity 72.9%

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

   10. Applied egg-rr 72.9%

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

   11. Taylor expanded in t around inf 76.9%

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

       1. associate--l+ 76.9%

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

       2. distribute-lft-out-- 76.9%

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

       3. div-sub 77.9%

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

       4. mul-1-neg 77.9%

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

       5. unsub-neg 77.9%

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

       6. div-sub 76.9%

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

       7. associate-/l* 81.6%

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

       8. associate-/l* 76.8%

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

       9. distribute-rgt-out-- 82.6%

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

   13. Simplified 82.6%

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

   if 1.9999999999999999e-77 < a

   1. Initial program 75.1%

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

      1. associate-/l* 93.3%

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

      2. *-commutative 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around inf 66.6%

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

      1. associate-/l* 79.5%

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

   7. Simplified 79.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-77}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.4e-65)
   (+ x (/ y (/ (- a t) (- z t))))
   (if (<= y 7.5e-159)
     (* x (+ 1.0 (/ (- z t) (- t a))))
     (+ x (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.4e-65) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (y <= 7.5e-159) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.4d-65)) then
        tmp = x + (y / ((a - t) / (z - t)))
    else if (y <= 7.5d-159) then
        tmp = x * (1.0d0 + ((z - t) / (t - a)))
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.4e-65) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (y <= 7.5e-159) {
		tmp = x * (1.0 + ((z - t) / (t - a)));
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.4e-65:
		tmp = x + (y / ((a - t) / (z - t)))
	elif y <= 7.5e-159:
		tmp = x * (1.0 + ((z - t) / (t - a)))
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.4e-65)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	elseif (y <= 7.5e-159)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.4e-65)
		tmp = x + (y / ((a - t) / (z - t)));
	elseif (y <= 7.5e-159)
		tmp = x * (1.0 + ((z - t) / (t - a)));
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.4e-65], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-159], N[(x * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $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 y < -3.39999999999999987e-65

   1. Initial program 66.9%

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

      1. associate-/l* 92.0%

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

      2. *-commutative 92.0%

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

   4. Applied egg-rr 92.0%

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

      1. clear-num 92.0%

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

      2. inv-pow 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. unpow-1 92.0%

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

   8. Simplified 92.0%

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

      1. associate-*l/ 92.1%

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

      2. *-un-lft-identity 92.1%

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

   10. Applied egg-rr 92.1%

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

   11. Taylor expanded in y around inf 84.6%

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

   if -3.39999999999999987e-65 < y < 7.5e-159

   1. Initial program 67.0%

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

      1. +-commutative 67.0%

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

      2. associate-/l* 72.1%

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

      3. fma-define 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-lft-identity 56.9%

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

      3. *-commutative 56.9%

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

      4. *-rgt-identity 56.9%

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

      5. times-frac 63.2%

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

      6. /-rgt-identity 63.2%

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

      7. distribute-lft-neg-out 63.2%

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

      8. mul-1-neg 63.2%

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

      9. distribute-rgt-in 63.2%

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

      10. mul-1-neg 63.2%

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

      11. unsub-neg 63.2%

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

   7. Simplified 63.2%

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

   if 7.5e-159 < y

   1. Initial program 69.4%

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

      1. associate-/l* 89.9%

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

      2. *-commutative 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in y around inf 63.0%

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

      1. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - t}{t - a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -65000 \lor \neg \left(t \leq 7.5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -65000.0) (not (<= t 7.5e+82)))
   (* y (- (- -1.0) (/ z t)))
   (+ x (/ (- y x) (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -65000.0) || !(t <= 7.5e+82)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	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 <= (-65000.0d0)) .or. (.not. (t <= 7.5d+82))) then
        tmp = y * (-(-1.0d0) - (z / t))
    else
        tmp = x + ((y - x) / (a / z))
    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 <= -65000.0) || !(t <= 7.5e+82)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -65000.0) or not (t <= 7.5e+82):
		tmp = y * (-(-1.0) - (z / t))
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -65000.0) || !(t <= 7.5e+82))
		tmp = Float64(y * Float64(Float64(-(-1.0)) - Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -65000.0) || ~((t <= 7.5e+82)))
		tmp = y * (-(-1.0) - (z / t));
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -65000.0], N[Not[LessEqual[t, 7.5e+82]], $MachinePrecision]], N[(y * N[((--1.0) - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -65000 or 7.4999999999999999e82 < t

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

      2. *-lft-identity 38.1%

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

      3. times-frac 57.3%

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

      4. /-rgt-identity 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in a around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in y around -inf 60.2%

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

   if -65000 < t < 7.4999999999999999e82

   1. Initial program 87.7%

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

      1. associate-/l* 92.9%

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

      2. *-commutative 92.9%

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

   4. Applied egg-rr 92.9%

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

      1. clear-num 92.5%

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

      2. inv-pow 92.5%

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

   6. Applied egg-rr 92.5%

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

      1. unpow-1 92.5%

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

   8. Simplified 92.5%

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

      1. associate-*l/ 92.6%

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

      2. *-un-lft-identity 92.6%

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

   10. Applied egg-rr 92.6%

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

   11. Taylor expanded in t around 0 71.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -65000 \lor \neg \left(t \leq 7.5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1050000000 \lor \neg \left(t \leq 10^{+82}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1050000000.0) (not (<= t 1e+82)))
   (* y (- (- -1.0) (/ z t)))
   (+ x (* (- y x) (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1050000000.0) || !(t <= 1e+82)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + ((y - x) * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1050000000.0d0)) .or. (.not. (t <= 1d+82))) then
        tmp = y * (-(-1.0d0) - (z / t))
    else
        tmp = x + ((y - x) * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1050000000.0) || !(t <= 1e+82)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + ((y - x) * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1050000000.0) or not (t <= 1e+82):
		tmp = y * (-(-1.0) - (z / t))
	else:
		tmp = x + ((y - x) * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1050000000.0) || !(t <= 1e+82))
		tmp = Float64(y * Float64(Float64(-(-1.0)) - Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1050000000.0) || ~((t <= 1e+82)))
		tmp = y * (-(-1.0) - (z / t));
	else
		tmp = x + ((y - x) * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1050000000.0], N[Not[LessEqual[t, 1e+82]], $MachinePrecision]], N[(y * N[((--1.0) - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e9 or 9.9999999999999996e81 < t

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

      2. *-lft-identity 38.1%

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

      3. times-frac 57.3%

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

      4. /-rgt-identity 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in a around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in y around -inf 60.2%

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

   if -1.05e9 < t < 9.9999999999999996e81

   1. Initial program 87.7%

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

      1. associate-/l* 92.9%

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

      2. *-commutative 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in t around 0 71.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1050000000 \lor \neg \left(t \leq 10^{+82}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -70000000 \lor \neg \left(t \leq 8.2 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -70000000.0) (not (<= t 8.2e+81)))
   (* y (- (- -1.0) (/ z t)))
   (+ x (* z (/ (- y x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -70000000.0) || !(t <= 8.2e+81)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-70000000.0d0)) .or. (.not. (t <= 8.2d+81))) then
        tmp = y * (-(-1.0d0) - (z / t))
    else
        tmp = x + (z * ((y - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -70000000.0) || !(t <= 8.2e+81)) {
		tmp = y * (-(-1.0) - (z / t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -70000000.0) or not (t <= 8.2e+81):
		tmp = y * (-(-1.0) - (z / t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -70000000.0) || !(t <= 8.2e+81))
		tmp = Float64(y * Float64(Float64(-(-1.0)) - Float64(z / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -70000000.0) || ~((t <= 8.2e+81)))
		tmp = y * (-(-1.0) - (z / t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -70000000.0], N[Not[LessEqual[t, 8.2e+81]], $MachinePrecision]], N[(y * N[((--1.0) - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7e7 or 8.20000000000000024e81 < t

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

      2. *-lft-identity 38.1%

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

      3. times-frac 57.3%

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

      4. /-rgt-identity 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in a around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in y around -inf 60.2%

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

   if -7e7 < t < 8.20000000000000024e81

   1. Initial program 87.7%

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

   3. Taylor expanded in t around 0 66.3%

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

      1. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -70000000 \lor \neg \left(t \leq 8.2 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot \left(\left(--1\right) - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+156}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e+61) y (if (<= t 3e+156) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+61) {
		tmp = y;
	} else if (t <= 3e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.02d+61)) then
        tmp = y
    else if (t <= 3d+156) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e+61) {
		tmp = y;
	} else if (t <= 3e+156) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e+61:
		tmp = y
	elif t <= 3e+156:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e+61)
		tmp = y;
	elseif (t <= 3e+156)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e+61)
		tmp = y;
	elseif (t <= 3e+156)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e+61], y, If[LessEqual[t, 3e+156], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.01999999999999999e61 or 3e156 < t

   1. Initial program 37.8%

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

   3. Taylor expanded in y around inf 32.8%

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

      1. *-commutative 32.8%

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

      2. *-lft-identity 32.8%

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

      3. times-frac 57.7%

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

      4. /-rgt-identity 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in t around inf 55.4%

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

      1. +-commutative 55.4%

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

   8. Simplified 55.4%

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

   9. Taylor expanded in y around inf 63.4%

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

   if -1.01999999999999999e61 < t < 3e156

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. *-lft-identity 65.8%

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

      3. times-frac 67.8%

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

      4. /-rgt-identity 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around 0 50.9%

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

      1. associate-/l* 54.5%

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

   8. Simplified 54.5%

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

Alternative 15: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+66) y (if (<= t 1e+87) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+66) {
		tmp = y;
	} else if (t <= 1e+87) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d+66)) then
        tmp = y
    else if (t <= 1d+87) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+66) {
		tmp = y;
	} else if (t <= 1e+87) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+66:
		tmp = y
	elif t <= 1e+87:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+66)
		tmp = y;
	elseif (t <= 1e+87)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+66)
		tmp = y;
	elseif (t <= 1e+87)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+66], y, If[LessEqual[t, 1e+87], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000005e66 or 9.9999999999999996e86 < t

   1. Initial program 41.6%

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

   3. Taylor expanded in y around inf 36.5%

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

      1. *-commutative 36.5%

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

      2. *-lft-identity 36.5%

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

      3. times-frac 58.6%

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

      4. /-rgt-identity 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around inf 50.0%

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

      1. +-commutative 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in y around inf 56.3%

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

   if -2.10000000000000005e66 < t < 9.9999999999999996e86

   1. Initial program 85.1%

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

   3. Taylor expanded in t around 0 62.2%

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

   4. Taylor expanded in x around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   6. Simplified 49.9%

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

Alternative 16: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -530000000000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -530000000000.0) y (if (<= t 1.3e+64) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -530000000000.0) {
		tmp = y;
	} else if (t <= 1.3e+64) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-530000000000.0d0)) then
        tmp = y
    else if (t <= 1.3d+64) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -530000000000.0) {
		tmp = y;
	} else if (t <= 1.3e+64) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -530000000000.0:
		tmp = y
	elif t <= 1.3e+64:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -530000000000.0)
		tmp = y;
	elseif (t <= 1.3e+64)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -530000000000.0)
		tmp = y;
	elseif (t <= 1.3e+64)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -530000000000.0], y, If[LessEqual[t, 1.3e+64], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.3e11 or 1.29999999999999998e64 < t

   1. Initial program 45.7%

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

   3. Taylor expanded in y around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-lft-identity 40.2%

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

      3. times-frac 59.8%

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

      4. /-rgt-identity 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in t around inf 46.5%

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

      1. +-commutative 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in y around inf 50.7%

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

   if -5.3e11 < t < 1.29999999999999998e64

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-/l* 91.9%

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

      3. fma-define 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 37.9%

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

Alternative 17: 24.4% 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 67.9%

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

   1. +-commutative 67.9%

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

   2. associate-/l* 85.1%

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

   3. fma-define 85.1%

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

3. Simplified 85.1%

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

5. Taylor expanded in a around inf 25.2%

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

Developer Target 1: 86.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

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

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