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

Percentage Accurate: 68.3% → 88.7%

Time: 15.8s

Alternatives: 16

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(\left(\frac{t}{a - t} + 1\right) + \left(y \cdot \frac{z - t}{x \cdot \left(a - t\right)} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -5e-259)
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (if (<= t_1 0.0)
       (+ y (/ (* (- y x) (- a z)) t))
       (if (<= t_1 2e+61)
         (*
          x
          (+
           (+ (/ t (- a t)) 1.0)
           (+ (* y (/ (- z t) (* x (- a t)))) (/ z (- t a)))))
         (fma (- z t) (/ (- y x) (- a t)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -5e-259) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+61) {
		tmp = x * (((t / (a - t)) + 1.0) + ((y * ((z - t) / (x * (a - t)))) + (z / (t - a))));
	} else {
		tmp = fma((z - t), ((y - x) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-259)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 2e+61)
		tmp = Float64(x * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) + Float64(Float64(y * Float64(Float64(z - t) / Float64(x * Float64(a - t)))) + Float64(z / Float64(t - a)))));
	else
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-259], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+61], N[(x * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[(y * N[(N[(z - t), $MachinePrecision] / N[(x * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259

   1. Initial program 75.7%

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

      1. +-commutative 75.7%

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

      2. associate-/l* 92.2%

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

      3. fma-define 92.2%

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

   3. Simplified 92.2%

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

      1. fma-undefine 92.2%

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

   6. Applied egg-rr 92.2%

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.9999999999999999e61

   1. Initial program 89.1%

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

   3. Taylor expanded in x around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

      7. associate-/l* 97.2%

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

      8. +-commutative 97.2%

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

   5. Simplified 97.2%

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

   if 1.9999999999999999e61 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 60.2%

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

   3. Taylor expanded in x around 0 63.2%

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

      1. distribute-rgt-in 63.2%

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

      2. *-lft-identity 63.2%

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

      3. mul-1-neg 63.2%

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

      4. distribute-lft-neg-out 63.2%

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

      5. /-rgt-identity 63.2%

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

      6. times-frac 57.7%

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

      7. *-commutative 57.7%

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

      8. *-rgt-identity 57.7%

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

      9. mul-1-neg 57.7%

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

      10. associate-/l* 68.7%

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

      11. div-sub 68.7%

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

      12. associate-+r+ 68.2%

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

      13. +-commutative 68.2%

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

   5. Simplified 89.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(\left(\frac{t}{a - t} + 1\right) + \left(y \cdot \frac{z - t}{x \cdot \left(a - t\right)} + \frac{z}{t - a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ (- a t) (- z t))))
     (if (<= t_1 -5e-259)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 1e+305) t_1 (+ x (* (- z t) (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (t_1 <= -5e-259) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (t_1 <= -5e-259) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / ((a - t) / (z - t)))
	elif t_1 <= -5e-259:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 1e+305:
		tmp = t_1
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= -5e-259)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / ((a - t) / (z - t)));
	elseif (t_1 <= -5e-259)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-259], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 40.0%

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

      1. +-commutative 40.0%

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

      2. associate-/l* 82.7%

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

      3. fma-define 82.7%

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

   3. Simplified 82.7%

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

      1. fma-undefine 82.7%

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

   6. Applied egg-rr 82.7%

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

      1. clear-num 82.7%

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

      2. un-div-inv 82.8%

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

      3. sub-neg 82.8%

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

      4. add-sqr-sqrt 47.1%

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

      5. sqrt-unprod 54.3%

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

      6. sqr-neg 54.3%

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

      7. sqrt-unprod 26.2%

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

      8. add-sqr-sqrt 61.5%

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

   8. Applied egg-rr 61.5%

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

   9. Taylor expanded in y around inf 65.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.9999999999999994e304

   1. Initial program 95.1%

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

   if 9.9999999999999994e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 41.6%

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

   3. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

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

      2. *-lft-identity 35.4%

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

      3. times-frac 70.9%

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

      4. /-rgt-identity 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-259}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+305}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-259} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -5e-259) (not (<= t_1 0.0)))
     (+ x (* (- y x) (/ (- z t) (- a t))))
     (+ y (/ (* (- y x) (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-259) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-5d-259)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -5e-259) || !(t_1 <= 0.0)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -5e-259) or not (t_1 <= 0.0):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -5e-259) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -5e-259) || ~((t_1 <= 0.0)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-259], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -4.99999999999999977e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 73.1%

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

      1. +-commutative 73.1%

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

      2. associate-/l* 90.5%

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

      3. fma-define 90.5%

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

   3. Simplified 90.5%

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

      1. fma-undefine 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -4.99999999999999977e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.3%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-259} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 13000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= t -5.9e+75)
     y
     (if (<= t -1.25e-12)
       t_1
       (if (<= t 13000.0) x (if (<= t 8.5e+204) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -5.9e+75) {
		tmp = y;
	} else if (t <= -1.25e-12) {
		tmp = t_1;
	} else if (t <= 13000.0) {
		tmp = x;
	} else if (t <= 8.5e+204) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (t <= (-5.9d+75)) then
        tmp = y
    else if (t <= (-1.25d-12)) then
        tmp = t_1
    else if (t <= 13000.0d0) then
        tmp = x
    else if (t <= 8.5d+204) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (t <= -5.9e+75) {
		tmp = y;
	} else if (t <= -1.25e-12) {
		tmp = t_1;
	} else if (t <= 13000.0) {
		tmp = x;
	} else if (t <= 8.5e+204) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if t <= -5.9e+75:
		tmp = y
	elif t <= -1.25e-12:
		tmp = t_1
	elif t <= 13000.0:
		tmp = x
	elif t <= 8.5e+204:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (t <= -5.9e+75)
		tmp = y;
	elseif (t <= -1.25e-12)
		tmp = t_1;
	elseif (t <= 13000.0)
		tmp = x;
	elseif (t <= 8.5e+204)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (t <= -5.9e+75)
		tmp = y;
	elseif (t <= -1.25e-12)
		tmp = t_1;
	elseif (t <= 13000.0)
		tmp = x;
	elseif (t <= 8.5e+204)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.9e+75], y, If[LessEqual[t, -1.25e-12], t$95$1, If[LessEqual[t, 13000.0], x, If[LessEqual[t, 8.5e+204], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.89999999999999983e75 or 8.5e204 < t

   1. Initial program 32.2%

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

   3. Taylor expanded in t around inf 65.0%

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

   if -5.89999999999999983e75 < t < -1.24999999999999992e-12 or 13000 < t < 8.5e204

   1. Initial program 63.5%

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

   3. Taylor expanded in x around -inf 44.9%

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

      1. associate-*r* 44.9%

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

      2. neg-mul-1 44.9%

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

      3. +-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in t around -inf 34.8%

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

      1. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

   if -1.24999999999999992e-12 < t < 13000

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 43.3%

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

Alternative 5: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-91}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -5e-38)
     t_1
     (if (<= t 4.6e-91)
       (+ x (* z (/ (- y x) a)))
       (if (<= t 1.7e+58) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5e-38) {
		tmp = t_1;
	} else if (t <= 4.6e-91) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.7e+58) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-5d-38)) then
        tmp = t_1
    else if (t <= 4.6d-91) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 1.7d+58) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -5e-38) {
		tmp = t_1;
	} else if (t <= 4.6e-91) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 1.7e+58) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -5e-38:
		tmp = t_1
	elif t <= 4.6e-91:
		tmp = x + (z * ((y - x) / a))
	elif t <= 1.7e+58:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -5e-38)
		tmp = t_1;
	elseif (t <= 4.6e-91)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 1.7e+58)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -5e-38)
		tmp = t_1;
	elseif (t <= 4.6e-91)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 1.7e+58)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-38], t$95$1, If[LessEqual[t, 4.6e-91], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+58], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000033e-38 or 1.7e58 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. fma-undefine 77.7%

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

   6. Applied egg-rr 77.7%

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

   7. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   9. Simplified 65.6%

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

   if -5.00000000000000033e-38 < t < 4.59999999999999991e-91

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

   if 4.59999999999999991e-91 < t < 1.7e58

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.6%

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

   3. Simplified 85.6%

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

      1. fma-undefine 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   9. Simplified 64.1%

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

Alternative 6: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.3e-39)
     t_1
     (if (<= t 2.4e-91)
       (+ x (* y (/ z a)))
       (if (<= t 8.8e+57) (* z (/ (- y x) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.3e-39) {
		tmp = t_1;
	} else if (t <= 2.4e-91) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.8e+57) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.3d-39)) then
        tmp = t_1
    else if (t <= 2.4d-91) then
        tmp = x + (y * (z / a))
    else if (t <= 8.8d+57) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.3e-39) {
		tmp = t_1;
	} else if (t <= 2.4e-91) {
		tmp = x + (y * (z / a));
	} else if (t <= 8.8e+57) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.3e-39:
		tmp = t_1
	elif t <= 2.4e-91:
		tmp = x + (y * (z / a))
	elif t <= 8.8e+57:
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.3e-39)
		tmp = t_1;
	elseif (t <= 2.4e-91)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 8.8e+57)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.3e-39)
		tmp = t_1;
	elseif (t <= 2.4e-91)
		tmp = x + (y * (z / a));
	elseif (t <= 8.8e+57)
		tmp = z * ((y - x) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-39], t$95$1, If[LessEqual[t, 2.4e-91], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+57], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.30000000000000008e-39 or 8.8000000000000003e57 < t

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

      1. fma-undefine 77.7%

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

   6. Applied egg-rr 77.7%

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

   7. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   9. Simplified 65.6%

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

   if -2.30000000000000008e-39 < t < 2.40000000000000011e-91

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in y around inf 70.8%

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

      1. associate-/l* 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in z around inf 68.8%

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

       1. associate-/l* 70.1%

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

   11. Simplified 70.1%

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

   if 2.40000000000000011e-91 < t < 8.8000000000000003e57

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-/l* 85.6%

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

      3. fma-define 85.6%

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

   3. Simplified 85.6%

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

      1. fma-undefine 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   9. Simplified 64.1%

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

Alternative 7: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+80)
   y
   (if (<= t -1.7e-10)
     (* x (/ (- z a) t))
     (if (<= t 1.6e+61) (+ x (* y (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+80) {
		tmp = y;
	} else if (t <= -1.7e-10) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.6e+61) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.95d+80)) then
        tmp = y
    else if (t <= (-1.7d-10)) then
        tmp = x * ((z - a) / t)
    else if (t <= 1.6d+61) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+80) {
		tmp = y;
	} else if (t <= -1.7e-10) {
		tmp = x * ((z - a) / t);
	} else if (t <= 1.6e+61) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+80:
		tmp = y
	elif t <= -1.7e-10:
		tmp = x * ((z - a) / t)
	elif t <= 1.6e+61:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+80)
		tmp = y;
	elseif (t <= -1.7e-10)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 1.6e+61)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+80)
		tmp = y;
	elseif (t <= -1.7e-10)
		tmp = x * ((z - a) / t);
	elseif (t <= 1.6e+61)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+80], y, If[LessEqual[t, -1.7e-10], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+61], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999999e80 or 1.5999999999999999e61 < t

   1. Initial program 39.2%

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

   3. Taylor expanded in t around inf 55.6%

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

   if -1.94999999999999999e80 < t < -1.70000000000000007e-10

   1. Initial program 74.8%

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

   3. Taylor expanded in x around -inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

      3. +-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in t around -inf 42.7%

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

      1. associate-/l* 42.7%

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

   8. Simplified 42.7%

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

   if -1.70000000000000007e-10 < t < 1.5999999999999999e61

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf 68.8%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf 63.6%

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

      1. associate-/l* 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in z around inf 62.3%

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

       1. associate-/l* 63.9%

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

   11. Simplified 63.9%

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

Alternative 8: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-177} \lor \neg \left(y \leq 1.3 \cdot 10^{-66}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.45e-177) (not (<= y 1.3e-66)))
   (+ x (/ y (/ (- a t) (- z t))))
   (+ x (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e-177) || !(y <= 1.3e-66)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = x + (z * ((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 ((y <= (-1.45d-177)) .or. (.not. (y <= 1.3d-66))) then
        tmp = x + (y / ((a - t) / (z - t)))
    else
        tmp = x + (z * ((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 ((y <= -1.45e-177) || !(y <= 1.3e-66)) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.45e-177) or not (y <= 1.3e-66):
		tmp = x + (y / ((a - t) / (z - t)))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.45e-177) || !(y <= 1.3e-66))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.45e-177) || ~((y <= 1.3e-66)))
		tmp = x + (y / ((a - t) / (z - t)));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.45e-177], N[Not[LessEqual[y, 1.3e-66]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999999e-177 or 1.2999999999999999e-66 < y

   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* 88.5%

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

      3. fma-define 88.5%

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

   3. Simplified 88.5%

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

      1. fma-undefine 88.5%

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

   6. Applied egg-rr 88.5%

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

      1. clear-num 88.4%

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

      2. un-div-inv 88.4%

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

      3. sub-neg 88.4%

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

      4. add-sqr-sqrt 51.4%

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

      5. sqrt-unprod 68.4%

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

      6. sqr-neg 68.4%

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

      7. sqrt-unprod 32.7%

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

      8. add-sqr-sqrt 78.3%

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

   8. Applied egg-rr 78.3%

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

   9. Taylor expanded in y around inf 79.6%

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

   if -1.44999999999999999e-177 < y < 1.2999999999999999e-66

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 68.1%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-177} \lor \neg \left(y \leq 1.3 \cdot 10^{-66}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+74} \lor \neg \left(t \leq 1.02 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+74) (not (<= t 1.02e+65)))
   (* y (/ (- z t) (- a t)))
   (+ x (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+74) || !(t <= 1.02e+65)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((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 ((t <= (-1.05d+74)) .or. (.not. (t <= 1.02d+65))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (z * ((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 ((t <= -1.05e+74) || !(t <= 1.02e+65)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+74) or not (t <= 1.02e+65):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+74) || !(t <= 1.02e+65))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+74) || ~((t <= 1.02e+65)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+74], N[Not[LessEqual[t, 1.02e+65]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e74 or 1.02000000000000005e65 < t

   1. Initial program 38.9%

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

      1. +-commutative 38.9%

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

      2. associate-/l* 75.3%

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

      3. fma-define 75.3%

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

   3. Simplified 75.3%

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

      1. fma-undefine 75.3%

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

   6. Applied egg-rr 75.3%

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

   7. Taylor expanded in y around inf 69.1%

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

      1. div-sub 69.1%

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

   9. Simplified 69.1%

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

   if -1.0499999999999999e74 < t < 1.02000000000000005e65

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 77.4%

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

      1. associate-/l* 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+74} \lor \neg \left(t \leq 1.02 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e-96)
   (+ x (/ y (/ (- a t) (- z t))))
   (if (<= a 5.5e-41)
     (+ y (/ (* (- y x) (- a z)) t))
     (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-96) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (a <= 5.5e-41) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d-96)) then
        tmp = x + (y / ((a - t) / (z - t)))
    else if (a <= 5.5d-41) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-96) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else if (a <= 5.5e-41) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e-96:
		tmp = x + (y / ((a - t) / (z - t)))
	elif a <= 5.5e-41:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e-96)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	elseif (a <= 5.5e-41)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e-96)
		tmp = x + (y / ((a - t) / (z - t)));
	elseif (a <= 5.5e-41)
		tmp = y + (((y - x) * (a - z)) / t);
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e-96], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-41], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9999999999999998e-96

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 91.5%

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

      3. fma-define 91.5%

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

   3. Simplified 91.5%

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

      1. fma-undefine 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. clear-num 91.4%

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

      2. un-div-inv 91.4%

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

      3. sub-neg 91.4%

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

      4. add-sqr-sqrt 46.6%

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

      5. sqrt-unprod 67.5%

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

      6. sqr-neg 67.5%

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

      7. sqrt-unprod 40.5%

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

      8. add-sqr-sqrt 80.0%

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

   8. Applied egg-rr 80.0%

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

   9. Taylor expanded in y around inf 80.3%

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

   if -1.9999999999999998e-96 < a < 5.50000000000000022e-41

   1. Initial program 69.5%

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

   3. Taylor expanded in t around inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. associate-*r/ 86.7%

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

      3. associate-*r/ 86.7%

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

      4. mul-1-neg 86.7%

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

      5. div-sub 86.8%

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

      6. mul-1-neg 86.8%

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

      7. distribute-lft-out-- 86.8%

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

      8. associate-*r/ 86.8%

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

      9. mul-1-neg 86.8%

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

      10. unsub-neg 86.8%

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

      11. distribute-rgt-out-- 86.8%

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

   5. Simplified 86.8%

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

   if 5.50000000000000022e-41 < a

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-lft-identity 63.0%

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

      3. times-frac 74.1%

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

      4. /-rgt-identity 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-41} \lor \neg \left(t \leq 4.4 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e-41) (not (<= t 4.4e-69)))
   (* y (/ (- z t) (- a t)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-41) || !(t <= 4.4e-69)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.5d-41)) .or. (.not. (t <= 4.4d-69))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-41) || !(t <= 4.4e-69)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e-41) or not (t <= 4.4e-69):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e-41) || !(t <= 4.4e-69))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e-41) || ~((t <= 4.4e-69)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e-41], N[Not[LessEqual[t, 4.4e-69]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999997e-41 or 4.4e-69 < t

   1. Initial program 53.2%

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

      1. +-commutative 53.2%

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

      2. associate-/l* 79.0%

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

      3. fma-define 79.0%

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

   3. Simplified 79.0%

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

      1. fma-undefine 79.0%

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

   6. Applied egg-rr 79.0%

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

   7. Taylor expanded in y around inf 63.0%

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

      1. div-sub 63.0%

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

   9. Simplified 63.0%

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

   if -9.4999999999999997e-41 < t < 4.4e-69

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 76.9%

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

      1. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around inf 69.8%

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

      1. associate-/l* 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in z around inf 67.9%

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

       1. associate-/l* 69.1%

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

   11. Simplified 69.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-41} \lor \neg \left(t \leq 4.4 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e+84)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 2.25e+98) (* y (/ (- z t) (- a t))) (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+84) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 2.25e+98) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.2d+84)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 2.25d+98) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+84) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 2.25e+98) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e+84:
		tmp = x + (y * ((z - t) / a))
	elif a <= 2.25e+98:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.2e+84)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 2.25e+98)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.2e+84)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 2.25e+98)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.2e+84], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+98], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999998e84

   1. Initial program 72.4%

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

   3. Taylor expanded in a around inf 64.3%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around inf 71.1%

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

      1. associate-/l* 80.9%

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

   8. Simplified 80.9%

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

   if -2.1999999999999998e84 < a < 2.2500000000000001e98

   1. Initial program 71.7%

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

      1. +-commutative 71.7%

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

      2. associate-/l* 82.9%

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

      3. fma-define 82.9%

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

   3. Simplified 82.9%

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

      1. fma-undefine 82.9%

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

   6. Applied egg-rr 82.9%

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

   7. Taylor expanded in y around inf 61.0%

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

      1. div-sub 61.0%

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

   9. Simplified 61.0%

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

   if 2.2500000000000001e98 < a

   1. Initial program 55.9%

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

   3. Taylor expanded in x around -inf 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

      3. +-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 71.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.25e+76)
   y
   (if (<= t -8.5e-14) (/ (* x z) t) (if (<= t 7.8e+60) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+76) {
		tmp = y;
	} else if (t <= -8.5e-14) {
		tmp = (x * z) / t;
	} else if (t <= 7.8e+60) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.25d+76)) then
        tmp = y
    else if (t <= (-8.5d-14)) then
        tmp = (x * z) / t
    else if (t <= 7.8d+60) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.25e+76) {
		tmp = y;
	} else if (t <= -8.5e-14) {
		tmp = (x * z) / t;
	} else if (t <= 7.8e+60) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.25e+76:
		tmp = y
	elif t <= -8.5e-14:
		tmp = (x * z) / t
	elif t <= 7.8e+60:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.25e+76)
		tmp = y;
	elseif (t <= -8.5e-14)
		tmp = Float64(Float64(x * z) / t);
	elseif (t <= 7.8e+60)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.25e+76)
		tmp = y;
	elseif (t <= -8.5e-14)
		tmp = (x * z) / t;
	elseif (t <= 7.8e+60)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.25e+76], y, If[LessEqual[t, -8.5e-14], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7.8e+60], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999998e76 or 7.8000000000000006e60 < t

   1. Initial program 39.2%

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

   3. Taylor expanded in t around inf 55.6%

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

   if -1.24999999999999998e76 < t < -8.50000000000000038e-14

   1. Initial program 74.8%

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

   3. Taylor expanded in x around -inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

      3. +-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around 0 34.4%

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

   if -8.50000000000000038e-14 < t < 7.8000000000000006e60

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf 42.1%

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

Alternative 14: 38.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+79)
   y
   (if (<= t -2.05e-10) (* x (/ z t)) (if (<= t 7.5e+68) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+79) {
		tmp = y;
	} else if (t <= -2.05e-10) {
		tmp = x * (z / t);
	} else if (t <= 7.5e+68) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.9d+79)) then
        tmp = y
    else if (t <= (-2.05d-10)) then
        tmp = x * (z / t)
    else if (t <= 7.5d+68) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+79) {
		tmp = y;
	} else if (t <= -2.05e-10) {
		tmp = x * (z / t);
	} else if (t <= 7.5e+68) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e+79:
		tmp = y
	elif t <= -2.05e-10:
		tmp = x * (z / t)
	elif t <= 7.5e+68:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+79)
		tmp = y;
	elseif (t <= -2.05e-10)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 7.5e+68)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e+79)
		tmp = y;
	elseif (t <= -2.05e-10)
		tmp = x * (z / t);
	elseif (t <= 7.5e+68)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+79], y, If[LessEqual[t, -2.05e-10], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+68], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.89999999999999992e79 or 7.49999999999999959e68 < t

   1. Initial program 39.2%

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

   3. Taylor expanded in t around inf 55.6%

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

   if -2.89999999999999992e79 < t < -2.0499999999999999e-10

   1. Initial program 74.8%

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

   3. Taylor expanded in x around -inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

      3. +-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around 0 34.4%

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

      1. associate-/l* 34.4%

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

   8. Simplified 34.4%

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

   if -2.0499999999999999e-10 < t < 7.49999999999999959e68

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf 42.1%

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

Alternative 15: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e-10) y (if (<= t 1.35e+58) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e-10) {
		tmp = y;
	} else if (t <= 1.35e+58) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.3d-10)) then
        tmp = y
    else if (t <= 1.35d+58) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e-10) {
		tmp = y;
	} else if (t <= 1.35e+58) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e-10:
		tmp = y
	elif t <= 1.35e+58:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e-10)
		tmp = y;
	elseif (t <= 1.35e+58)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e-10)
		tmp = y;
	elseif (t <= 1.35e+58)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e-10], y, If[LessEqual[t, 1.35e+58], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999991e-10 or 1.3500000000000001e58 < t

   1. Initial program 46.1%

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

   3. Taylor expanded in t around inf 47.0%

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

   if -1.29999999999999991e-10 < t < 1.3500000000000001e58

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf 42.1%

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

Alternative 16: 25.5% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 69.3%

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

3. Taylor expanded in a around inf 27.6%

   \[\leadsto \color{blue}{x} \]
4. 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 2024137 
(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))))