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

Percentage Accurate: 69.2% → 90.4%

Time: 17.4s

Alternatives: 25

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: 69.2% 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: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - z\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ t_2 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t z) (* (- y x) (/ -1.0 (- a t))))))
        (t_2 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_2 -2e+254)
     t_1
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ 1.0 (/ t (* (- z a) (- x y)))))
         (if (<= t_2 2e+263) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - z) * ((y - x) * (-1.0 / (a - t))));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+254) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	} else if (t_2 <= 2e+263) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - z) * ((y - x) * ((-1.0d0) / (a - t))))
    t_2 = x + (((x - y) * (t - z)) / (a - t))
    if (t_2 <= (-2d+254)) then
        tmp = t_1
    else if (t_2 <= (-2d-275)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = y + (1.0d0 / (t / ((z - a) * (x - y))))
    else if (t_2 <= 2d+263) then
        tmp = t_2
    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 + ((t - z) * ((y - x) * (-1.0 / (a - t))));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -2e+254) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	} else if (t_2 <= 2e+263) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - z) * ((y - x) * (-1.0 / (a - t))))
	t_2 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -2e+254:
		tmp = t_1
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (1.0 / (t / ((z - a) * (x - y))))
	elif t_2 <= 2e+263:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - z) * Float64(Float64(y - x) * Float64(-1.0 / Float64(a - t)))))
	t_2 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e+254)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(1.0 / Float64(t / Float64(Float64(z - a) * Float64(x - y)))));
	elseif (t_2 <= 2e+263)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - z) * ((y - x) * (-1.0 / (a - t))));
	t_2 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e+254)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	elseif (t_2 <= 2e+263)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - z), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+254], t$95$1, If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(1.0 / N[(t / N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+263], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e254 or 2.00000000000000003e263 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 39.7%

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

      1. div-inv 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*l* 83.8%

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

   4. Applied egg-rr 83.8%

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

   if -1.9999999999999999e254 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000003e263

   1. Initial program 96.8%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. unpow-1 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{+254}:\\ \;\;\;\;x + \left(t - z\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+263}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - z\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{a - t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-275} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-275) (not (<= t_1 0.0)))
     (fma (- y x) (/ (- z t) (- a t)) x)
     (+ y (/ 1.0 (/ t (* (- z a) (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-275) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(1.0 / Float64(t / Float64(Float64(z - a) * Float64(x - y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(1.0 / N[(t / N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.1%

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

      1. +-commutative 73.1%

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

      2. associate-/l* 89.5%

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

      3. fma-define 89.5%

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

   3. Simplified 89.5%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. unpow-1 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275} \lor \neg \left(x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ 1.0 (/ t (* (- z a) (- x y)))))
         (if (<= t_2 2e+288) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	} else if (t_2 <= 2e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	} else if (t_2 <= 2e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (1.0 / (t / ((z - a) * (x - y))))
	elif t_2 <= 2e+288:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(1.0 / Float64(t / Float64(Float64(z - a) * Float64(x - y)))));
	elseif (t_2 <= 2e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (1.0 / (t / ((z - a) * (x - y))));
	elseif (t_2 <= 2e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(1.0 / N[(t / N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+288], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 2e288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-/l* 84.0%

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

      3. fma-define 84.0%

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

   3. Simplified 84.0%

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

      1. add-cube-cbrt 83.2%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 83.2%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 83.2%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate--l+ 43.9%

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

      3. mul-1-neg 43.9%

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

      4. associate-*r/ 43.9%

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

      5. associate-*r/ 43.9%

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

      6. div-sub 45.1%

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

      7. distribute-lft-out-- 45.1%

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

      8. distribute-rgt-out-- 46.5%

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

      9. associate-*r/ 46.5%

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

      10. distribute-rgt-out-- 45.1%

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

      11. mul-1-neg 45.1%

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

      12. div-sub 43.9%

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

   9. Simplified 72.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2e288

   1. Initial program 96.3%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. unpow-1 99.7%

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

   11. Simplified 99.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{1}{\frac{t}{\left(z - a\right) \cdot \left(x - y\right)}}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ t_2 := x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t))))
        (t_2 (+ x (/ (* (- x y) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-275)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* x (- z a)) t))
         (if (<= t_2 2e+288) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 2e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double t_2 = x + (((x - y) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-275) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((x * (z - a)) / t);
	} else if (t_2 <= 2e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	t_2 = x + (((x - y) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-275:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((x * (z - a)) / t)
	elif t_2 <= 2e+288:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	t_2 = Float64(x + Float64(Float64(Float64(x - y) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(x * Float64(z - a)) / t));
	elseif (t_2 <= 2e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	t_2 = x + (((x - y) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-275)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((x * (z - a)) / t);
	elseif (t_2 <= 2e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(x - y), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-275], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+288], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 2e288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-/l* 84.0%

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

      3. fma-define 84.0%

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

   3. Simplified 84.0%

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

      1. add-cube-cbrt 83.2%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 83.2%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 83.2%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate--l+ 43.9%

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

      3. mul-1-neg 43.9%

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

      4. associate-*r/ 43.9%

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

      5. associate-*r/ 43.9%

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

      6. div-sub 45.1%

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

      7. distribute-lft-out-- 45.1%

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

      8. distribute-rgt-out-- 46.5%

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

      9. associate-*r/ 46.5%

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

      10. distribute-rgt-out-- 45.1%

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

      11. mul-1-neg 45.1%

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

      12. div-sub 43.9%

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

   9. Simplified 72.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.99999999999999987e-275 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2e288

   1. Initial program 96.3%

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

   if -1.99999999999999987e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

      1. +-commutative 4.7%

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

      2. associate-/l* 4.7%

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

      3. fma-define 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in t around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. associate-*r/ 99.6%

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

      4. mul-1-neg 99.6%

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

      5. div-sub 99.6%

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

      6. mul-1-neg 99.6%

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

      7. distribute-lft-out-- 99.6%

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

      8. associate-*r/ 99.6%

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

      9. mul-1-neg 99.6%

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

      10. unsub-neg 99.6%

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

      11. distribute-rgt-out-- 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

   10. Simplified 99.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-275}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;x + \frac{\left(x - y\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-287}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -2.85e+54)
     t_1
     (if (<= t 4.7e-287)
       (+ x (* y (/ z a)))
       (if (<= t 2.85e-150)
         (* z (/ (- y x) a))
         (if (<= t 2.15e+101) (- x (/ (* y t) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -2.85e+54) {
		tmp = t_1;
	} else if (t <= 4.7e-287) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.85e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.15e+101) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (x / t))
    if (t <= (-2.85d+54)) then
        tmp = t_1
    else if (t <= 4.7d-287) then
        tmp = x + (y * (z / a))
    else if (t <= 2.85d-150) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.15d+101) then
        tmp = x - ((y * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -2.85e+54) {
		tmp = t_1;
	} else if (t <= 4.7e-287) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.85e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.15e+101) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -2.85e+54:
		tmp = t_1
	elif t <= 4.7e-287:
		tmp = x + (y * (z / a))
	elif t <= 2.85e-150:
		tmp = z * ((y - x) / a)
	elif t <= 2.15e+101:
		tmp = x - ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -2.85e+54)
		tmp = t_1;
	elseif (t <= 4.7e-287)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.85e-150)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.15e+101)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -2.85e+54)
		tmp = t_1;
	elseif (t <= 4.7e-287)
		tmp = x + (y * (z / a));
	elseif (t <= 2.85e-150)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.15e+101)
		tmp = x - ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.85e+54], t$95$1, If[LessEqual[t, 4.7e-287], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.85e-150], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+101], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8499999999999998e54 or 2.15e101 < t

   1. Initial program 35.4%

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

      1. +-commutative 35.4%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 49.8%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 49.8%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 43.9%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 58.0%

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

      1. associate-*r/ 65.8%

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

   10. Simplified 65.8%

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

   11. Taylor expanded in y around 0 57.8%

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

       1. neg-mul-1 57.8%

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

   13. Simplified 57.8%

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

   if -2.8499999999999998e54 < t < 4.6999999999999999e-287

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 72.8%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

      1. clear-num 77.8%

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

      2. inv-pow 77.8%

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

   7. Applied egg-rr 77.8%

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

      1. unpow-1 77.8%

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

   9. Simplified 77.8%

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

   10. Taylor expanded in y around inf 63.9%

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

       1. associate-*r/ 70.2%

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

   12. Simplified 70.2%

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

   13. Taylor expanded in z around inf 68.8%

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

   if 4.6999999999999999e-287 < t < 2.8500000000000001e-150

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in a around inf 66.5%

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

   if 2.8500000000000001e-150 < t < 2.15e101

   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 a around inf 53.9%

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

      1. associate-/l* 57.4%

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

   5. Simplified 57.4%

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

      1. clear-num 57.4%

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

      2. inv-pow 57.4%

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

   7. Applied egg-rr 57.4%

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

      1. unpow-1 57.4%

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

   9. Simplified 57.4%

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

   10. Taylor expanded in y around inf 50.5%

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

       1. associate-*r/ 50.4%

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

   12. Simplified 50.4%

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

   13. Taylor expanded in z around 0 48.9%

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

       1. mul-1-neg 48.9%

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

       2. *-commutative 48.9%

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

   15. Simplified 48.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+54}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-287}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-286}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))))
   (if (<= t -1.32e+54)
     t_1
     (if (<= t 1.06e-286)
       (+ x (* y (/ z a)))
       (if (<= t 2.8e-150)
         (* z (/ (- y x) a))
         (if (<= t 2.25e+101) (- x (/ (* y t) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double tmp;
	if (t <= -1.32e+54) {
		tmp = t_1;
	} else if (t <= 1.06e-286) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.8e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.25e+101) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (y * (z / t))
    if (t <= (-1.32d+54)) then
        tmp = t_1
    else if (t <= 1.06d-286) then
        tmp = x + (y * (z / a))
    else if (t <= 2.8d-150) then
        tmp = z * ((y - x) / a)
    else if (t <= 2.25d+101) then
        tmp = x - ((y * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double tmp;
	if (t <= -1.32e+54) {
		tmp = t_1;
	} else if (t <= 1.06e-286) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.8e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 2.25e+101) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	tmp = 0
	if t <= -1.32e+54:
		tmp = t_1
	elif t <= 1.06e-286:
		tmp = x + (y * (z / a))
	elif t <= 2.8e-150:
		tmp = z * ((y - x) / a)
	elif t <= 2.25e+101:
		tmp = x - ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.32e+54)
		tmp = t_1;
	elseif (t <= 1.06e-286)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.8e-150)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 2.25e+101)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	tmp = 0.0;
	if (t <= -1.32e+54)
		tmp = t_1;
	elseif (t <= 1.06e-286)
		tmp = x + (y * (z / a));
	elseif (t <= 2.8e-150)
		tmp = z * ((y - x) / a);
	elseif (t <= 2.25e+101)
		tmp = x - ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.32e+54], t$95$1, If[LessEqual[t, 1.06e-286], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-150], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+101], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3200000000000001e54 or 2.2500000000000001e101 < t

   1. Initial program 35.4%

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

      1. +-commutative 35.4%

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

      2. associate-/l* 70.7%

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

      3. fma-define 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 49.8%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 49.8%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 43.9%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 58.0%

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

      1. associate-*r/ 65.8%

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

   10. Simplified 65.8%

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

   11. Taylor expanded in x around 0 45.4%

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

       1. associate-/l* 50.5%

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

   13. Simplified 50.5%

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

   if -1.3200000000000001e54 < t < 1.0599999999999999e-286

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 72.8%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

      1. clear-num 77.8%

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

      2. inv-pow 77.8%

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

   7. Applied egg-rr 77.8%

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

      1. unpow-1 77.8%

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

   9. Simplified 77.8%

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

   10. Taylor expanded in y around inf 63.9%

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

       1. associate-*r/ 70.2%

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

   12. Simplified 70.2%

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

   13. Taylor expanded in z around inf 68.8%

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

   if 1.0599999999999999e-286 < t < 2.79999999999999996e-150

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in a around inf 66.5%

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

   if 2.79999999999999996e-150 < t < 2.2500000000000001e101

   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 a around inf 53.9%

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

      1. associate-/l* 57.4%

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

   5. Simplified 57.4%

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

      1. clear-num 57.4%

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

      2. inv-pow 57.4%

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

   7. Applied egg-rr 57.4%

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

      1. unpow-1 57.4%

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

   9. Simplified 57.4%

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

   10. Taylor expanded in y around inf 50.5%

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

       1. associate-*r/ 50.4%

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

   12. Simplified 50.4%

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

   13. Taylor expanded in z around 0 48.9%

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

       1. mul-1-neg 48.9%

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

       2. *-commutative 48.9%

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

   15. Simplified 48.9%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+54}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-286}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+101}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-286}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+199}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+54)
   y
   (if (<= t 4e-286)
     (+ x (* y (/ z a)))
     (if (<= t 2.7e-150)
       (* z (/ (- y x) a))
       (if (<= t 1.15e+199) (- x (* y (/ t a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+54) {
		tmp = y;
	} else if (t <= 4e-286) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.15e+199) {
		tmp = x - (y * (t / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d+54)) then
        tmp = y
    else if (t <= 4d-286) then
        tmp = x + (y * (z / a))
    else if (t <= 2.7d-150) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.15d+199) then
        tmp = x - (y * (t / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+54) {
		tmp = y;
	} else if (t <= 4e-286) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e-150) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.15e+199) {
		tmp = x - (y * (t / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+54:
		tmp = y
	elif t <= 4e-286:
		tmp = x + (y * (z / a))
	elif t <= 2.7e-150:
		tmp = z * ((y - x) / a)
	elif t <= 1.15e+199:
		tmp = x - (y * (t / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+54)
		tmp = y;
	elseif (t <= 4e-286)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.7e-150)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.15e+199)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+54)
		tmp = y;
	elseif (t <= 4e-286)
		tmp = x + (y * (z / a));
	elseif (t <= 2.7e-150)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.15e+199)
		tmp = x - (y * (t / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+54], y, If[LessEqual[t, 4e-286], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-150], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+199], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.39999999999999998e54 or 1.14999999999999997e199 < t

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 69.1%

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

      3. fma-define 69.1%

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

   3. Simplified 69.1%

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

      1. add-cube-cbrt 67.7%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 67.7%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 67.7%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 47.4%

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

   if -2.39999999999999998e54 < t < 4.0000000000000002e-286

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf 72.8%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

      1. clear-num 77.8%

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

      2. inv-pow 77.8%

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

   7. Applied egg-rr 77.8%

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

      1. unpow-1 77.8%

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

   9. Simplified 77.8%

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

   10. Taylor expanded in y around inf 63.9%

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

       1. associate-*r/ 70.2%

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

   12. Simplified 70.2%

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

   13. Taylor expanded in z around inf 68.8%

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

   if 4.0000000000000002e-286 < t < 2.7000000000000001e-150

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around inf 69.8%

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

   6. Taylor expanded in a around inf 66.5%

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

   if 2.7000000000000001e-150 < t < 1.14999999999999997e199

   1. Initial program 68.0%

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

   3. Taylor expanded in a around inf 42.1%

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

      1. associate-/l* 50.1%

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

   5. Simplified 50.1%

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

      1. clear-num 50.2%

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

      2. inv-pow 50.2%

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

   7. Applied egg-rr 50.2%

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

      1. unpow-1 50.2%

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

   9. Simplified 50.2%

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

   10. Taylor expanded in y around inf 41.3%

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

       1. associate-*r/ 47.0%

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

   12. Simplified 47.0%

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

   13. Taylor expanded in z around 0 40.1%

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

       1. mul-1-neg 40.1%

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

       2. unsub-neg 40.1%

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

       3. *-commutative 40.1%

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

       4. *-lft-identity 40.1%

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

       5. times-frac 41.4%

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

       6. /-rgt-identity 41.4%

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

   15. Simplified 41.4%

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

Alternative 8: 34.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+200}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= z -2.2e+224)
     (/ x (/ t z))
     (if (<= z -1e+34)
       t_1
       (if (<= z 4.8e-44) x (if (<= z 2.1e+200) (* x (/ (- z a) t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.2e+224) {
		tmp = x / (t / z);
	} else if (z <= -1e+34) {
		tmp = t_1;
	} else if (z <= 4.8e-44) {
		tmp = x;
	} else if (z <= 2.1e+200) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (a - t))
    if (z <= (-2.2d+224)) then
        tmp = x / (t / z)
    else if (z <= (-1d+34)) then
        tmp = t_1
    else if (z <= 4.8d-44) then
        tmp = x
    else if (z <= 2.1d+200) then
        tmp = x * ((z - a) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.2e+224) {
		tmp = x / (t / z);
	} else if (z <= -1e+34) {
		tmp = t_1;
	} else if (z <= 4.8e-44) {
		tmp = x;
	} else if (z <= 2.1e+200) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if z <= -2.2e+224:
		tmp = x / (t / z)
	elif z <= -1e+34:
		tmp = t_1
	elif z <= 4.8e-44:
		tmp = x
	elif z <= 2.1e+200:
		tmp = x * ((z - a) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.2e+224)
		tmp = Float64(x / Float64(t / z));
	elseif (z <= -1e+34)
		tmp = t_1;
	elseif (z <= 4.8e-44)
		tmp = x;
	elseif (z <= 2.1e+200)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (z <= -2.2e+224)
		tmp = x / (t / z);
	elseif (z <= -1e+34)
		tmp = t_1;
	elseif (z <= 4.8e-44)
		tmp = x;
	elseif (z <= 2.1e+200)
		tmp = x * ((z - a) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+224], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+34], t$95$1, If[LessEqual[z, 4.8e-44], x, If[LessEqual[z, 2.1e+200], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2e224

   1. Initial program 53.2%

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

      1. +-commutative 53.2%

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

      2. associate-/l* 86.6%

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

      3. fma-define 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 89.1%

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

   6. Taylor expanded in y around 0 59.1%

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

      1. neg-mul-1 59.1%

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

      2. distribute-neg-frac 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in a around 0 20.5%

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

       1. associate-/l* 51.4%

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

   11. Simplified 51.4%

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

       1. clear-num 51.4%

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

       2. un-div-inv 51.7%

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

   13. Applied egg-rr 51.7%

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

   if -2.2e224 < z < -9.99999999999999946e33 or 2.09999999999999997e200 < z

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-/l* 94.7%

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

      3. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around inf 76.4%

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

   6. Taylor expanded in y around inf 48.5%

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

   if -9.99999999999999946e33 < z < 4.80000000000000017e-44

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-/l* 81.3%

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

      3. fma-define 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in a around inf 40.9%

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

   if 4.80000000000000017e-44 < z < 2.09999999999999997e200

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 75.5%

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

      3. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-*r/ 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

      5. div-sub 64.0%

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

      6. mul-1-neg 64.0%

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

      7. distribute-lft-out-- 64.0%

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

      8. associate-*r/ 64.0%

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

      9. mul-1-neg 64.0%

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

      10. unsub-neg 64.0%

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

      11. distribute-rgt-out-- 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in y around 0 42.0%

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

      1. associate-/l* 49.8%

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

   10. Simplified 49.8%

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

Alternative 9: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{x - y}{a - t}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ (- x y) (- a t))))))
   (if (<= z -1e+142)
     t_1
     (if (<= z 6.2e-55)
       (- x (* (/ y (- a t)) (- t z)))
       (if (<= z 4.9e+20) (+ y (* z (/ (- x y) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * ((x - y) / (a - t)));
	double tmp;
	if (z <= -1e+142) {
		tmp = t_1;
	} else if (z <= 6.2e-55) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (z <= 4.9e+20) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * ((x - y) / (a - t)))
    if (z <= (-1d+142)) then
        tmp = t_1
    else if (z <= 6.2d-55) then
        tmp = x - ((y / (a - t)) * (t - z))
    else if (z <= 4.9d+20) then
        tmp = y + (z * ((x - y) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * ((x - y) / (a - t)));
	double tmp;
	if (z <= -1e+142) {
		tmp = t_1;
	} else if (z <= 6.2e-55) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (z <= 4.9e+20) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * ((x - y) / (a - t)))
	tmp = 0
	if z <= -1e+142:
		tmp = t_1
	elif z <= 6.2e-55:
		tmp = x - ((y / (a - t)) * (t - z))
	elif z <= 4.9e+20:
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(Float64(x - y) / Float64(a - t))))
	tmp = 0.0
	if (z <= -1e+142)
		tmp = t_1;
	elseif (z <= 6.2e-55)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (z <= 4.9e+20)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * ((x - y) / (a - t)));
	tmp = 0.0;
	if (z <= -1e+142)
		tmp = t_1;
	elseif (z <= 6.2e-55)
		tmp = x - ((y / (a - t)) * (t - z));
	elseif (z <= 4.9e+20)
		tmp = y + (z * ((x - y) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+142], t$95$1, If[LessEqual[z, 6.2e-55], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+20], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000005e142 or 4.9e20 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 82.7%

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

   5. Simplified 82.7%

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

   if -1.00000000000000005e142 < z < 6.19999999999999993e-55

   1. Initial program 69.1%

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

   3. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. *-lft-identity 66.5%

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

      3. times-frac 73.2%

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

      4. /-rgt-identity 73.2%

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

   5. Simplified 73.2%

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

   if 6.19999999999999993e-55 < z < 4.9e20

   1. Initial program 51.0%

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

      1. +-commutative 51.0%

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

      2. associate-/l* 57.7%

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

      3. fma-define 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in t around inf 74.7%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 74.7%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 74.7%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 68.6%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 86.8%

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

      1. associate-*r/ 86.9%

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

   10. Simplified 86.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+142}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -4.3e+61)
     t_1
     (if (<= t 6.5e+98)
       (- x (* z (/ (- x y) (- a t))))
       (if (<= t 2.9e+198) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -4.3e+61) {
		tmp = t_1;
	} else if (t <= 6.5e+98) {
		tmp = x - (z * ((x - y) / (a - t)));
	} else if (t <= 2.9e+198) {
		tmp = y * ((z - t) / (a - t));
	} 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 + (z * ((x - y) / t))
    if (t <= (-4.3d+61)) then
        tmp = t_1
    else if (t <= 6.5d+98) then
        tmp = x - (z * ((x - y) / (a - t)))
    else if (t <= 2.9d+198) then
        tmp = y * ((z - t) / (a - t))
    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 + (z * ((x - y) / t));
	double tmp;
	if (t <= -4.3e+61) {
		tmp = t_1;
	} else if (t <= 6.5e+98) {
		tmp = x - (z * ((x - y) / (a - t)));
	} else if (t <= 2.9e+198) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if t <= -4.3e+61:
		tmp = t_1
	elif t <= 6.5e+98:
		tmp = x - (z * ((x - y) / (a - t)))
	elif t <= 2.9e+198:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -4.3e+61)
		tmp = t_1;
	elseif (t <= 6.5e+98)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / Float64(a - t))));
	elseif (t <= 2.9e+198)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -4.3e+61)
		tmp = t_1;
	elseif (t <= 6.5e+98)
		tmp = x - (z * ((x - y) / (a - t)));
	elseif (t <= 2.9e+198)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+61], t$95$1, If[LessEqual[t, 6.5e+98], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+198], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3000000000000001e61 or 2.9000000000000001e198 < t

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-/l* 69.1%

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

      3. fma-define 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in t around inf 51.6%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 51.6%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 51.6%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 44.7%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 64.8%

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

      1. associate-*r/ 71.7%

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

   10. Simplified 71.7%

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

   if -4.3000000000000001e61 < t < 6.4999999999999999e98

   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 z around inf 77.8%

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

      1. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

   if 6.4999999999999999e98 < t < 2.9000000000000001e198

   1. Initial program 36.9%

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

      1. +-commutative 36.9%

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

      2. associate-/l* 74.7%

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

      3. fma-define 74.7%

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

   3. Simplified 74.7%

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

      1. add-cube-cbrt 74.3%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 74.5%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 74.5%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.2%

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

   9. Simplified 65.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+61}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+98}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -9e-20)
     t_1
     (if (<= t 1.1e+97)
       (+ x (* (- y x) (/ z a)))
       (if (<= t 3.9e+198) t_1 (+ y (* z (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -9e-20) {
		tmp = t_1;
	} else if (t <= 1.1e+97) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 3.9e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / 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 = y * ((z - t) / (a - t))
    if (t <= (-9d-20)) then
        tmp = t_1
    else if (t <= 1.1d+97) then
        tmp = x + ((y - x) * (z / a))
    else if (t <= 3.9d+198) then
        tmp = t_1
    else
        tmp = y + (z * (x / 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -9e-20) {
		tmp = t_1;
	} else if (t <= 1.1e+97) {
		tmp = x + ((y - x) * (z / a));
	} else if (t <= 3.9e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -9e-20:
		tmp = t_1
	elif t <= 1.1e+97:
		tmp = x + ((y - x) * (z / a))
	elif t <= 3.9e+198:
		tmp = t_1
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -9e-20)
		tmp = t_1;
	elseif (t <= 1.1e+97)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	elseif (t <= 3.9e+198)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -9e-20)
		tmp = t_1;
	elseif (t <= 1.1e+97)
		tmp = x + ((y - x) * (z / a));
	elseif (t <= 3.9e+198)
		tmp = t_1;
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-20], t$95$1, If[LessEqual[t, 1.1e+97], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+198], t$95$1, N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.0000000000000003e-20 or 1.1e97 < t < 3.9e198

   1. Initial program 48.7%

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

      1. +-commutative 48.7%

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

      2. associate-/l* 72.2%

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

      3. fma-define 72.2%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 71.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 71.4%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in y around inf 62.4%

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

      1. div-sub 62.4%

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

   9. Simplified 62.4%

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

   if -9.0000000000000003e-20 < t < 1.1e97

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in z around inf 70.8%

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

   if 3.9e198 < t

   1. Initial program 18.5%

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

      1. +-commutative 18.5%

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

      2. associate-/l* 71.3%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.2%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 59.5%

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

      1. associate-*r/ 81.3%

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

   10. Simplified 81.3%

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

   11. Taylor expanded in y around 0 75.0%

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

       1. neg-mul-1 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.4e-20)
     t_1
     (if (<= t 3.2e+97)
       (- x (* z (/ (- x y) a)))
       (if (<= t 3.4e+198) t_1 (+ y (* z (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.4e-20) {
		tmp = t_1;
	} else if (t <= 3.2e+97) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 3.4e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / 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 = y * ((z - t) / (a - t))
    if (t <= (-1.4d-20)) then
        tmp = t_1
    else if (t <= 3.2d+97) then
        tmp = x - (z * ((x - y) / a))
    else if (t <= 3.4d+198) then
        tmp = t_1
    else
        tmp = y + (z * (x / 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.4e-20) {
		tmp = t_1;
	} else if (t <= 3.2e+97) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 3.4e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.4e-20:
		tmp = t_1
	elif t <= 3.2e+97:
		tmp = x - (z * ((x - y) / a))
	elif t <= 3.4e+198:
		tmp = t_1
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.4e-20)
		tmp = t_1;
	elseif (t <= 3.2e+97)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	elseif (t <= 3.4e+198)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.4e-20)
		tmp = t_1;
	elseif (t <= 3.2e+97)
		tmp = x - (z * ((x - y) / a));
	elseif (t <= 3.4e+198)
		tmp = t_1;
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-20], t$95$1, If[LessEqual[t, 3.2e+97], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+198], t$95$1, N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-20 or 3.20000000000000016e97 < t < 3.4e198

   1. Initial program 48.7%

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

      1. +-commutative 48.7%

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

      2. associate-/l* 72.2%

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

      3. fma-define 72.2%

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

   3. Simplified 72.2%

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

      1. add-cube-cbrt 71.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 71.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 71.4%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in y around inf 62.4%

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

      1. div-sub 62.4%

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

   9. Simplified 62.4%

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

   if -1.4000000000000001e-20 < t < 3.20000000000000016e97

   1. Initial program 88.4%

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

   3. Taylor expanded in t around 0 65.6%

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

      1. associate-/l* 66.2%

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

   5. Simplified 66.2%

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

   if 3.4e198 < t

   1. Initial program 18.5%

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

      1. +-commutative 18.5%

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

      2. associate-/l* 71.3%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.2%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 59.5%

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

      1. associate-*r/ 81.3%

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

   10. Simplified 81.3%

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

   11. Taylor expanded in y around 0 75.0%

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

       1. neg-mul-1 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+97}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.08e-11)
     t_1
     (if (<= t 1.75e-63)
       (+ x (* y (/ (- z t) a)))
       (if (<= t 4e+198) t_1 (+ y (* z (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.08e-11) {
		tmp = t_1;
	} else if (t <= 1.75e-63) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 4e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / 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 = y * ((z - t) / (a - t))
    if (t <= (-1.08d-11)) then
        tmp = t_1
    else if (t <= 1.75d-63) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 4d+198) then
        tmp = t_1
    else
        tmp = y + (z * (x / 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.08e-11) {
		tmp = t_1;
	} else if (t <= 1.75e-63) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 4e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.08e-11:
		tmp = t_1
	elif t <= 1.75e-63:
		tmp = x + (y * ((z - t) / a))
	elif t <= 4e+198:
		tmp = t_1
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.08e-11)
		tmp = t_1;
	elseif (t <= 1.75e-63)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 4e+198)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.08e-11)
		tmp = t_1;
	elseif (t <= 1.75e-63)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 4e+198)
		tmp = t_1;
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e-11], t$95$1, If[LessEqual[t, 1.75e-63], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+198], t$95$1, N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.07999999999999992e-11 or 1.75000000000000002e-63 < t < 4.00000000000000007e198

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. associate-/l* 77.5%

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

      3. fma-define 77.5%

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

   3. Simplified 77.5%

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

      1. add-cube-cbrt 76.5%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 76.5%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 76.5%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in y around inf 56.0%

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

      1. div-sub 56.0%

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

   9. Simplified 56.0%

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

   if -1.07999999999999992e-11 < t < 1.75000000000000002e-63

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 78.2%

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

      1. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

      1. clear-num 81.7%

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

      2. inv-pow 81.7%

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

   7. Applied egg-rr 81.7%

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

      1. unpow-1 81.7%

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

   9. Simplified 81.7%

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

   10. Taylor expanded in y around inf 63.6%

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

       1. associate-*r/ 67.8%

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

   12. Simplified 67.8%

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

   if 4.00000000000000007e198 < t

   1. Initial program 18.5%

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

      1. +-commutative 18.5%

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

      2. associate-/l* 71.3%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.2%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 59.5%

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

      1. associate-*r/ 81.3%

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

   10. Simplified 81.3%

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

   11. Taylor expanded in y around 0 75.0%

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

       1. neg-mul-1 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7.6e-18)
     t_1
     (if (<= t 7.6e-114)
       (+ x (* y (/ z a)))
       (if (<= t 2.7e+198) t_1 (+ y (* z (/ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.6e-18) {
		tmp = t_1;
	} else if (t <= 7.6e-114) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / 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 = y * ((z - t) / (a - t))
    if (t <= (-7.6d-18)) then
        tmp = t_1
    else if (t <= 7.6d-114) then
        tmp = x + (y * (z / a))
    else if (t <= 2.7d+198) then
        tmp = t_1
    else
        tmp = y + (z * (x / 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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -7.6e-18) {
		tmp = t_1;
	} else if (t <= 7.6e-114) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.7e+198) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -7.6e-18:
		tmp = t_1
	elif t <= 7.6e-114:
		tmp = x + (y * (z / a))
	elif t <= 2.7e+198:
		tmp = t_1
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -7.6e-18)
		tmp = t_1;
	elseif (t <= 7.6e-114)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.7e+198)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -7.6e-18)
		tmp = t_1;
	elseif (t <= 7.6e-114)
		tmp = x + (y * (z / a));
	elseif (t <= 2.7e+198)
		tmp = t_1;
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e-18], t$95$1, If[LessEqual[t, 7.6e-114], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+198], t$95$1, N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999996e-18 or 7.5999999999999997e-114 < t < 2.6999999999999999e198

   1. Initial program 60.5%

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

      1. +-commutative 60.5%

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

      2. associate-/l* 77.8%

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

      3. fma-define 77.8%

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

   3. Simplified 77.8%

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

      1. add-cube-cbrt 76.8%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 76.9%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 76.9%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in y around inf 55.9%

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

      1. div-sub 56.0%

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

   9. Simplified 56.0%

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

   if -7.5999999999999996e-18 < t < 7.5999999999999997e-114

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 79.8%

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

      1. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

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

   7. Applied egg-rr 83.7%

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

      1. unpow-1 83.7%

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

   9. Simplified 83.7%

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

   10. Taylor expanded in y around inf 63.6%

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

       1. associate-*r/ 68.3%

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

   12. Simplified 68.3%

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

   13. Taylor expanded in z around inf 67.3%

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

   if 2.6999999999999999e198 < t

   1. Initial program 18.5%

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

      1. +-commutative 18.5%

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

      2. associate-/l* 71.3%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.2%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 38.7%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 59.5%

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

      1. associate-*r/ 81.3%

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

   10. Simplified 81.3%

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

   11. Taylor expanded in y around 0 75.0%

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

       1. neg-mul-1 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z t)))))
   (if (<= t -3.2e+54)
     t_1
     (if (<= t 9.5e+28)
       (+ x (* y (/ z a)))
       (if (<= t 6e+112) (* z (/ (- x y) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / t));
	double tmp;
	if (t <= -3.2e+54) {
		tmp = t_1;
	} else if (t <= 9.5e+28) {
		tmp = x + (y * (z / a));
	} else if (t <= 6e+112) {
		tmp = z * ((x - y) / t);
	} 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 - (y * (z / t))
    if (t <= (-3.2d+54)) then
        tmp = t_1
    else if (t <= 9.5d+28) then
        tmp = x + (y * (z / a))
    else if (t <= 6d+112) then
        tmp = z * ((x - y) / t)
    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 - (y * (z / t));
	double tmp;
	if (t <= -3.2e+54) {
		tmp = t_1;
	} else if (t <= 9.5e+28) {
		tmp = x + (y * (z / a));
	} else if (t <= 6e+112) {
		tmp = z * ((x - y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / t))
	tmp = 0
	if t <= -3.2e+54:
		tmp = t_1
	elif t <= 9.5e+28:
		tmp = x + (y * (z / a))
	elif t <= 6e+112:
		tmp = z * ((x - y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -3.2e+54)
		tmp = t_1;
	elseif (t <= 9.5e+28)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 6e+112)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / t));
	tmp = 0.0;
	if (t <= -3.2e+54)
		tmp = t_1;
	elseif (t <= 9.5e+28)
		tmp = x + (y * (z / a));
	elseif (t <= 6e+112)
		tmp = z * ((x - y) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+54], t$95$1, If[LessEqual[t, 9.5e+28], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+112], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2e54 or 5.99999999999999958e112 < t

   1. Initial program 35.2%

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

      1. +-commutative 35.2%

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

      2. associate-/l* 70.8%

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

      3. fma-define 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in t around inf 49.1%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 49.1%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 49.1%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 43.0%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 57.6%

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

      1. associate-*r/ 64.7%

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

   10. Simplified 64.7%

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

   11. Taylor expanded in x around 0 46.7%

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

       1. associate-/l* 51.0%

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

   13. Simplified 51.0%

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

   if -3.2e54 < t < 9.49999999999999927e28

   1. Initial program 88.9%

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

   3. Taylor expanded in a around inf 71.5%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

      1. clear-num 75.0%

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

      2. inv-pow 75.0%

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

   7. Applied egg-rr 75.0%

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

      1. unpow-1 75.0%

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

   9. Simplified 75.0%

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

   10. Taylor expanded in y around inf 58.0%

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

       1. associate-*r/ 62.0%

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

   12. Simplified 62.0%

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

   13. Taylor expanded in z around inf 58.5%

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

   if 9.49999999999999927e28 < t < 5.99999999999999958e112

   1. Initial program 74.4%

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

      1. +-commutative 74.4%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in z around inf 58.2%

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

   6. Taylor expanded in a around 0 54.3%

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

      1. distribute-lft-out-- 54.3%

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

      2. div-sub 54.3%

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

      3. neg-mul-1 54.3%

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

      4. distribute-rgt-neg-in 54.3%

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

      5. distribute-lft-neg-in 54.3%

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

      6. *-commutative 54.3%

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

   8. Simplified 54.3%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+54}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+209}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+37)
   (* z (/ (- y x) a))
   (if (<= z 5e-45)
     x
     (if (<= z 1e+209) (* x (/ (- z a) t)) (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+37) {
		tmp = z * ((y - x) / a);
	} else if (z <= 5e-45) {
		tmp = x;
	} else if (z <= 1e+209) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+37)) then
        tmp = z * ((y - x) / a)
    else if (z <= 5d-45) then
        tmp = x
    else if (z <= 1d+209) then
        tmp = x * ((z - a) / t)
    else
        tmp = z * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+37) {
		tmp = z * ((y - x) / a);
	} else if (z <= 5e-45) {
		tmp = x;
	} else if (z <= 1e+209) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+37:
		tmp = z * ((y - x) / a)
	elif z <= 5e-45:
		tmp = x
	elif z <= 1e+209:
		tmp = x * ((z - a) / t)
	else:
		tmp = z * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+37)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (z <= 5e-45)
		tmp = x;
	elseif (z <= 1e+209)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = Float64(z * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+37)
		tmp = z * ((y - x) / a);
	elseif (z <= 5e-45)
		tmp = x;
	elseif (z <= 1e+209)
		tmp = x * ((z - a) / t);
	else
		tmp = z * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+37], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-45], x, If[LessEqual[z, 1e+209], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.39999999999999973e37

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. associate-/l* 88.9%

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

      3. fma-define 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around inf 76.8%

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

   6. Taylor expanded in a around inf 45.0%

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

   if -5.39999999999999973e37 < z < 4.99999999999999976e-45

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-/l* 81.3%

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

      3. fma-define 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in a around inf 40.9%

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

   if 4.99999999999999976e-45 < z < 1.0000000000000001e209

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 75.5%

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

      3. fma-define 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. associate-*r/ 63.7%

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

      3. associate-*r/ 63.7%

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

      4. mul-1-neg 63.7%

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

      5. div-sub 64.0%

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

      6. mul-1-neg 64.0%

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

      7. distribute-lft-out-- 64.0%

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

      8. associate-*r/ 64.0%

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

      9. mul-1-neg 64.0%

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

      10. unsub-neg 64.0%

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

      11. distribute-rgt-out-- 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in y around 0 42.0%

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

      1. associate-/l* 49.8%

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

   10. Simplified 49.8%

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

   if 1.0000000000000001e209 < z

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 84.0%

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

   6. Taylor expanded in y around inf 50.5%

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

Alternative 17: 32.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;z \leq -42000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= z -42000000000.0)
     t_1
     (if (<= z 7.2e-42) x (if (<= z 5.2e+235) t_1 (* (/ z t) (- y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (z <= -42000000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-42) {
		tmp = x;
	} else if (z <= 5.2e+235) {
		tmp = t_1;
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (z <= (-42000000000.0d0)) then
        tmp = t_1
    else if (z <= 7.2d-42) then
        tmp = x
    else if (z <= 5.2d+235) then
        tmp = t_1
    else
        tmp = (z / t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (z <= -42000000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-42) {
		tmp = x;
	} else if (z <= 5.2e+235) {
		tmp = t_1;
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if z <= -42000000000.0:
		tmp = t_1
	elif z <= 7.2e-42:
		tmp = x
	elif z <= 5.2e+235:
		tmp = t_1
	else:
		tmp = (z / t) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (z <= -42000000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-42)
		tmp = x;
	elseif (z <= 5.2e+235)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (z <= -42000000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-42)
		tmp = x;
	elseif (z <= 5.2e+235)
		tmp = t_1;
	else
		tmp = (z / t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -42000000000.0], t$95$1, If[LessEqual[z, 7.2e-42], x, If[LessEqual[z, 5.2e+235], t$95$1, N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e10 or 7.2000000000000004e-42 < z < 5.1999999999999996e235

   1. Initial program 68.1%

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

      1. +-commutative 68.1%

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

      2. associate-/l* 82.7%

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

      3. fma-define 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. associate--l+ 49.5%

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

      2. associate-*r/ 49.5%

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

      3. associate-*r/ 49.5%

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

      4. mul-1-neg 49.5%

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

      5. div-sub 49.6%

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

      6. mul-1-neg 49.6%

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

      7. distribute-lft-out-- 49.6%

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

      8. associate-*r/ 49.6%

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

      9. mul-1-neg 49.6%

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

      10. unsub-neg 49.6%

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

      11. distribute-rgt-out-- 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in y around 0 30.6%

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

      1. associate-/l* 42.9%

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

   10. Simplified 42.9%

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

   if -4.2e10 < z < 7.2000000000000004e-42

   1. Initial program 69.1%

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

      1. +-commutative 69.1%

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

      2. associate-/l* 81.6%

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

      3. fma-define 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in a around inf 41.0%

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

   if 5.1999999999999996e235 < z

   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* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.7%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.7%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 29.1%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 49.4%

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

      1. associate-*r/ 53.8%

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

   10. Simplified 53.8%

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

   11. Taylor expanded in x around 0 38.4%

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

       1. associate-/l* 52.4%

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

   13. Simplified 52.4%

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

   14. Taylor expanded in z around inf 38.4%

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

       1. associate-*r/ 52.4%

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

       2. neg-mul-1 52.4%

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

       3. distribute-rgt-neg-in 52.4%

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

       4. distribute-neg-frac2 52.4%

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

   16. Simplified 52.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -42000000000:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+53} \lor \neg \left(t \leq 2.25 \cdot 10^{+101}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e+53) (not (<= t 2.25e+101)))
   (+ y (* (- z a) (/ (- x y) t)))
   (- x (* z (/ (- x y) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+53) || !(t <= 2.25e+101)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x - (z * ((x - y) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.2d+53)) .or. (.not. (t <= 2.25d+101))) then
        tmp = y + ((z - a) * ((x - y) / t))
    else
        tmp = x - (z * ((x - y) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e+53) || !(t <= 2.25e+101)) {
		tmp = y + ((z - a) * ((x - y) / t));
	} else {
		tmp = x - (z * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e+53) or not (t <= 2.25e+101):
		tmp = y + ((z - a) * ((x - y) / t))
	else:
		tmp = x - (z * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e+53) || !(t <= 2.25e+101))
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.2e+53) || ~((t <= 2.25e+101)))
		tmp = y + ((z - a) * ((x - y) / t));
	else
		tmp = x - (z * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e+53], N[Not[LessEqual[t, 2.25e+101]], $MachinePrecision]], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e53 or 2.2500000000000001e101 < t

   1. Initial program 35.0%

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

      1. +-commutative 35.0%

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

      2. associate-/l* 70.0%

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

      3. fma-define 70.0%

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

   3. Simplified 70.0%

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

      1. add-cube-cbrt 68.9%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 69.0%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 69.0%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate--l+ 57.3%

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

      3. mul-1-neg 57.3%

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

      4. associate-*r/ 57.3%

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

      5. associate-*r/ 57.3%

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

      6. div-sub 57.3%

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

      7. distribute-lft-out-- 57.3%

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

      8. distribute-rgt-out-- 57.3%

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

      9. associate-*r/ 57.3%

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

      10. distribute-rgt-out-- 57.3%

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

      11. mul-1-neg 57.3%

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

      12. div-sub 57.3%

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

   9. Simplified 75.2%

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

   if -3.2e53 < t < 2.2500000000000001e101

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 77.6%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+53} \lor \neg \left(t \leq 2.25 \cdot 10^{+101}\right):\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+142)
   (/ x (/ t z))
   (if (<= z 4.7e-45) x (if (<= z 7.8e+235) (* x (/ z t)) (* (/ z t) (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+142) {
		tmp = x / (t / z);
	} else if (z <= 4.7e-45) {
		tmp = x;
	} else if (z <= 7.8e+235) {
		tmp = x * (z / t);
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+142)) then
        tmp = x / (t / z)
    else if (z <= 4.7d-45) then
        tmp = x
    else if (z <= 7.8d+235) then
        tmp = x * (z / t)
    else
        tmp = (z / t) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+142) {
		tmp = x / (t / z);
	} else if (z <= 4.7e-45) {
		tmp = x;
	} else if (z <= 7.8e+235) {
		tmp = x * (z / t);
	} else {
		tmp = (z / t) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+142:
		tmp = x / (t / z)
	elif z <= 4.7e-45:
		tmp = x
	elif z <= 7.8e+235:
		tmp = x * (z / t)
	else:
		tmp = (z / t) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+142)
		tmp = Float64(x / Float64(t / z));
	elseif (z <= 4.7e-45)
		tmp = x;
	elseif (z <= 7.8e+235)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = Float64(Float64(z / t) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+142)
		tmp = x / (t / z);
	elseif (z <= 4.7e-45)
		tmp = x;
	elseif (z <= 7.8e+235)
		tmp = x * (z / t);
	else
		tmp = (z / t) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+142], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-45], x, If[LessEqual[z, 7.8e+235], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.49999999999999987e142

   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* 86.0%

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

      3. fma-define 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 87.1%

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

   6. Taylor expanded in y around 0 53.3%

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

      1. neg-mul-1 53.3%

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

      2. distribute-neg-frac 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in a around 0 19.8%

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

       1. associate-/l* 46.7%

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

   11. Simplified 46.7%

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

       1. clear-num 46.7%

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

       2. un-div-inv 46.9%

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

   13. Applied egg-rr 46.9%

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

   if -1.49999999999999987e142 < z < 4.6999999999999998e-45

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 82.7%

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

      3. fma-define 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in a around inf 38.0%

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

   if 4.6999999999999998e-45 < z < 7.8000000000000005e235

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 78.1%

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

      3. fma-define 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in z around inf 76.2%

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

   6. Taylor expanded in y around 0 49.8%

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

      1. neg-mul-1 49.8%

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

      2. distribute-neg-frac 49.8%

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

   8. Simplified 49.8%

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

   9. Taylor expanded in a around 0 41.0%

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

       1. associate-/l* 46.2%

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

   11. Simplified 46.2%

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

   if 7.8000000000000005e235 < z

   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* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 42.7%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 42.7%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 42.7%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 29.1%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 49.4%

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

      1. associate-*r/ 53.8%

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

   10. Simplified 53.8%

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

   11. Taylor expanded in x around 0 38.4%

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

       1. associate-/l* 52.4%

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

   13. Simplified 52.4%

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

   14. Taylor expanded in z around inf 38.4%

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

       1. associate-*r/ 52.4%

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

       2. neg-mul-1 52.4%

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

       3. distribute-rgt-neg-in 52.4%

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

       4. distribute-neg-frac2 52.4%

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

   16. Simplified 52.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+235}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-40)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 1.6e-41) (+ y (* z (/ (- x y) t))) (+ x (* (- y x) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-40) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.6e-41) {
		tmp = y + (z * ((x - y) / 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 (a <= (-9.5d-40)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 1.6d-41) then
        tmp = y + (z * ((x - y) / 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 (a <= -9.5e-40) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.6e-41) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x + ((y - x) * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-40:
		tmp = x + (y * ((z - t) / a))
	elif a <= 1.6e-41:
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = x + ((y - x) * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-40)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 1.6e-41)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / 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 (a <= -9.5e-40)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 1.6e-41)
		tmp = y + (z * ((x - y) / t));
	else
		tmp = x + ((y - x) * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-40], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-41], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000006e-40

   1. Initial program 70.9%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. associate-/l* 71.2%

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

   5. Simplified 71.2%

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

      1. clear-num 71.2%

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

      2. inv-pow 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. unpow-1 71.2%

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

   9. Simplified 71.2%

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

   10. Taylor expanded in y around inf 63.4%

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

       1. associate-*r/ 69.0%

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

   12. Simplified 69.0%

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

   if -9.5000000000000006e-40 < a < 1.60000000000000006e-41

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-/l* 78.1%

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

      3. fma-define 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in t around inf 59.1%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 59.1%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 59.1%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 53.3%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 71.5%

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

      1. associate-*r/ 74.6%

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

   10. Simplified 74.6%

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

   if 1.60000000000000006e-41 < a

   1. Initial program 65.9%

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

   3. Taylor expanded in a around inf 59.4%

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

      1. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in z around inf 65.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-41}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+53} \lor \neg \left(t \leq 2.5 \cdot 10^{+101}\right):\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+53) (not (<= t 2.5e+101)))
   (- y (* y (/ z t)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+53) || !(t <= 2.5e+101)) {
		tmp = y - (y * (z / t));
	} else {
		tmp = x + (y * (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 <= (-8.5d+53)) .or. (.not. (t <= 2.5d+101))) then
        tmp = y - (y * (z / t))
    else
        tmp = x + (y * (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 <= -8.5e+53) || !(t <= 2.5e+101)) {
		tmp = y - (y * (z / t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+53) or not (t <= 2.5e+101):
		tmp = y - (y * (z / t))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+53) || !(t <= 2.5e+101))
		tmp = Float64(y - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+53) || ~((t <= 2.5e+101)))
		tmp = y - (y * (z / t));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+53], N[Not[LessEqual[t, 2.5e+101]], $MachinePrecision]], N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000002e53 or 2.49999999999999994e101 < t

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 71.4%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around inf 49.3%

      \[\leadsto \color{blue}{\left(y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right)\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 49.3%

         \[\leadsto \color{blue}{y + \left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. sub-neg 49.3%

         \[\leadsto y + \color{blue}{\left(\left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} + \frac{a \cdot \left(-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)\right)}{{t}^{2}}\right) + \left(--1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)\right)} \]

   7. Simplified 43.3%

      \[\leadsto \color{blue}{y + \left(\left(\frac{\left(\left(y - x\right) \cdot \left(z - a\right)\right) \cdot \left(-a\right)}{{t}^{2}} - z \cdot \frac{y - x}{t}\right) + a \cdot \frac{y - x}{t}\right)} \]

   8. Taylor expanded in a around 0 57.6%

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

      1. associate-*r/ 65.5%

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

   10. Simplified 65.5%

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

   11. Taylor expanded in x around 0 45.9%

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

       1. associate-/l* 51.0%

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

   13. Simplified 51.0%

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

   if -8.5000000000000002e53 < t < 2.49999999999999994e101

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 68.2%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

      1. clear-num 71.8%

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

      2. inv-pow 71.8%

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

   7. Applied egg-rr 71.8%

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

      1. unpow-1 71.8%

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

   9. Simplified 71.8%

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

   10. Taylor expanded in y around inf 56.0%

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

       1. associate-*r/ 59.4%

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

   12. Simplified 59.4%

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

   13. Taylor expanded in z around inf 55.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+53} \lor \neg \left(t \leq 2.5 \cdot 10^{+101}\right):\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+54) y (if (<= t 9.5e+102) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+54) {
		tmp = y;
	} else if (t <= 9.5e+102) {
		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 <= (-3.4d+54)) then
        tmp = y
    else if (t <= 9.5d+102) 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 <= -3.4e+54) {
		tmp = y;
	} else if (t <= 9.5e+102) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+54:
		tmp = y
	elif t <= 9.5e+102:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+54)
		tmp = y;
	elseif (t <= 9.5e+102)
		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 <= -3.4e+54)
		tmp = y;
	elseif (t <= 9.5e+102)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+54], y, If[LessEqual[t, 9.5e+102], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e54 or 9.4999999999999992e102 < t

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 71.4%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

      1. add-cube-cbrt 70.3%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 70.3%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 70.3%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 41.5%

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

   if -3.4000000000000001e54 < t < 9.4999999999999992e102

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 68.2%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

      1. clear-num 71.8%

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

      2. inv-pow 71.8%

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

   7. Applied egg-rr 71.8%

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

      1. unpow-1 71.8%

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

   9. Simplified 71.8%

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

   10. Taylor expanded in y around inf 56.0%

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

       1. associate-*r/ 59.4%

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

   12. Simplified 59.4%

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

   13. Taylor expanded in z around inf 55.2%

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

Alternative 23: 36.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e-34) x (if (<= a 2e-41) (* x (/ z t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-34) {
		tmp = x;
	} else if (a <= 2e-41) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.6d-34)) then
        tmp = x
    else if (a <= 2d-41) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e-34) {
		tmp = x;
	} else if (a <= 2e-41) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e-34:
		tmp = x
	elif a <= 2e-41:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e-34)
		tmp = x;
	elseif (a <= 2e-41)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e-34)
		tmp = x;
	elseif (a <= 2e-41)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e-34], x, If[LessEqual[a, 2e-41], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5999999999999999e-34 or 2.00000000000000001e-41 < a

   1. Initial program 68.1%

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

      1. +-commutative 68.1%

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

      2. associate-/l* 87.8%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 41.8%

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

   if -2.5999999999999999e-34 < a < 2.00000000000000001e-41

   1. Initial program 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 78.3%

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

      3. fma-define 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 58.4%

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

   6. Taylor expanded in y around 0 37.7%

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

      1. neg-mul-1 37.7%

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

      2. distribute-neg-frac 37.7%

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

   8. Simplified 37.7%

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

   9. Taylor expanded in a around 0 30.3%

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

       1. associate-/l* 38.6%

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

   11. Simplified 38.6%

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

Alternative 24: 39.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e+53) y (if (<= t 8.5e+102) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e+53) {
		tmp = y;
	} else if (t <= 8.5e+102) {
		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 <= (-7.5d+53)) then
        tmp = y
    else if (t <= 8.5d+102) 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 <= -7.5e+53) {
		tmp = y;
	} else if (t <= 8.5e+102) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e+53:
		tmp = y
	elif t <= 8.5e+102:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e+53)
		tmp = y;
	elseif (t <= 8.5e+102)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.5e+53)
		tmp = y;
	elseif (t <= 8.5e+102)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e+53], y, If[LessEqual[t, 8.5e+102], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4999999999999997e53 or 8.4999999999999996e102 < t

   1. Initial program 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-/l* 71.4%

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

      3. fma-define 71.4%

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

   3. Simplified 71.4%

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

      1. add-cube-cbrt 70.3%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}, x\right) \]

      2. pow3 70.3%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   6. Applied egg-rr 70.3%

      \[\leadsto \mathsf{fma}\left(y - x, \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{3}}}, x\right) \]

   7. Taylor expanded in t around inf 41.5%

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

   if -7.4999999999999997e53 < t < 8.4999999999999996e102

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      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

   5. Taylor expanded in a around inf 35.1%

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

Alternative 25: 26.4% 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 68.3%

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

   1. +-commutative 68.3%

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

   2. associate-/l* 83.5%

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

   3. fma-define 83.5%

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

3. Simplified 83.5%

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

5. Taylor expanded in a around inf 26.1%

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

Developer Target 1: 86.7% 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 2024180 
(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))))