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

Percentage Accurate: 67.3% → 90.2%

Time: 17.1s

Alternatives: 21

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-16} \lor \neg \left(x \leq 28\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(y \cdot \frac{\frac{t - z}{x}}{t - a} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8.2e-16) (not (<= x 28.0)))
   (*
    x
    (+
     (- 1.0 (/ t (- t a)))
     (+ (* y (/ (/ (- t z) x) (- t a))) (/ z (- t a)))))
   (fma (- y x) (/ (- t z) (- t a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e-16) || !(x <= 28.0)) {
		tmp = x * ((1.0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))));
	} else {
		tmp = fma((y - x), ((t - z) / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8.2e-16) || !(x <= 28.0))
		tmp = Float64(x * Float64(Float64(1.0 - Float64(t / Float64(t - a))) + Float64(Float64(y * Float64(Float64(Float64(t - z) / x) / Float64(t - a))) + Float64(z / Float64(t - a)))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(t - z) / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8.2e-16], N[Not[LessEqual[x, 28.0]], $MachinePrecision]], N[(x * N[(N[(1.0 - N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000012e-16 or 28 < x

   1. Initial program 62.2%

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

      1. +-commutative 62.2%

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

      2. associate-/l* 77.9%

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

      3. fma-define 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in x around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. distribute-rgt-neg-in 76.4%

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

      3. +-commutative 76.4%

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

      4. mul-1-neg 76.4%

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

      5. unsub-neg 76.4%

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

      6. associate-/r* 80.4%

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

      7. associate-/l* 89.8%

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

      8. *-lft-identity 89.8%

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

      9. times-frac 93.3%

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

      10. /-rgt-identity 93.3%

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

      11. +-commutative 93.3%

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

   7. Simplified 93.3%

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

   if -8.20000000000000012e-16 < x < 28

   1. Initial program 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-16} \lor \neg \left(x \leq 28\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(y \cdot \frac{\frac{t - z}{x}}{t - a} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{t - z}{t - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-74} \lor \neg \left(x \leq 1.15 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(y \cdot \frac{\frac{t - z}{x}}{t - a} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2e-74) (not (<= x 1.15e-35)))
   (*
    x
    (+
     (- 1.0 (/ t (- t a)))
     (+ (* y (/ (/ (- t z) x) (- t a))) (/ z (- t a)))))
   (+ x (/ (* (- z t) (- y x)) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e-74) || !(x <= 1.15e-35)) {
		tmp = x * ((1.0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))));
	} else {
		tmp = x + (((z - t) * (y - x)) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2d-74)) .or. (.not. (x <= 1.15d-35))) then
        tmp = x * ((1.0d0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))))
    else
        tmp = x + (((z - t) * (y - x)) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2e-74) || !(x <= 1.15e-35)) {
		tmp = x * ((1.0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))));
	} else {
		tmp = x + (((z - t) * (y - x)) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2e-74) or not (x <= 1.15e-35):
		tmp = x * ((1.0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))))
	else:
		tmp = x + (((z - t) * (y - x)) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2e-74) || !(x <= 1.15e-35))
		tmp = Float64(x * Float64(Float64(1.0 - Float64(t / Float64(t - a))) + Float64(Float64(y * Float64(Float64(Float64(t - z) / x) / Float64(t - a))) + Float64(z / Float64(t - a)))));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2e-74) || ~((x <= 1.15e-35)))
		tmp = x * ((1.0 - (t / (t - a))) + ((y * (((t - z) / x) / (t - a))) + (z / (t - a))));
	else
		tmp = x + (((z - t) * (y - x)) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2e-74], N[Not[LessEqual[x, 1.15e-35]], $MachinePrecision]], N[(x * N[(N[(1.0 - N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999992e-74 or 1.1499999999999999e-35 < x

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 80.7%

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

      3. fma-define 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around -inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. +-commutative 74.9%

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

      4. mul-1-neg 74.9%

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

      5. unsub-neg 74.9%

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

      6. associate-/r* 78.4%

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

      7. associate-/l* 86.6%

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

      8. *-lft-identity 86.6%

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

      9. times-frac 92.2%

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

      10. /-rgt-identity 92.2%

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

      11. +-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -1.99999999999999992e-74 < x < 1.1499999999999999e-35

   1. Initial program 86.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-74} \lor \neg \left(x \leq 1.15 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \left(\left(1 - \frac{t}{t - a}\right) + \left(y \cdot \frac{\frac{t - z}{x}}{t - a} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))))
   (if (<= a -3.1e+24)
     (+ x (* z (/ (- y x) a)))
     (if (<= a -7.5e-145)
       t_1
       (if (<= a 2.2e-253)
         (* y (- 1.0 (/ z t)))
         (if (<= a 1.72e+75) t_1 (+ x (/ (* y (- z t)) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -3.1e+24) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= -7.5e-145) {
		tmp = t_1;
	} else if (a <= 2.2e-253) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 1.72e+75) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    if (a <= (-3.1d+24)) then
        tmp = x + (z * ((y - x) / a))
    else if (a <= (-7.5d-145)) then
        tmp = t_1
    else if (a <= 2.2d-253) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= 1.72d+75) then
        tmp = t_1
    else
        tmp = x + ((y * (z - t)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double tmp;
	if (a <= -3.1e+24) {
		tmp = x + (z * ((y - x) / a));
	} else if (a <= -7.5e-145) {
		tmp = t_1;
	} else if (a <= 2.2e-253) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 1.72e+75) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	tmp = 0
	if a <= -3.1e+24:
		tmp = x + (z * ((y - x) / a))
	elif a <= -7.5e-145:
		tmp = t_1
	elif a <= 2.2e-253:
		tmp = y * (1.0 - (z / t))
	elif a <= 1.72e+75:
		tmp = t_1
	else:
		tmp = x + ((y * (z - t)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	tmp = 0.0
	if (a <= -3.1e+24)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (a <= -7.5e-145)
		tmp = t_1;
	elseif (a <= 2.2e-253)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= 1.72e+75)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	tmp = 0.0;
	if (a <= -3.1e+24)
		tmp = x + (z * ((y - x) / a));
	elseif (a <= -7.5e-145)
		tmp = t_1;
	elseif (a <= 2.2e-253)
		tmp = y * (1.0 - (z / t));
	elseif (a <= 1.72e+75)
		tmp = t_1;
	else
		tmp = x + ((y * (z - t)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+24], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-145], t$95$1, If[LessEqual[a, 2.2e-253], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.72e+75], t$95$1, N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.10000000000000011e24

   1. Initial program 72.7%

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

   3. Taylor expanded in t around 0 70.4%

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

      1. associate-/l* 76.8%

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

   5. Simplified 76.8%

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

   if -3.10000000000000011e24 < a < -7.4999999999999996e-145 or 2.19999999999999996e-253 < a < 1.72e75

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. associate-/l* 82.6%

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

      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 y around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. div-sub 76.7%

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

      3. mul-1-neg 76.7%

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

      4. associate-/l* 77.2%

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

      5. distribute-lft-neg-in 77.2%

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

      6. distribute-rgt-in 82.6%

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

      7. sub-neg 82.6%

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

      8. associate-*l/ 76.2%

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

      9. associate-*r/ 76.3%

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

      10. +-commutative 76.3%

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

      11. fma-define 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around inf 62.9%

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

      1. div-sub 62.9%

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

   10. Simplified 62.9%

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

   if -7.4999999999999996e-145 < a < 2.19999999999999996e-253

   1. Initial program 59.6%

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

      1. +-commutative 59.6%

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

      2. associate-/l* 78.2%

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

      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 y around inf 71.0%

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

   6. Taylor expanded in a around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

   if 1.72e75 < a

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. *-lft-identity 85.6%

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

      3. times-frac 83.4%

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

      4. /-rgt-identity 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in a around inf 80.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+24}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= a -5.1e+28)
     t_2
     (if (<= a -7.2e-145)
       t_1
       (if (<= a 1.95e-254)
         (* y (- 1.0 (/ z t)))
         (if (<= a 7.2e+73) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -5.1e+28) {
		tmp = t_2;
	} else if (a <= -7.2e-145) {
		tmp = t_1;
	} else if (a <= 1.95e-254) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 7.2e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    t_2 = x + (z * ((y - x) / a))
    if (a <= (-5.1d+28)) then
        tmp = t_2
    else if (a <= (-7.2d-145)) then
        tmp = t_1
    else if (a <= 1.95d-254) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= 7.2d+73) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (a <= -5.1e+28) {
		tmp = t_2;
	} else if (a <= -7.2e-145) {
		tmp = t_1;
	} else if (a <= 1.95e-254) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 7.2e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if a <= -5.1e+28:
		tmp = t_2
	elif a <= -7.2e-145:
		tmp = t_1
	elif a <= 1.95e-254:
		tmp = y * (1.0 - (z / t))
	elif a <= 7.2e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (a <= -5.1e+28)
		tmp = t_2;
	elseif (a <= -7.2e-145)
		tmp = t_1;
	elseif (a <= 1.95e-254)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= 7.2e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (a <= -5.1e+28)
		tmp = t_2;
	elseif (a <= -7.2e-145)
		tmp = t_1;
	elseif (a <= 1.95e-254)
		tmp = y * (1.0 - (z / t));
	elseif (a <= 7.2e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+28], t$95$2, If[LessEqual[a, -7.2e-145], t$95$1, If[LessEqual[a, 1.95e-254], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+73], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.1000000000000004e28 or 7.1999999999999998e73 < a

   1. Initial program 75.4%

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

   3. Taylor expanded in t around 0 69.1%

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

      1. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   if -5.1000000000000004e28 < a < -7.2000000000000001e-145 or 1.95e-254 < a < 7.1999999999999998e73

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 82.5%

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

      3. fma-define 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. div-sub 76.5%

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

      3. mul-1-neg 76.5%

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

      4. associate-/l* 77.0%

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

      5. distribute-lft-neg-in 77.0%

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

      6. distribute-rgt-in 82.5%

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

      7. sub-neg 82.5%

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

      8. associate-*l/ 76.8%

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

      9. associate-*r/ 76.1%

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

      10. +-commutative 76.1%

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

      11. fma-define 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   10. Simplified 63.5%

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

   if -7.2000000000000001e-145 < a < 1.95e-254

   1. Initial program 59.6%

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

      1. +-commutative 59.6%

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

      2. associate-/l* 78.2%

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

      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 y around inf 71.0%

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

   6. Taylor expanded in a around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t - a}\\ t_2 := x + \frac{z \cdot y}{a}\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) (- t a)))) (t_2 (+ x (/ (* z y) a))))
   (if (<= a -9.2e+29)
     t_2
     (if (<= a -7.2e-145)
       t_1
       (if (<= a 1.65e-254)
         (* y (- 1.0 (/ z t)))
         (if (<= a 9e+73) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double t_2 = x + ((z * y) / a);
	double tmp;
	if (a <= -9.2e+29) {
		tmp = t_2;
	} else if (a <= -7.2e-145) {
		tmp = t_1;
	} else if (a <= 1.65e-254) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x - y) / (t - a))
    t_2 = x + ((z * y) / a)
    if (a <= (-9.2d+29)) then
        tmp = t_2
    else if (a <= (-7.2d-145)) then
        tmp = t_1
    else if (a <= 1.65d-254) then
        tmp = y * (1.0d0 - (z / t))
    else if (a <= 9d+73) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / (t - a));
	double t_2 = x + ((z * y) / a);
	double tmp;
	if (a <= -9.2e+29) {
		tmp = t_2;
	} else if (a <= -7.2e-145) {
		tmp = t_1;
	} else if (a <= 1.65e-254) {
		tmp = y * (1.0 - (z / t));
	} else if (a <= 9e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / (t - a))
	t_2 = x + ((z * y) / a)
	tmp = 0
	if a <= -9.2e+29:
		tmp = t_2
	elif a <= -7.2e-145:
		tmp = t_1
	elif a <= 1.65e-254:
		tmp = y * (1.0 - (z / t))
	elif a <= 9e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / Float64(t - a)))
	t_2 = Float64(x + Float64(Float64(z * y) / a))
	tmp = 0.0
	if (a <= -9.2e+29)
		tmp = t_2;
	elseif (a <= -7.2e-145)
		tmp = t_1;
	elseif (a <= 1.65e-254)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (a <= 9e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / (t - a));
	t_2 = x + ((z * y) / a);
	tmp = 0.0;
	if (a <= -9.2e+29)
		tmp = t_2;
	elseif (a <= -7.2e-145)
		tmp = t_1;
	elseif (a <= 1.65e-254)
		tmp = y * (1.0 - (z / t));
	elseif (a <= 9e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+29], t$95$2, If[LessEqual[a, -7.2e-145], t$95$1, If[LessEqual[a, 1.65e-254], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+73], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.2000000000000004e29 or 8.99999999999999969e73 < a

   1. Initial program 75.4%

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

   3. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. *-lft-identity 78.9%

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

      3. times-frac 86.3%

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

      4. /-rgt-identity 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in t around 0 67.6%

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

   if -9.2000000000000004e29 < a < -7.2000000000000001e-145 or 1.65000000000000008e-254 < a < 8.99999999999999969e73

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-/l* 82.5%

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

      3. fma-define 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. div-sub 76.5%

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

      3. mul-1-neg 76.5%

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

      4. associate-/l* 77.0%

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

      5. distribute-lft-neg-in 77.0%

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

      6. distribute-rgt-in 82.5%

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

      7. sub-neg 82.5%

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

      8. associate-*l/ 76.8%

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

      9. associate-*r/ 76.1%

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

      10. +-commutative 76.1%

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

      11. fma-define 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in z around inf 63.5%

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

      1. div-sub 63.5%

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

   10. Simplified 63.5%

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

   if -7.2000000000000001e-145 < a < 1.65000000000000008e-254

   1. Initial program 59.6%

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

      1. +-commutative 59.6%

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

      2. associate-/l* 78.2%

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

      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 y around inf 71.0%

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

   6. Taylor expanded in a around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \frac{x - y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (- z a) (/ (- y x) t)))))
   (if (<= t -9.5e+34)
     t_1
     (if (<= t 5.5e+41)
       (+ x (/ (* (- z t) (- y x)) (- a t)))
       (if (<= t 9.5e+212) (+ x (* (- t z) (/ y (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((z - a) * ((y - x) / t));
	double tmp;
	if (t <= -9.5e+34) {
		tmp = t_1;
	} else if (t <= 5.5e+41) {
		tmp = x + (((z - t) * (y - x)) / (a - t));
	} else if (t <= 9.5e+212) {
		tmp = x + ((t - z) * (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 - a) * ((y - x) / t))
    if (t <= (-9.5d+34)) then
        tmp = t_1
    else if (t <= 5.5d+41) then
        tmp = x + (((z - t) * (y - x)) / (a - t))
    else if (t <= 9.5d+212) then
        tmp = x + ((t - z) * (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 - a) * ((y - x) / t));
	double tmp;
	if (t <= -9.5e+34) {
		tmp = t_1;
	} else if (t <= 5.5e+41) {
		tmp = x + (((z - t) * (y - x)) / (a - t));
	} else if (t <= 9.5e+212) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((z - a) * ((y - x) / t))
	tmp = 0
	if t <= -9.5e+34:
		tmp = t_1
	elif t <= 5.5e+41:
		tmp = x + (((z - t) * (y - x)) / (a - t))
	elif t <= 9.5e+212:
		tmp = x + ((t - z) * (y / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(z - a) * Float64(Float64(y - x) / t)))
	tmp = 0.0
	if (t <= -9.5e+34)
		tmp = t_1;
	elseif (t <= 5.5e+41)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 9.5e+212)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((z - a) * ((y - x) / t));
	tmp = 0.0;
	if (t <= -9.5e+34)
		tmp = t_1;
	elseif (t <= 5.5e+41)
		tmp = x + (((z - t) * (y - x)) / (a - t));
	elseif (t <= 9.5e+212)
		tmp = x + ((t - z) * (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[(N[(z - a), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+34], t$95$1, If[LessEqual[t, 5.5e+41], N[(x + N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+212], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999999e34 or 9.4999999999999993e212 < t

   1. Initial program 40.7%

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

      1. +-commutative 40.7%

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

      2. associate-/l* 66.2%

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

      3. fma-define 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-*r/ 65.3%

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

      3. associate-*r/ 65.3%

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

      4. mul-1-neg 65.3%

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

      5. div-sub 65.3%

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

      6. mul-1-neg 65.3%

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

      7. distribute-lft-out-- 65.3%

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

      8. associate-*r/ 65.3%

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

      9. mul-1-neg 65.3%

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

      10. unsub-neg 65.3%

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

      11. distribute-rgt-out-- 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-*r/ 82.0%

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

      3. *-commutative 82.0%

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

      4. distribute-lft-neg-in 82.0%

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

      5. cancel-sign-sub-inv 82.0%

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

      6. associate-*l/ 65.3%

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

      7. associate-*r/ 82.9%

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

   10. Simplified 82.9%

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

   if -9.4999999999999999e34 < t < 5.5000000000000003e41

   1. Initial program 94.0%

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

   if 5.5000000000000003e41 < t < 9.4999999999999993e212

   1. Initial program 50.6%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-lft-identity 69.7%

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

      3. times-frac 88.3%

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

      4. /-rgt-identity 88.3%

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

   5. Simplified 88.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+205}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (- z a) (/ (- y x) t)))))
   (if (<= t -5.8e-35)
     t_1
     (if (<= t 1.15e-25)
       (+ x (/ (* z (- y x)) (- a t)))
       (if (<= t 1.2e+205) (+ x (* (- t z) (/ y (- t a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - ((z - a) * ((y - x) / t));
	double tmp;
	if (t <= -5.8e-35) {
		tmp = t_1;
	} else if (t <= 1.15e-25) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 1.2e+205) {
		tmp = x + ((t - z) * (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 - a) * ((y - x) / t))
    if (t <= (-5.8d-35)) then
        tmp = t_1
    else if (t <= 1.15d-25) then
        tmp = x + ((z * (y - x)) / (a - t))
    else if (t <= 1.2d+205) then
        tmp = x + ((t - z) * (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 - a) * ((y - x) / t));
	double tmp;
	if (t <= -5.8e-35) {
		tmp = t_1;
	} else if (t <= 1.15e-25) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 1.2e+205) {
		tmp = x + ((t - z) * (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - ((z - a) * ((y - x) / t))
	tmp = 0
	if t <= -5.8e-35:
		tmp = t_1
	elif t <= 1.15e-25:
		tmp = x + ((z * (y - x)) / (a - t))
	elif t <= 1.2e+205:
		tmp = x + ((t - z) * (y / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(z - a) * Float64(Float64(y - x) / t)))
	tmp = 0.0
	if (t <= -5.8e-35)
		tmp = t_1;
	elseif (t <= 1.15e-25)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 1.2e+205)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - ((z - a) * ((y - x) / t));
	tmp = 0.0;
	if (t <= -5.8e-35)
		tmp = t_1;
	elseif (t <= 1.15e-25)
		tmp = x + ((z * (y - x)) / (a - t));
	elseif (t <= 1.2e+205)
		tmp = x + ((t - z) * (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[(N[(z - a), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e-35], t$95$1, If[LessEqual[t, 1.15e-25], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+205], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8000000000000004e-35 or 1.19999999999999993e205 < t

   1. Initial program 46.0%

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

      1. +-commutative 46.0%

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

      2. associate-/l* 69.4%

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

      3. fma-define 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-*r/ 65.3%

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

      3. associate-*r/ 65.3%

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

      4. mul-1-neg 65.3%

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

      5. div-sub 65.3%

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

      6. mul-1-neg 65.3%

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

      7. distribute-lft-out-- 65.3%

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

      8. associate-*r/ 65.3%

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

      9. mul-1-neg 65.3%

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

      10. unsub-neg 65.3%

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

      11. distribute-rgt-out-- 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-*r/ 79.9%

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

      3. *-commutative 79.9%

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

      4. distribute-lft-neg-in 79.9%

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

      5. cancel-sign-sub-inv 79.9%

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

      6. associate-*l/ 65.3%

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

      7. associate-*r/ 80.7%

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

   10. Simplified 80.7%

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

   if -5.8000000000000004e-35 < t < 1.15e-25

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 90.6%

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

   if 1.15e-25 < t < 1.19999999999999993e205

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. *-lft-identity 72.2%

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

      3. times-frac 83.6%

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

      4. /-rgt-identity 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-35}:\\ \;\;\;\;y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+205}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - a\right) \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -3.3e-34)
     t_1
     (if (<= t 4.6e-26)
       (+ x (/ (* z (- y x)) (- a t)))
       (if (<= t 1.25e+212) (+ x (* (- t z) (/ y (- t a)))) 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 <= -3.3e-34) {
		tmp = t_1;
	} else if (t <= 4.6e-26) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 1.25e+212) {
		tmp = x + ((t - z) * (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 - y) / t))
    if (t <= (-3.3d-34)) then
        tmp = t_1
    else if (t <= 4.6d-26) then
        tmp = x + ((z * (y - x)) / (a - t))
    else if (t <= 1.25d+212) then
        tmp = x + ((t - z) * (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 - y) / t));
	double tmp;
	if (t <= -3.3e-34) {
		tmp = t_1;
	} else if (t <= 4.6e-26) {
		tmp = x + ((z * (y - x)) / (a - t));
	} else if (t <= 1.25e+212) {
		tmp = x + ((t - z) * (y / (t - a)));
	} 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 <= -3.3e-34:
		tmp = t_1
	elif t <= 4.6e-26:
		tmp = x + ((z * (y - x)) / (a - t))
	elif t <= 1.25e+212:
		tmp = x + ((t - z) * (y / (t - a)))
	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 <= -3.3e-34)
		tmp = t_1;
	elseif (t <= 4.6e-26)
		tmp = Float64(x + Float64(Float64(z * Float64(y - x)) / Float64(a - t)));
	elseif (t <= 1.25e+212)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -3.3e-34)
		tmp = t_1;
	elseif (t <= 4.6e-26)
		tmp = x + ((z * (y - x)) / (a - t));
	elseif (t <= 1.25e+212)
		tmp = x + ((t - z) * (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[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-34], t$95$1, If[LessEqual[t, 4.6e-26], N[(x + N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+212], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.29999999999999983e-34 or 1.24999999999999998e212 < t

   1. Initial program 46.0%

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

      1. +-commutative 46.0%

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

      2. associate-/l* 69.4%

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

      3. fma-define 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-*r/ 65.3%

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

      3. associate-*r/ 65.3%

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

      4. mul-1-neg 65.3%

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

      5. div-sub 65.3%

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

      6. mul-1-neg 65.3%

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

      7. distribute-lft-out-- 65.3%

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

      8. associate-*r/ 65.3%

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

      9. mul-1-neg 65.3%

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

      10. unsub-neg 65.3%

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

      11. distribute-rgt-out-- 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in z around inf 64.4%

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

      1. associate-/l* 76.7%

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

   10. Simplified 76.7%

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

   if -3.29999999999999983e-34 < t < 4.60000000000000018e-26

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 90.6%

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

   if 4.60000000000000018e-26 < t < 1.24999999999999998e212

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. *-lft-identity 72.2%

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

      3. times-frac 83.6%

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

      4. /-rgt-identity 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-34}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+205}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -3.8e-34)
     t_1
     (if (<= t 5.5e-25)
       (+ x (* z (/ (- x y) (- t a))))
       (if (<= t 1.16e+205) (+ x (* (- t z) (/ y (- t a)))) 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 <= -3.8e-34) {
		tmp = t_1;
	} else if (t <= 5.5e-25) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else if (t <= 1.16e+205) {
		tmp = x + ((t - z) * (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 - y) / t))
    if (t <= (-3.8d-34)) then
        tmp = t_1
    else if (t <= 5.5d-25) then
        tmp = x + (z * ((x - y) / (t - a)))
    else if (t <= 1.16d+205) then
        tmp = x + ((t - z) * (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 - y) / t));
	double tmp;
	if (t <= -3.8e-34) {
		tmp = t_1;
	} else if (t <= 5.5e-25) {
		tmp = x + (z * ((x - y) / (t - a)));
	} else if (t <= 1.16e+205) {
		tmp = x + ((t - z) * (y / (t - a)));
	} 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 <= -3.8e-34:
		tmp = t_1
	elif t <= 5.5e-25:
		tmp = x + (z * ((x - y) / (t - a)))
	elif t <= 1.16e+205:
		tmp = x + ((t - z) * (y / (t - a)))
	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 <= -3.8e-34)
		tmp = t_1;
	elseif (t <= 5.5e-25)
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	elseif (t <= 1.16e+205)
		tmp = Float64(x + Float64(Float64(t - z) * Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -3.8e-34)
		tmp = t_1;
	elseif (t <= 5.5e-25)
		tmp = x + (z * ((x - y) / (t - a)));
	elseif (t <= 1.16e+205)
		tmp = x + ((t - z) * (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[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e-34], t$95$1, If[LessEqual[t, 5.5e-25], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+205], N[(x + N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000001e-34 or 1.16000000000000001e205 < t

   1. Initial program 46.0%

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

      1. +-commutative 46.0%

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

      2. associate-/l* 69.4%

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

      3. fma-define 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-*r/ 65.3%

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

      3. associate-*r/ 65.3%

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

      4. mul-1-neg 65.3%

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

      5. div-sub 65.3%

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

      6. mul-1-neg 65.3%

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

      7. distribute-lft-out-- 65.3%

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

      8. associate-*r/ 65.3%

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

      9. mul-1-neg 65.3%

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

      10. unsub-neg 65.3%

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

      11. distribute-rgt-out-- 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in z around inf 64.4%

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

      1. associate-/l* 76.7%

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

   10. Simplified 76.7%

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

   if -3.8000000000000001e-34 < t < 5.50000000000000004e-25

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   if 5.50000000000000004e-25 < t < 1.16000000000000001e205

   1. Initial program 66.1%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. *-lft-identity 72.2%

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

      3. times-frac 83.6%

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

      4. /-rgt-identity 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-34}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+205}:\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.18e+113)
   (* y (/ t (- t a)))
   (if (<= t -5.5e+53)
     (/ (* z (- x y)) t)
     (if (<= t 1.1e+23) (+ x (/ (* z y) a)) (* y (- 1.0 (/ z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.18e+113) {
		tmp = y * (t / (t - a));
	} else if (t <= -5.5e+53) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 1.1e+23) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.18d+113)) then
        tmp = y * (t / (t - a))
    else if (t <= (-5.5d+53)) then
        tmp = (z * (x - y)) / t
    else if (t <= 1.1d+23) then
        tmp = x + ((z * y) / a)
    else
        tmp = y * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.18e+113) {
		tmp = y * (t / (t - a));
	} else if (t <= -5.5e+53) {
		tmp = (z * (x - y)) / t;
	} else if (t <= 1.1e+23) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.18e+113:
		tmp = y * (t / (t - a))
	elif t <= -5.5e+53:
		tmp = (z * (x - y)) / t
	elif t <= 1.1e+23:
		tmp = x + ((z * y) / a)
	else:
		tmp = y * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.18e+113)
		tmp = Float64(y * Float64(t / Float64(t - a)));
	elseif (t <= -5.5e+53)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	elseif (t <= 1.1e+23)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.18e+113)
		tmp = y * (t / (t - a));
	elseif (t <= -5.5e+53)
		tmp = (z * (x - y)) / t;
	elseif (t <= 1.1e+23)
		tmp = x + ((z * y) / a);
	else
		tmp = y * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.18e+113], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e+53], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.1e+23], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.18000000000000008e113

   1. Initial program 44.5%

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

      1. +-commutative 44.5%

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

      2. associate-/l* 73.1%

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

      3. fma-define 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around inf 70.9%

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

   6. Taylor expanded in z around 0 68.7%

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

      1. neg-mul-1 68.7%

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

      2. distribute-neg-frac 68.7%

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

   8. Simplified 68.7%

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

   if -1.18000000000000008e113 < t < -5.49999999999999975e53

   1. Initial program 46.7%

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

      1. +-commutative 46.7%

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

      2. associate-/l* 55.7%

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

      3. fma-define 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in y around 0 55.3%

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

      1. +-commutative 55.3%

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

      2. div-sub 55.3%

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

      3. mul-1-neg 55.3%

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

      4. associate-/l* 55.7%

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

      5. distribute-lft-neg-in 55.7%

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

      6. distribute-rgt-in 55.7%

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

      7. sub-neg 55.7%

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

      8. associate-*l/ 46.7%

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

      9. associate-*r/ 55.5%

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

      10. +-commutative 55.5%

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

      11. fma-define 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in z around -inf 73.2%

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

   9. Taylor expanded in a around 0 73.0%

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

       1. associate-*r/ 73.0%

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

       2. associate-*r* 73.0%

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

       3. *-commutative 73.0%

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

       4. neg-mul-1 73.0%

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

   11. Simplified 73.0%

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

   if -5.49999999999999975e53 < t < 1.10000000000000004e23

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. *-lft-identity 71.7%

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

      3. times-frac 71.0%

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

      4. /-rgt-identity 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0 58.9%

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

   if 1.10000000000000004e23 < t

   1. Initial program 50.1%

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

      1. +-commutative 50.1%

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

      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 y around inf 58.4%

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

   6. Taylor expanded in a around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t} \cdot y\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z (- a t)) y)))
   (if (<= z -3.15e-6)
     t_1
     (if (<= z 7e+101) (+ x y) (if (<= z 4.6e+183) t_1 (* x (/ (- z a) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / (a - t)) * y;
	double tmp;
	if (z <= -3.15e-6) {
		tmp = t_1;
	} else if (z <= 7e+101) {
		tmp = x + y;
	} else if (z <= 4.6e+183) {
		tmp = t_1;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / (a - t)) * y
    if (z <= (-3.15d-6)) then
        tmp = t_1
    else if (z <= 7d+101) then
        tmp = x + y
    else if (z <= 4.6d+183) then
        tmp = t_1
    else
        tmp = x * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / (a - t)) * y;
	double tmp;
	if (z <= -3.15e-6) {
		tmp = t_1;
	} else if (z <= 7e+101) {
		tmp = x + y;
	} else if (z <= 4.6e+183) {
		tmp = t_1;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / (a - t)) * y
	tmp = 0
	if z <= -3.15e-6:
		tmp = t_1
	elif z <= 7e+101:
		tmp = x + y
	elif z <= 4.6e+183:
		tmp = t_1
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / Float64(a - t)) * y)
	tmp = 0.0
	if (z <= -3.15e-6)
		tmp = t_1;
	elseif (z <= 7e+101)
		tmp = Float64(x + y);
	elseif (z <= 4.6e+183)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / (a - t)) * y;
	tmp = 0.0;
	if (z <= -3.15e-6)
		tmp = t_1;
	elseif (z <= 7e+101)
		tmp = x + y;
	elseif (z <= 4.6e+183)
		tmp = t_1;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -3.15e-6], t$95$1, If[LessEqual[z, 7e+101], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.6e+183], t$95$1, N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.14999999999999991e-6 or 7.00000000000000046e101 < z < 4.5999999999999996e183

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      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 y around inf 61.2%

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

   6. Taylor expanded in z around inf 48.8%

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

   if -3.14999999999999991e-6 < z < 7.00000000000000046e101

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. *-lft-identity 67.6%

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

      3. times-frac 68.8%

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

      4. /-rgt-identity 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around inf 50.0%

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

   if 4.5999999999999996e183 < z

   1. Initial program 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 93.2%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around inf 39.2%

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

      1. associate--l+ 39.2%

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

      2. associate-*r/ 39.2%

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

      3. associate-*r/ 39.2%

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

      4. mul-1-neg 39.2%

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

      5. div-sub 45.4%

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

      6. mul-1-neg 45.4%

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

      7. distribute-lft-out-- 45.4%

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

      8. associate-*r/ 45.4%

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

      9. mul-1-neg 45.4%

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

      10. unsub-neg 45.4%

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

      11. distribute-rgt-out-- 45.4%

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

   7. Simplified 45.4%

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

   8. Taylor expanded in y around 0 52.3%

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

      1. associate-/l* 63.7%

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

   10. Simplified 63.7%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-34} \lor \neg \left(t \leq 10^{+119}\right):\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e-34) (not (<= t 1e+119)))
   (+ y (* z (/ (- x y) t)))
   (+ x (* z (/ (- x y) (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e-34) || !(t <= 1e+119)) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x + (z * ((x - y) / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.6d-34)) .or. (.not. (t <= 1d+119))) then
        tmp = y + (z * ((x - y) / t))
    else
        tmp = x + (z * ((x - y) / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e-34) || !(t <= 1e+119)) {
		tmp = y + (z * ((x - y) / t));
	} else {
		tmp = x + (z * ((x - y) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e-34) or not (t <= 1e+119):
		tmp = y + (z * ((x - y) / t))
	else:
		tmp = x + (z * ((x - y) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e-34) || !(t <= 1e+119))
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(x - y) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e-34) || ~((t <= 1e+119)))
		tmp = y + (z * ((x - y) / t));
	else
		tmp = x + (z * ((x - y) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e-34], N[Not[LessEqual[t, 1e+119]], $MachinePrecision]], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(x - y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999999e-34 or 9.99999999999999944e118 < t

   1. Initial program 44.7%

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

      1. +-commutative 44.7%

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

      2. associate-/l* 71.1%

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

      3. fma-define 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in t around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-*r/ 64.7%

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

      3. associate-*r/ 64.7%

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

      4. mul-1-neg 64.7%

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

      5. div-sub 64.7%

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

      6. mul-1-neg 64.7%

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

      7. distribute-lft-out-- 64.7%

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

      8. associate-*r/ 64.7%

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

      9. mul-1-neg 64.7%

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

      10. unsub-neg 64.7%

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

      11. distribute-rgt-out-- 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in z around inf 63.9%

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

      1. associate-/l* 75.7%

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

   10. Simplified 75.7%

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

   if -2.5999999999999999e-34 < t < 9.99999999999999944e118

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-34} \lor \neg \left(t \leq 10^{+119}\right):\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{x - y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+22} \lor \neg \left(a \leq 1.65 \cdot 10^{-96}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e+22) (not (<= a 1.65e-96)))
   (+ x (* z (/ (- y x) a)))
   (+ y (* z (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e+22) || !(a <= 1.65e-96)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.35d+22)) .or. (.not. (a <= 1.65d-96))) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = y + (z * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e+22) || !(a <= 1.65e-96)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e+22) or not (a <= 1.65e-96):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e+22) || !(a <= 1.65e-96))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.35e+22) || ~((a <= 1.65e-96)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e+22], N[Not[LessEqual[a, 1.65e-96]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3500000000000001e22 or 1.64999999999999995e-96 < a

   1. Initial program 76.3%

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

   3. Taylor expanded in t around 0 65.3%

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

      1. associate-/l* 71.0%

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

   5. Simplified 71.0%

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

   if -1.3500000000000001e22 < a < 1.64999999999999995e-96

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 78.0%

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

      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 75.2%

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

      1. associate--l+ 75.2%

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

      2. associate-*r/ 75.2%

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

      3. associate-*r/ 75.2%

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

      4. mul-1-neg 75.2%

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

      5. div-sub 76.1%

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

      6. mul-1-neg 76.1%

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

      7. distribute-lft-out-- 76.1%

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

      8. associate-*r/ 76.1%

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

      9. mul-1-neg 76.1%

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

      10. unsub-neg 76.1%

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

      11. distribute-rgt-out-- 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+22} \lor \neg \left(a \leq 1.65 \cdot 10^{-96}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+173}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e+110) x (if (<= a 1.05e-38) y (if (<= a 1.6e+173) (+ x y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+110) {
		tmp = x;
	} else if (a <= 1.05e-38) {
		tmp = y;
	} else if (a <= 1.6e+173) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.1d+110)) then
        tmp = x
    else if (a <= 1.05d-38) then
        tmp = y
    else if (a <= 1.6d+173) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e+110) {
		tmp = x;
	} else if (a <= 1.05e-38) {
		tmp = y;
	} else if (a <= 1.6e+173) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e+110:
		tmp = x
	elif a <= 1.05e-38:
		tmp = y
	elif a <= 1.6e+173:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e+110)
		tmp = x;
	elseif (a <= 1.05e-38)
		tmp = y;
	elseif (a <= 1.6e+173)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e+110)
		tmp = x;
	elseif (a <= 1.05e-38)
		tmp = y;
	elseif (a <= 1.6e+173)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e+110], x, If[LessEqual[a, 1.05e-38], y, If[LessEqual[a, 1.6e+173], N[(x + y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.10000000000000017e110 or 1.6000000000000001e173 < a

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in a around inf 59.9%

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

   if -3.10000000000000017e110 < a < 1.05000000000000006e-38

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. associate-/l* 81.0%

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

      3. fma-define 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. div-sub 71.6%

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

      3. mul-1-neg 71.6%

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

      4. associate-/l* 75.3%

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

      5. distribute-lft-neg-in 75.3%

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

      6. distribute-rgt-in 81.0%

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

      7. sub-neg 81.0%

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

      8. associate-*l/ 70.1%

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

      9. associate-*r/ 74.2%

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

      10. +-commutative 74.2%

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

      11. fma-define 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in t around inf 33.8%

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

   if 1.05000000000000006e-38 < a < 1.6000000000000001e173

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. *-lft-identity 67.3%

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

      3. times-frac 78.1%

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

      4. /-rgt-identity 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around inf 44.2%

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

Alternative 15: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-76} \lor \neg \left(t \leq 1.02 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e-76) (not (<= t 1.02e+24)))
   (* y (- 1.0 (/ z t)))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-76) || !(t <= 1.02e+24)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.2d-76)) .or. (.not. (t <= 1.02d+24))) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x + ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-76) || !(t <= 1.02e+24)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e-76) or not (t <= 1.02e+24):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e-76) || !(t <= 1.02e+24))
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e-76) || ~((t <= 1.02e+24)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e-76], N[Not[LessEqual[t, 1.02e+24]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999999e-76 or 1.02000000000000004e24 < t

   1. Initial program 53.1%

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

      1. +-commutative 53.1%

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

      2. associate-/l* 78.0%

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

      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 y around inf 61.3%

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

   6. Taylor expanded in a around 0 53.3%

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

      1. associate-*r/ 53.3%

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

      2. neg-mul-1 53.3%

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

   8. Simplified 53.3%

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

   if -5.1999999999999999e-76 < t < 1.02000000000000004e24

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. *-lft-identity 74.6%

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

      3. times-frac 72.3%

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

      4. /-rgt-identity 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0 63.0%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-76} \lor \neg \left(t \leq 1.02 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+84) y (if (<= t 5.5e+65) (+ x (/ (* z y) a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+84) {
		tmp = y;
	} else if (t <= 5.5e+65) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.5d+84)) then
        tmp = y
    else if (t <= 5.5d+65) then
        tmp = x + ((z * y) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+84) {
		tmp = y;
	} else if (t <= 5.5e+65) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+84:
		tmp = y
	elif t <= 5.5e+65:
		tmp = x + ((z * y) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+84)
		tmp = y;
	elseif (t <= 5.5e+65)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+84)
		tmp = y;
	elseif (t <= 5.5e+65)
		tmp = x + ((z * y) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+84], y, If[LessEqual[t, 5.5e+65], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999998e84

   1. Initial program 43.7%

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

      1. +-commutative 43.7%

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

      2. associate-/l* 69.7%

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

      3. fma-define 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. +-commutative 56.4%

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

      2. div-sub 56.4%

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

      3. mul-1-neg 56.4%

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

      4. associate-/l* 69.7%

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

      5. distribute-lft-neg-in 69.7%

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

      6. distribute-rgt-in 69.7%

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

      7. sub-neg 69.7%

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

      8. associate-*l/ 43.7%

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

      9. associate-*r/ 58.3%

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

      10. +-commutative 58.3%

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

      11. fma-define 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around inf 54.1%

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

   if -1.49999999999999998e84 < t < 5.4999999999999996e65

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-lft-identity 71.6%

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

      3. times-frac 71.4%

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

      4. /-rgt-identity 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 56.4%

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

   if 5.4999999999999996e65 < t

   1. Initial program 37.1%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. *-lft-identity 49.3%

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

      3. times-frac 63.3%

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

      4. /-rgt-identity 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in t around inf 51.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+212}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+200}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.25e+212)
   (/ (* z y) (- t))
   (if (<= z 2.8e+200) (+ x y) (* x (/ (- z a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.25e+212) {
		tmp = (z * y) / -t;
	} else if (z <= 2.8e+200) {
		tmp = x + y;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.25d+212)) then
        tmp = (z * y) / -t
    else if (z <= 2.8d+200) then
        tmp = x + y
    else
        tmp = x * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.25e+212) {
		tmp = (z * y) / -t;
	} else if (z <= 2.8e+200) {
		tmp = x + y;
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.25e+212:
		tmp = (z * y) / -t
	elif z <= 2.8e+200:
		tmp = x + y
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.25e+212)
		tmp = Float64(Float64(z * y) / Float64(-t));
	elseif (z <= 2.8e+200)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.25e+212)
		tmp = (z * y) / -t;
	elseif (z <= 2.8e+200)
		tmp = x + y;
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.25e+212], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 2.8e+200], N[(x + y), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.24999999999999999e212

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 89.7%

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

      3. fma-define 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. div-sub 69.5%

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

      3. mul-1-neg 69.5%

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

      4. associate-/l* 68.7%

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

      5. distribute-lft-neg-in 68.7%

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

      6. distribute-rgt-in 89.7%

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

      7. sub-neg 89.7%

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

      8. associate-*l/ 85.3%

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

      9. associate-*r/ 90.0%

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

      10. +-commutative 90.0%

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

      11. fma-define 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in z around -inf 84.9%

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

   9. Taylor expanded in y around inf 68.8%

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

   10. Taylor expanded in a around 0 53.1%

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

       1. associate-*r/ 53.1%

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

       2. *-commutative 53.1%

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

       3. neg-mul-1 53.1%

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

       4. distribute-rgt-neg-in 53.1%

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

   12. Simplified 53.1%

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

   if -3.24999999999999999e212 < z < 2.79999999999999985e200

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. *-lft-identity 63.1%

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

      3. times-frac 67.8%

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

      4. /-rgt-identity 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 41.1%

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

   if 2.79999999999999985e200 < z

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-/l* 92.9%

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

      3. fma-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 41.8%

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

      1. associate--l+ 41.8%

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

      2. associate-*r/ 41.8%

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

      3. associate-*r/ 41.8%

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

      4. mul-1-neg 41.8%

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

      5. div-sub 48.4%

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

      6. mul-1-neg 48.4%

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

      7. distribute-lft-out-- 48.4%

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

      8. associate-*r/ 48.4%

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

      9. mul-1-neg 48.4%

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

      10. unsub-neg 48.4%

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

      11. distribute-rgt-out-- 48.4%

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

   7. Simplified 48.4%

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

   8. Taylor expanded in y around 0 55.7%

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

      1. associate-/l* 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+212}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+200}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+123} \lor \neg \left(z \leq 5.2 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e+123) (not (<= z 5.2e+101))) (* y (/ z a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+123) || !(z <= 5.2e+101)) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.2d+123)) .or. (.not. (z <= 5.2d+101))) then
        tmp = y * (z / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+123) || !(z <= 5.2e+101)) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e+123) or not (z <= 5.2e+101):
		tmp = y * (z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e+123) || !(z <= 5.2e+101))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e+123) || ~((z <= 5.2e+101)))
		tmp = y * (z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e+123], N[Not[LessEqual[z, 5.2e+101]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999962e123 or 5.2e101 < z

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 59.5%

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

   6. Taylor expanded in t around 0 38.2%

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

   if -9.19999999999999962e123 < z < 5.2e101

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 67.8%

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

      4. /-rgt-identity 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 45.3%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+123} \lor \neg \left(z \leq 5.2 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+214}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+214)
   (/ (* z y) (- t))
   (if (<= z 4.6e+101) (+ x y) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+214) {
		tmp = (z * y) / -t;
	} else if (z <= 4.6e+101) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= (-2d+214)) then
        tmp = (z * y) / -t
    else if (z <= 4.6d+101) then
        tmp = x + y
    else
        tmp = 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 (z <= -2e+214) {
		tmp = (z * y) / -t;
	} else if (z <= 4.6e+101) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+214:
		tmp = (z * y) / -t
	elif z <= 4.6e+101:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+214)
		tmp = Float64(Float64(z * y) / Float64(-t));
	elseif (z <= 4.6e+101)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+214)
		tmp = (z * y) / -t;
	elseif (z <= 4.6e+101)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+214], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 4.6e+101], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e214

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-/l* 89.7%

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

      3. fma-define 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. div-sub 69.5%

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

      3. mul-1-neg 69.5%

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

      4. associate-/l* 68.7%

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

      5. distribute-lft-neg-in 68.7%

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

      6. distribute-rgt-in 89.7%

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

      7. sub-neg 89.7%

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

      8. associate-*l/ 85.3%

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

      9. associate-*r/ 90.0%

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

      10. +-commutative 90.0%

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

      11. fma-define 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in z around -inf 84.9%

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

   9. Taylor expanded in y around inf 68.8%

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

   10. Taylor expanded in a around 0 53.1%

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

       1. associate-*r/ 53.1%

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

       2. *-commutative 53.1%

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

       3. neg-mul-1 53.1%

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

       4. distribute-rgt-neg-in 53.1%

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

   12. Simplified 53.1%

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

   if -1.9999999999999999e214 < z < 4.6000000000000003e101

   1. Initial program 72.8%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. *-lft-identity 64.4%

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

      3. times-frac 67.5%

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

      4. /-rgt-identity 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in t around inf 43.1%

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

   if 4.6000000000000003e101 < z

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. associate-/l* 96.7%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 56.6%

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

   6. Taylor expanded in t around 0 41.0%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+214}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+101}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+104}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+110) x (if (<= a 2.9e+104) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+110) {
		tmp = x;
	} else if (a <= 2.9e+104) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d+110)) then
        tmp = x
    else if (a <= 2.9d+104) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+110) {
		tmp = x;
	} else if (a <= 2.9e+104) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+110:
		tmp = x
	elif a <= 2.9e+104:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+110)
		tmp = x;
	elseif (a <= 2.9e+104)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+110)
		tmp = x;
	elseif (a <= 2.9e+104)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+110], x, If[LessEqual[a, 2.9e+104], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999987e110 or 2.8999999999999998e104 < a

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. associate-/l* 92.8%

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

      3. fma-define 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 59.6%

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

   if -2.79999999999999987e110 < a < 2.8999999999999998e104

   1. Initial program 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 83.0%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. div-sub 75.0%

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

      3. mul-1-neg 75.0%

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

      4. associate-/l* 78.0%

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

      5. distribute-lft-neg-in 78.0%

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

      6. distribute-rgt-in 83.0%

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

      7. sub-neg 83.0%

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

      8. associate-*l/ 71.1%

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

      9. associate-*r/ 76.6%

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

      10. +-commutative 76.6%

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

      11. fma-define 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in t around inf 32.5%

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

Alternative 21: 25.1% 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 72.9%

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

   1. +-commutative 72.9%

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

   2. associate-/l* 86.1%

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

   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 a around inf 26.0%

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

Developer Target 1: 86.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024165 
(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))))