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

Percentage Accurate: 67.9% → 91.4%

Time: 29.5s

Alternatives: 23

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- z t) (/ (- a t) (- y x))))
     (if (<= t_1 -2e-301)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_1 2e+296) t_1 (+ x (* (- z t) (/ (- y x) (- 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 + ((z - t) / ((a - t) / (y - x)));
	} else if (t_1 <= -2e-301) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+296) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * ((y - x) / (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 + ((z - t) / ((a - t) / (y - x)));
	} else if (t_1 <= -2e-301) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_1 <= 2e+296) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * ((y - x) / (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 + ((z - t) / ((a - t) / (y - x)))
	elif t_1 <= -2e-301:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_1 <= 2e+296:
		tmp = t_1
	else:
		tmp = x + ((z - t) * ((y - x) / (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(Float64(z - t) / Float64(Float64(a - t) / Float64(y - x))));
	elseif (t_1 <= -2e-301)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_1 <= 2e+296)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / 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 + ((z - t) / ((a - t) / (y - x)));
	elseif (t_1 <= -2e-301)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_1 <= 2e+296)
		tmp = t_1;
	else
		tmp = x + ((z - t) * ((y - x) / (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[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-301], 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, 2e+296], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / 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 40.3%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

      1. *-commutative 91.5%

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

      2. clear-num 91.8%

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

      3. un-div-inv 92.0%

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

   6. Applied egg-rr 92.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000013e-301 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999996e296

   1. Initial program 96.2%

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

   if -2.00000000000000013e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. +-commutative 4.8%

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

      2. associate-*l/ 4.7%

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

      3. fma-def 5.4%

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

   3. Simplified 5.4%

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

      1. fma-udef 4.7%

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

      2. associate-/r/ 4.8%

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

      3. div-inv 4.8%

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

      4. clear-num 4.8%

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

   6. Applied egg-rr 4.8%

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

   7. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r* 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. div-sub 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. associate-*r/ 99.9%

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

      13. mul-1-neg 99.9%

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

      14. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

   if 1.99999999999999996e296 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 50.0%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+296}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -2e-301)
     (+ x (* (- x y) (/ (- t z) (- a t))))
     (if (<= t_1 0.0)
       (- y (/ (* (- y x) (- z a)) t))
       (fma (/ (- z t) (- a t)) (- y x) 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 <= -2e-301) {
		tmp = x + ((x - y) * ((t - z) / (a - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), 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 <= -2e-301)
		tmp = Float64(x + Float64(Float64(x - y) * Float64(Float64(t - z) / Float64(a - t))));
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), 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, -2e-301], N[(x + N[(N[(x - y), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000013e-301

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-*l/ 86.9%

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

      3. fma-def 87.0%

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

   3. Simplified 87.0%

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

      1. fma-udef 86.9%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 93.9%

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

      4. clear-num 94.0%

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

   6. Applied egg-rr 94.0%

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

   if -2.00000000000000013e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. +-commutative 4.8%

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

      2. associate-*l/ 4.7%

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

      3. fma-def 5.4%

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

   3. Simplified 5.4%

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

      1. fma-udef 4.7%

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

      2. associate-/r/ 4.8%

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

      3. div-inv 4.8%

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

      4. clear-num 4.8%

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

   6. Applied egg-rr 4.8%

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

   7. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r* 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. div-sub 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. associate-*r/ 99.9%

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

      13. mul-1-neg 99.9%

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

      14. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

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

   1. Initial program 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-/l* 85.6%

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

      4. associate-/r/ 94.1%

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

      5. fma-def 94.2%

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

   3. Simplified 94.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) (- a t)))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-301)
       t_2
       (if (<= t_2 0.0)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t_2 2e+296) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / (a - t)));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t_2 <= 2e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / (a - t)))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-301:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t_2 <= 2e+296:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t_2 <= 2e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / (a - t)));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t_2 <= 2e+296)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-301], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+296], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 1.99999999999999996e296 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 45.0%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000013e-301 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 1.99999999999999996e296

   1. Initial program 96.2%

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

   if -2.00000000000000013e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. +-commutative 4.8%

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

      2. associate-*l/ 4.7%

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

      3. fma-def 5.4%

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

   3. Simplified 5.4%

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

      1. fma-udef 4.7%

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

      2. associate-/r/ 4.8%

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

      3. div-inv 4.8%

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

      4. clear-num 4.8%

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

   6. Applied egg-rr 4.8%

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

   7. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r* 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. div-sub 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. associate-*r/ 99.9%

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

      13. mul-1-neg 99.9%

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

      14. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+296}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-301} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-301) (not (<= t_1 0.0)))
     (+ x (* (- x y) (/ (- t z) (- a t))))
     (- y (/ (* (- y x) (- z 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 <= -2e-301) || !(t_1 <= 0.0)) {
		tmp = x + ((x - y) * ((t - z) / (a - t)));
	} else {
		tmp = y - (((y - x) * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) * (z - t)) / (a - t))
    if ((t_1 <= (-2d-301)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - y) * ((t - z) / (a - t)))
    else
        tmp = y - (((y - x) * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-301) || !(t_1 <= 0.0)) {
		tmp = x + ((x - y) * ((t - z) / (a - t)));
	} else {
		tmp = y - (((y - x) * (z - 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 <= -2e-301) or not (t_1 <= 0.0):
		tmp = x + ((x - y) * ((t - z) / (a - t)))
	else:
		tmp = y - (((y - x) * (z - 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 <= -2e-301) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - y) * Float64(Float64(t - z) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - 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 <= -2e-301) || ~((t_1 <= 0.0)))
		tmp = x + ((x - y) * ((t - z) / (a - t)));
	else
		tmp = y - (((y - x) * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-301], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - y), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $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))) < -2.00000000000000013e-301 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-*l/ 86.2%

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

      3. fma-def 86.3%

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

   3. Simplified 86.3%

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

      1. fma-udef 86.2%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. clear-num 94.1%

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

   6. Applied egg-rr 94.1%

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

   if -2.00000000000000013e-301 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.8%

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

      1. +-commutative 4.8%

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

      2. associate-*l/ 4.7%

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

      3. fma-def 5.4%

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

   3. Simplified 5.4%

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

      1. fma-udef 4.7%

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

      2. associate-/r/ 4.8%

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

      3. div-inv 4.8%

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

      4. clear-num 4.8%

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

   6. Applied egg-rr 4.8%

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

   7. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r* 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. div-sub 99.9%

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

      8. *-commutative 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. associate-*r/ 99.9%

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

      13. mul-1-neg 99.9%

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

      14. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-301} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(x - y\right) \cdot \frac{t - z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -1.6e+24)
     (- x (/ (- x y) (/ a (- z t))))
     (if (<= a -4.9e-111)
       t_1
       (if (<= a 9.2e-200)
         (- y (/ (* (- y x) (- z a)) t))
         (if (<= a 1.5e-119) t_1 (+ x (* (- z t) (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.6e+24) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (a <= -4.9e-111) {
		tmp = t_1;
	} else if (a <= 9.2e-200) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (a <= 1.5e-119) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-1.6d+24)) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (a <= (-4.9d-111)) then
        tmp = t_1
    else if (a <= 9.2d-200) then
        tmp = y - (((y - x) * (z - a)) / t)
    else if (a <= 1.5d-119) then
        tmp = t_1
    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 t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -1.6e+24) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (a <= -4.9e-111) {
		tmp = t_1;
	} else if (a <= 9.2e-200) {
		tmp = y - (((y - x) * (z - a)) / t);
	} else if (a <= 1.5e-119) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -1.6e+24:
		tmp = x - ((x - y) / (a / (z - t)))
	elif a <= -4.9e-111:
		tmp = t_1
	elif a <= 9.2e-200:
		tmp = y - (((y - x) * (z - a)) / t)
	elif a <= 1.5e-119:
		tmp = t_1
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.6e+24)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (a <= -4.9e-111)
		tmp = t_1;
	elseif (a <= 9.2e-200)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * Float64(z - a)) / t));
	elseif (a <= 1.5e-119)
		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 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -1.6e+24)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (a <= -4.9e-111)
		tmp = t_1;
	elseif (a <= 9.2e-200)
		tmp = y - (((y - x) * (z - a)) / t);
	elseif (a <= 1.5e-119)
		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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+24], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.9e-111], t$95$1, If[LessEqual[a, 9.2e-200], N[(y - N[(N[(N[(y - x), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-119], 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 a < -1.5999999999999999e24

   1. Initial program 81.9%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf 74.3%

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

      1. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

   if -1.5999999999999999e24 < a < -4.90000000000000019e-111 or 9.2000000000000003e-200 < a < 1.5000000000000001e-119

   1. Initial program 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-*l/ 77.1%

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

      3. fma-def 77.2%

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

   3. Simplified 77.2%

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

      1. fma-udef 77.1%

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

      2. associate-/r/ 85.3%

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

      3. div-inv 85.3%

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

      4. clear-num 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in y around -inf 58.1%

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

      1. expm1-log1p-u 40.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 19.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 24.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 24.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 46.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 78.3%

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

       3. associate-/r/ 61.9%

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

       4. *-commutative 61.9%

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

       5. associate-*r/ 58.1%

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

       6. *-commutative 58.1%

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

       7. associate-*r/ 78.4%

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

   11. Simplified 78.4%

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

   if -4.90000000000000019e-111 < a < 9.2000000000000003e-200

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. associate-*l/ 61.4%

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

      3. fma-def 61.4%

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

   3. Simplified 61.4%

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

      1. fma-udef 61.4%

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

      2. associate-/r/ 75.3%

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

      3. div-inv 75.4%

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

      4. clear-num 75.4%

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

   6. Applied egg-rr 75.4%

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

   7. Taylor expanded in t around inf 85.5%

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

      1. associate--l+ 85.5%

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

      2. associate-*r/ 85.5%

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

      3. associate-*r* 85.5%

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

      4. neg-mul-1 85.5%

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

      5. *-commutative 85.5%

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

      6. associate-*r/ 85.5%

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

      7. div-sub 85.5%

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

      8. *-commutative 85.5%

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

      9. neg-mul-1 85.5%

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

      10. associate-*r* 85.5%

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

      11. distribute-lft-out-- 85.5%

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

      12. associate-*r/ 85.5%

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

      13. mul-1-neg 85.5%

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

      14. unsub-neg 85.5%

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

   9. Simplified 85.5%

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

   if 1.5000000000000001e-119 < a

   1. Initial program 76.9%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 67.3%

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

      1. associate-/l* 79.6%

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

      2. associate-/r/ 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t)))))
        (t_2 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -3.7e+47)
     t_2
     (if (<= t -3.8e-159)
       t_1
       (if (<= t 6e-68)
         (- x (/ (* z (- x y)) (- a t)))
         (if (<= t 3.4e+137) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -3.7e+47) {
		tmp = t_2;
	} else if (t <= -3.8e-159) {
		tmp = t_1;
	} else if (t <= 6e-68) {
		tmp = x - ((z * (x - y)) / (a - t));
	} else if (t <= 3.4e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * (y / (a - t)))
    t_2 = y + ((x - y) / (t / (z - a)))
    if (t <= (-3.7d+47)) then
        tmp = t_2
    else if (t <= (-3.8d-159)) then
        tmp = t_1
    else if (t <= 6d-68) then
        tmp = x - ((z * (x - y)) / (a - t))
    else if (t <= 3.4d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -3.7e+47) {
		tmp = t_2;
	} else if (t <= -3.8e-159) {
		tmp = t_1;
	} else if (t <= 6e-68) {
		tmp = x - ((z * (x - y)) / (a - t));
	} else if (t <= 3.4e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	t_2 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -3.7e+47:
		tmp = t_2
	elif t <= -3.8e-159:
		tmp = t_1
	elif t <= 6e-68:
		tmp = x - ((z * (x - y)) / (a - t))
	elif t <= 3.4e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -3.7e+47)
		tmp = t_2;
	elseif (t <= -3.8e-159)
		tmp = t_1;
	elseif (t <= 6e-68)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / Float64(a - t)));
	elseif (t <= 3.4e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * (y / (a - t)));
	t_2 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -3.7e+47)
		tmp = t_2;
	elseif (t <= -3.8e-159)
		tmp = t_1;
	elseif (t <= 6e-68)
		tmp = x - ((z * (x - y)) / (a - t));
	elseif (t <= 3.4e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+47], t$95$2, If[LessEqual[t, -3.8e-159], t$95$1, If[LessEqual[t, 6e-68], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+137], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.70000000000000041e47 or 3.39999999999999986e137 < t

   1. Initial program 44.9%

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

      1. associate-*l/ 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in t around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. associate-*r/ 72.2%

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

      3. associate-*r/ 72.2%

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

      4. div-sub 72.2%

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

      5. distribute-lft-out-- 72.2%

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

      6. mul-1-neg 72.2%

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

      7. distribute-neg-frac 72.2%

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

      8. unsub-neg 72.2%

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

      9. distribute-rgt-out-- 72.3%

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

      10. associate-/l* 87.8%

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

   7. Simplified 87.8%

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

   if -3.70000000000000041e47 < t < -3.8000000000000001e-159 or 6e-68 < t < 3.39999999999999986e137

   1. Initial program 83.9%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 77.6%

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

      2. associate-/r/ 74.5%

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

   7. Simplified 74.5%

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

   if -3.8000000000000001e-159 < t < 6e-68

   1. Initial program 94.1%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 89.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+47}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+137}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-123} \lor \neg \left(t \leq 2.9 \cdot 10^{-60}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.9e+115)
     t_1
     (if (<= t -4.2e+64)
       (* (- y x) (/ z (- a t)))
       (if (or (<= t -4.8e-123) (not (<= t 2.9e-60)))
         t_1
         (+ x (/ z (/ a (- y x)))))))))

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 <= -3.9e+115) {
		tmp = t_1;
	} else if (t <= -4.2e+64) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -4.8e-123) || !(t <= 2.9e-60)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-3.9d+115)) then
        tmp = t_1
    else if (t <= (-4.2d+64)) then
        tmp = (y - x) * (z / (a - t))
    else if ((t <= (-4.8d-123)) .or. (.not. (t <= 2.9d-60))) then
        tmp = t_1
    else
        tmp = x + (z / (a / (y - x)))
    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 <= -3.9e+115) {
		tmp = t_1;
	} else if (t <= -4.2e+64) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -4.8e-123) || !(t <= 2.9e-60)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.9e+115:
		tmp = t_1
	elif t <= -4.2e+64:
		tmp = (y - x) * (z / (a - t))
	elif (t <= -4.8e-123) or not (t <= 2.9e-60):
		tmp = t_1
	else:
		tmp = x + (z / (a / (y - x)))
	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 <= -3.9e+115)
		tmp = t_1;
	elseif (t <= -4.2e+64)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif ((t <= -4.8e-123) || !(t <= 2.9e-60))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	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 <= -3.9e+115)
		tmp = t_1;
	elseif (t <= -4.2e+64)
		tmp = (y - x) * (z / (a - t));
	elseif ((t <= -4.8e-123) || ~((t <= 2.9e-60)))
		tmp = t_1;
	else
		tmp = x + (z / (a / (y - x)));
	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, -3.9e+115], t$95$1, If[LessEqual[t, -4.2e+64], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.8e-123], N[Not[LessEqual[t, 2.9e-60]], $MachinePrecision]], t$95$1, N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.90000000000000006e115 or -4.2000000000000001e64 < t < -4.8e-123 or 2.8999999999999999e-60 < t

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-*l/ 74.0%

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

      3. fma-def 74.2%

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

   3. Simplified 74.2%

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

      1. fma-udef 74.0%

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

      2. associate-/r/ 81.9%

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

      3. div-inv 81.8%

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

      4. clear-num 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around -inf 51.2%

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

      1. expm1-log1p-u 39.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 15.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 20.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 20.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 44.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 67.9%

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

       3. associate-/r/ 54.5%

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

       4. *-commutative 54.5%

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

       5. associate-*r/ 51.2%

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

       6. *-commutative 51.2%

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

       7. associate-*r/ 67.9%

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

   11. Simplified 67.9%

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

   if -3.90000000000000006e115 < t < -4.2000000000000001e64

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*l/ 82.5%

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

      3. fma-def 82.3%

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

   3. Simplified 82.3%

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

      1. fma-udef 82.5%

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

      2. associate-/r/ 91.1%

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

      3. div-inv 90.9%

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

      4. clear-num 91.2%

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

   6. Applied egg-rr 91.2%

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

   7. Taylor expanded in z around inf 55.8%

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

      1. div-sub 55.9%

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

      2. associate-*r/ 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-*r/ 64.7%

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

      5. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if -4.8e-123 < t < 2.8999999999999999e-60

   1. Initial program 93.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 80.6%

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

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-123} \lor \neg \left(t \leq 2.9 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-125} \lor \neg \left(t \leq 1.75 \cdot 10^{-60}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.36e+116)
     t_1
     (if (<= t -2.1e+64)
       (* (- y x) (/ z (- a t)))
       (if (or (<= t -2.3e-125) (not (<= t 1.75e-60)))
         t_1
         (- x (/ (* z (- x y)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.36e+116) {
		tmp = t_1;
	} else if (t <= -2.1e+64) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -2.3e-125) || !(t <= 1.75e-60)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * (x - y)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-1.36d+116)) then
        tmp = t_1
    else if (t <= (-2.1d+64)) then
        tmp = (y - x) * (z / (a - t))
    else if ((t <= (-2.3d-125)) .or. (.not. (t <= 1.75d-60))) then
        tmp = t_1
    else
        tmp = x - ((z * (x - y)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.36e+116) {
		tmp = t_1;
	} else if (t <= -2.1e+64) {
		tmp = (y - x) * (z / (a - t));
	} else if ((t <= -2.3e-125) || !(t <= 1.75e-60)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * (x - y)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.36e+116:
		tmp = t_1
	elif t <= -2.1e+64:
		tmp = (y - x) * (z / (a - t))
	elif (t <= -2.3e-125) or not (t <= 1.75e-60):
		tmp = t_1
	else:
		tmp = x - ((z * (x - y)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.36e+116)
		tmp = t_1;
	elseif (t <= -2.1e+64)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	elseif ((t <= -2.3e-125) || !(t <= 1.75e-60))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.36e+116)
		tmp = t_1;
	elseif (t <= -2.1e+64)
		tmp = (y - x) * (z / (a - t));
	elseif ((t <= -2.3e-125) || ~((t <= 1.75e-60)))
		tmp = t_1;
	else
		tmp = x - ((z * (x - y)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+116], t$95$1, If[LessEqual[t, -2.1e+64], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.3e-125], N[Not[LessEqual[t, 1.75e-60]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.36e116 or -2.1e64 < t < -2.2999999999999999e-125 or 1.74999999999999988e-60 < t

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-*l/ 74.0%

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

      3. fma-def 74.2%

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

   3. Simplified 74.2%

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

      1. fma-udef 74.0%

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

      2. associate-/r/ 81.9%

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

      3. div-inv 81.8%

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

      4. clear-num 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around -inf 51.2%

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

      1. expm1-log1p-u 39.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 15.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 20.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 20.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 44.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 67.9%

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

       3. associate-/r/ 54.5%

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

       4. *-commutative 54.5%

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

       5. associate-*r/ 51.2%

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

       6. *-commutative 51.2%

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

       7. associate-*r/ 67.9%

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

   11. Simplified 67.9%

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

   if -1.36e116 < t < -2.1e64

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*l/ 82.5%

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

      3. fma-def 82.3%

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

   3. Simplified 82.3%

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

      1. fma-udef 82.5%

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

      2. associate-/r/ 91.1%

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

      3. div-inv 90.9%

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

      4. clear-num 91.2%

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

   6. Applied egg-rr 91.2%

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

   7. Taylor expanded in z around inf 55.8%

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

      1. div-sub 55.9%

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

      2. associate-*r/ 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-*r/ 64.7%

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

      5. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if -2.2999999999999999e-125 < t < 1.74999999999999988e-60

   1. Initial program 93.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 80.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+64}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-125} \lor \neg \left(t \leq 1.75 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+64}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-123} \lor \neg \left(t \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.4e+116)
     t_1
     (if (<= t -2.1e+64)
       (- x (/ z (/ t (- y x))))
       (if (or (<= t -1.3e-123) (not (<= t 5.1e-61)))
         t_1
         (- x (/ (* z (- x y)) a)))))))

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 <= -2.4e+116) {
		tmp = t_1;
	} else if (t <= -2.1e+64) {
		tmp = x - (z / (t / (y - x)));
	} else if ((t <= -1.3e-123) || !(t <= 5.1e-61)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * (x - y)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.4d+116)) then
        tmp = t_1
    else if (t <= (-2.1d+64)) then
        tmp = x - (z / (t / (y - x)))
    else if ((t <= (-1.3d-123)) .or. (.not. (t <= 5.1d-61))) then
        tmp = t_1
    else
        tmp = x - ((z * (x - y)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.4e+116) {
		tmp = t_1;
	} else if (t <= -2.1e+64) {
		tmp = x - (z / (t / (y - x)));
	} else if ((t <= -1.3e-123) || !(t <= 5.1e-61)) {
		tmp = t_1;
	} else {
		tmp = x - ((z * (x - y)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.4e+116:
		tmp = t_1
	elif t <= -2.1e+64:
		tmp = x - (z / (t / (y - x)))
	elif (t <= -1.3e-123) or not (t <= 5.1e-61):
		tmp = t_1
	else:
		tmp = x - ((z * (x - y)) / a)
	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 <= -2.4e+116)
		tmp = t_1;
	elseif (t <= -2.1e+64)
		tmp = Float64(x - Float64(z / Float64(t / Float64(y - x))));
	elseif ((t <= -1.3e-123) || !(t <= 5.1e-61))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	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 <= -2.4e+116)
		tmp = t_1;
	elseif (t <= -2.1e+64)
		tmp = x - (z / (t / (y - x)));
	elseif ((t <= -1.3e-123) || ~((t <= 5.1e-61)))
		tmp = t_1;
	else
		tmp = x - ((z * (x - y)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+116], t$95$1, If[LessEqual[t, -2.1e+64], N[(x - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.3e-123], N[Not[LessEqual[t, 5.1e-61]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e116 or -2.1e64 < t < -1.29999999999999998e-123 or 5.09999999999999968e-61 < t

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-*l/ 74.0%

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

      3. fma-def 74.2%

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

   3. Simplified 74.2%

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

      1. fma-udef 74.0%

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

      2. associate-/r/ 81.9%

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

      3. div-inv 81.8%

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

      4. clear-num 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around -inf 51.2%

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

      1. expm1-log1p-u 39.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 15.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 20.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 20.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 44.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 67.9%

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

       3. associate-/r/ 54.5%

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

       4. *-commutative 54.5%

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

       5. associate-*r/ 51.2%

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

       6. *-commutative 51.2%

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

       7. associate-*r/ 67.9%

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

   11. Simplified 67.9%

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

   if -2.4e116 < t < -2.1e64

   1. Initial program 83.1%

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

      1. associate-*l/ 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around inf 73.7%

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

   6. Taylor expanded in a around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

   if -1.29999999999999998e-123 < t < 5.09999999999999968e-61

   1. Initial program 93.8%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 80.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+64}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-123} \lor \neg \left(t \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 320000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= a -1.9e+25)
     t_2
     (if (<= a 7e-72)
       t_1
       (if (<= a 320000.0)
         t_2
         (if (<= a 9.5e+161) t_1 (+ x (/ y (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.9e+25) {
		tmp = t_2;
	} else if (a <= 7e-72) {
		tmp = t_1;
	} else if (a <= 320000.0) {
		tmp = t_2;
	} else if (a <= 9.5e+161) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (a <= (-1.9d+25)) then
        tmp = t_2
    else if (a <= 7d-72) then
        tmp = t_1
    else if (a <= 320000.0d0) then
        tmp = t_2
    else if (a <= 9.5d+161) then
        tmp = t_1
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.9e+25) {
		tmp = t_2;
	} else if (a <= 7e-72) {
		tmp = t_1;
	} else if (a <= 320000.0) {
		tmp = t_2;
	} else if (a <= 9.5e+161) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -1.9e+25:
		tmp = t_2
	elif a <= 7e-72:
		tmp = t_1
	elif a <= 320000.0:
		tmp = t_2
	elif a <= 9.5e+161:
		tmp = t_1
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -1.9e+25)
		tmp = t_2;
	elseif (a <= 7e-72)
		tmp = t_1;
	elseif (a <= 320000.0)
		tmp = t_2;
	elseif (a <= 9.5e+161)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -1.9e+25)
		tmp = t_2;
	elseif (a <= 7e-72)
		tmp = t_1;
	elseif (a <= 320000.0)
		tmp = t_2;
	elseif (a <= 9.5e+161)
		tmp = t_1;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+25], t$95$2, If[LessEqual[a, 7e-72], t$95$1, If[LessEqual[a, 320000.0], t$95$2, If[LessEqual[a, 9.5e+161], t$95$1, N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9e25 or 7.00000000000000001e-72 < a < 3.2e5

   1. Initial program 78.9%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 65.4%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   8. Simplified 67.4%

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

   if -1.9e25 < a < 7.00000000000000001e-72 or 3.2e5 < a < 9.50000000000000061e161

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-*l/ 73.9%

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

      3. fma-def 73.9%

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

   3. Simplified 73.9%

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

      1. fma-udef 73.9%

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

      2. associate-/r/ 83.6%

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

      3. div-inv 83.6%

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

      4. clear-num 83.7%

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

   6. Applied egg-rr 83.7%

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

   7. Taylor expanded in y around -inf 56.6%

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

      1. expm1-log1p-u 40.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 20.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 23.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 23.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 43.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 67.2%

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

       3. associate-/r/ 52.1%

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

       4. *-commutative 52.1%

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

       5. associate-*r/ 56.6%

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

       6. *-commutative 56.6%

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

       7. associate-*r/ 67.3%

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

   11. Simplified 67.3%

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

   if 9.50000000000000061e161 < a

   1. Initial program 74.0%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 68.1%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. associate-/l* 78.5%

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

   8. Simplified 78.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 320000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -48:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{+34}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.9e+119)
     t_2
     (if (<= t -48.0)
       t_1
       (if (<= t -1.55e-124)
         t_2
         (if (<= t 1e+34) (- x (/ (* z (- x y)) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.9e+119) {
		tmp = t_2;
	} else if (t <= -48.0) {
		tmp = t_1;
	} else if (t <= -1.55e-124) {
		tmp = t_2;
	} else if (t <= 1e+34) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (z / (t / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-2.9d+119)) then
        tmp = t_2
    else if (t <= (-48.0d0)) then
        tmp = t_1
    else if (t <= (-1.55d-124)) then
        tmp = t_2
    else if (t <= 1d+34) then
        tmp = x - ((z * (x - y)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.9e+119) {
		tmp = t_2;
	} else if (t <= -48.0) {
		tmp = t_1;
	} else if (t <= -1.55e-124) {
		tmp = t_2;
	} else if (t <= 1e+34) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (t / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.9e+119:
		tmp = t_2
	elif t <= -48.0:
		tmp = t_1
	elif t <= -1.55e-124:
		tmp = t_2
	elif t <= 1e+34:
		tmp = x - ((z * (x - y)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.9e+119)
		tmp = t_2;
	elseif (t <= -48.0)
		tmp = t_1;
	elseif (t <= -1.55e-124)
		tmp = t_2;
	elseif (t <= 1e+34)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (t / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.9e+119)
		tmp = t_2;
	elseif (t <= -48.0)
		tmp = t_1;
	elseif (t <= -1.55e-124)
		tmp = t_2;
	elseif (t <= 1e+34)
		tmp = x - ((z * (x - y)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+119], t$95$2, If[LessEqual[t, -48.0], t$95$1, If[LessEqual[t, -1.55e-124], t$95$2, If[LessEqual[t, 1e+34], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000007e119 or -48 < t < -1.5499999999999999e-124

   1. Initial program 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-*l/ 77.0%

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

      3. fma-def 77.2%

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

   3. Simplified 77.2%

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

      1. fma-udef 77.0%

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

      2. associate-/r/ 87.9%

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

      3. div-inv 87.8%

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

      4. clear-num 87.8%

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

   6. Applied egg-rr 87.8%

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

   7. Taylor expanded in y around -inf 57.7%

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

      1. expm1-log1p-u 39.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 14.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 21.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 21.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 46.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 77.7%

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

       3. associate-/r/ 63.7%

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

       4. *-commutative 63.7%

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

       5. associate-*r/ 57.7%

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

       6. *-commutative 57.7%

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

       7. associate-*r/ 77.6%

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

   11. Simplified 77.6%

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

   if -2.90000000000000007e119 < t < -48 or 9.99999999999999946e33 < t

   1. Initial program 54.3%

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

      1. associate-*l/ 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in t around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. associate-*r/ 61.9%

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

      3. associate-*r/ 61.9%

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

      4. div-sub 61.9%

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

      5. distribute-lft-out-- 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-frac 61.9%

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

      8. unsub-neg 61.9%

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

      9. distribute-rgt-out-- 61.9%

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

      10. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in z around inf 59.6%

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

      1. associate-/l* 68.5%

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

   10. Simplified 68.5%

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

   if -1.5499999999999999e-124 < t < 9.99999999999999946e33

   1. Initial program 93.8%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around 0 74.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -48:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-124}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 10^{+34}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -5.5e+49)
     y
     (if (<= t -2.7e-247)
       t_1
       (if (<= t 1.25e-230)
         (* x (- 1.0 (/ z a)))
         (if (<= t 1.08e+136) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -5.5e+49) {
		tmp = y;
	} else if (t <= -2.7e-247) {
		tmp = t_1;
	} else if (t <= 1.25e-230) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.08e+136) {
		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 + (y / (a / z))
    if (t <= (-5.5d+49)) then
        tmp = y
    else if (t <= (-2.7d-247)) then
        tmp = t_1
    else if (t <= 1.25d-230) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.08d+136) 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 + (y / (a / z));
	double tmp;
	if (t <= -5.5e+49) {
		tmp = y;
	} else if (t <= -2.7e-247) {
		tmp = t_1;
	} else if (t <= 1.25e-230) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.08e+136) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -5.5e+49:
		tmp = y
	elif t <= -2.7e-247:
		tmp = t_1
	elif t <= 1.25e-230:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.08e+136:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -5.5e+49)
		tmp = y;
	elseif (t <= -2.7e-247)
		tmp = t_1;
	elseif (t <= 1.25e-230)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.08e+136)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -5.5e+49)
		tmp = y;
	elseif (t <= -2.7e-247)
		tmp = t_1;
	elseif (t <= 1.25e-230)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.08e+136)
		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[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+49], y, If[LessEqual[t, -2.7e-247], t$95$1, If[LessEqual[t, 1.25e-230], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+136], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000042e49 or 1.07999999999999994e136 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 59.6%

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

   if -5.50000000000000042e49 < t < -2.70000000000000008e-247 or 1.25000000000000009e-230 < t < 1.07999999999999994e136

   1. Initial program 87.0%

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

      1. associate-*l/ 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around 0 57.1%

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

   6. Taylor expanded in y around inf 50.6%

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

      1. associate-/l* 54.5%

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

   8. Simplified 54.5%

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

   if -2.70000000000000008e-247 < t < 1.25000000000000009e-230

   1. Initial program 93.9%

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

      1. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 84.8%

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

   6. Taylor expanded in x around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

   8. Simplified 73.6%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-247}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -43:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-124}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))))
   (if (<= t -43.0)
     t_1
     (if (<= t -2.5e-124)
       (* y (/ (- z t) (- a t)))
       (if (<= t 3.2e+38) (- x (/ (* z (- x y)) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -43.0) {
		tmp = t_1;
	} else if (t <= -2.5e-124) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 3.2e+38) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / z))
    if (t <= (-43.0d0)) then
        tmp = t_1
    else if (t <= (-2.5d-124)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 3.2d+38) then
        tmp = x - ((z * (x - y)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -43.0) {
		tmp = t_1;
	} else if (t <= -2.5e-124) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 3.2e+38) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	tmp = 0
	if t <= -43.0:
		tmp = t_1
	elif t <= -2.5e-124:
		tmp = y * ((z - t) / (a - t))
	elif t <= 3.2e+38:
		tmp = x - ((z * (x - y)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (t <= -43.0)
		tmp = t_1;
	elseif (t <= -2.5e-124)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 3.2e+38)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	tmp = 0.0;
	if (t <= -43.0)
		tmp = t_1;
	elseif (t <= -2.5e-124)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 3.2e+38)
		tmp = x - ((z * (x - y)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -43.0], t$95$1, If[LessEqual[t, -2.5e-124], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+38], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -43 or 3.19999999999999985e38 < t

   1. Initial program 52.3%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. associate-*r/ 64.6%

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

      3. associate-*r/ 64.6%

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

      4. div-sub 64.6%

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

      5. distribute-lft-out-- 64.6%

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

      6. mul-1-neg 64.6%

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

      7. distribute-neg-frac 64.6%

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

      8. unsub-neg 64.6%

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

      9. distribute-rgt-out-- 64.7%

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

      10. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in z around inf 72.5%

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

   if -43 < t < -2.5000000000000001e-124

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-*l/ 92.7%

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

      3. fma-def 92.7%

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

   3. Simplified 92.7%

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

      1. fma-udef 92.7%

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

      2. associate-/r/ 96.1%

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

      3. div-inv 96.0%

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

      4. clear-num 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around -inf 65.1%

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

      1. expm1-log1p-u 31.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)\right)} \]

      2. expm1-udef 23.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)} - 1} \]

      3. associate-/l* 23.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right)} - 1 \]

   9. Applied egg-rr 23.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 31.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a - t}{z - t}}\right)\right)} \]

       2. expm1-log1p 68.9%

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

       3. associate-/r/ 65.0%

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

       4. *-commutative 65.0%

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

       5. associate-*r/ 65.1%

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

       6. *-commutative 65.1%

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

       7. associate-*r/ 68.8%

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

   11. Simplified 68.8%

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

   if -2.5000000000000001e-124 < t < 3.19999999999999985e38

   1. Initial program 93.8%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around 0 74.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -43:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-124}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -102:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))))
   (if (<= t -102.0)
     t_1
     (if (<= t -4.8e-123)
       (/ y (/ (- a t) (- z t)))
       (if (<= t 2.7e+28) (- x (/ (* z (- x y)) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -102.0) {
		tmp = t_1;
	} else if (t <= -4.8e-123) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 2.7e+28) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / z))
    if (t <= (-102.0d0)) then
        tmp = t_1
    else if (t <= (-4.8d-123)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 2.7d+28) then
        tmp = x - ((z * (x - y)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double tmp;
	if (t <= -102.0) {
		tmp = t_1;
	} else if (t <= -4.8e-123) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 2.7e+28) {
		tmp = x - ((z * (x - y)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	tmp = 0
	if t <= -102.0:
		tmp = t_1
	elif t <= -4.8e-123:
		tmp = y / ((a - t) / (z - t))
	elif t <= 2.7e+28:
		tmp = x - ((z * (x - y)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	tmp = 0.0
	if (t <= -102.0)
		tmp = t_1;
	elseif (t <= -4.8e-123)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 2.7e+28)
		tmp = Float64(x - Float64(Float64(z * Float64(x - y)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	tmp = 0.0;
	if (t <= -102.0)
		tmp = t_1;
	elseif (t <= -4.8e-123)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 2.7e+28)
		tmp = x - ((z * (x - y)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -102.0], t$95$1, If[LessEqual[t, -4.8e-123], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+28], N[(x - N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -102 or 2.7000000000000002e28 < t

   1. Initial program 52.3%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. associate-*r/ 64.6%

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

      3. associate-*r/ 64.6%

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

      4. div-sub 64.6%

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

      5. distribute-lft-out-- 64.6%

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

      6. mul-1-neg 64.6%

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

      7. distribute-neg-frac 64.6%

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

      8. unsub-neg 64.6%

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

      9. distribute-rgt-out-- 64.7%

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

      10. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in z around inf 72.5%

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

   if -102 < t < -4.8e-123

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-*l/ 92.7%

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

      3. fma-def 92.7%

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

   3. Simplified 92.7%

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

      1. fma-udef 92.7%

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

      2. associate-/r/ 96.1%

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

      3. div-inv 96.0%

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

      4. clear-num 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 68.8%

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

      1. div-sub 68.8%

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

      2. associate-*r/ 65.1%

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

      3. associate-/l* 68.9%

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

   9. Simplified 68.9%

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

   if -4.8e-123 < t < 2.7000000000000002e28

   1. Initial program 93.8%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around 0 74.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -102:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{z \cdot \left(x - y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+197} \lor \neg \left(t \leq 2.4 \cdot 10^{+146}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e+197) (not (<= t 2.4e+146)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+197) || !(t <= 2.4e+146)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.8d+197)) .or. (.not. (t <= 2.4d+146))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+197) || !(t <= 2.4e+146)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e+197) or not (t <= 2.4e+146):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e+197) || !(t <= 2.4e+146))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * 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 <= -3.8e+197) || ~((t <= 2.4e+146)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e+197], N[Not[LessEqual[t, 2.4e+146]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000001e197 or 2.4000000000000002e146 < t

   1. Initial program 36.8%

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

      1. associate-*l/ 52.5%

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

   3. Simplified 52.5%

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

   5. Taylor expanded in t around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-*r/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. div-sub 79.1%

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

      5. distribute-lft-out-- 79.1%

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

      6. mul-1-neg 79.1%

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

      7. distribute-neg-frac 79.1%

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

      8. unsub-neg 79.1%

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

      9. distribute-rgt-out-- 79.1%

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

      10. associate-/l* 96.1%

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

   7. Simplified 96.1%

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

   if -3.8000000000000001e197 < t < 2.4000000000000002e146

   1. Initial program 84.6%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+197} \lor \neg \left(t \leq 2.4 \cdot 10^{+146}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+49} \lor \neg \left(t \leq 8 \cdot 10^{+136}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+49) (not (<= t 8e+136)))
   (+ y (/ (- x y) (/ t z)))
   (- x (* z (/ (- x y) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+49) || !(t <= 8e+136)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - (z * ((x - y) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d+49)) .or. (.not. (t <= 8d+136))) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x - (z * ((x - y) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+49) || !(t <= 8e+136)) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x - (z * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+49) or not (t <= 8e+136):
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x - (z * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+49) || !(t <= 8e+136))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+49) || ~((t <= 8e+136)))
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x - (z * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+49], N[Not[LessEqual[t, 8e+136]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000011e49 or 8.00000000000000047e136 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 71.9%

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

      1. associate--l+ 71.9%

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

      2. associate-*r/ 71.9%

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

      3. associate-*r/ 71.9%

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

      4. div-sub 71.9%

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

      5. distribute-lft-out-- 71.9%

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

      6. mul-1-neg 71.9%

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

      7. distribute-neg-frac 71.9%

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

      8. unsub-neg 71.9%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around inf 80.6%

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

   if -2.10000000000000011e49 < t < 8.00000000000000047e136

   1. Initial program 88.3%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate-*r/ 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+49} \lor \neg \left(t \leq 8 \cdot 10^{+136}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-17} \lor \neg \left(a \leq 1.95 \cdot 10^{-84}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.2e-17) (not (<= a 1.95e-84)))
   (+ x (* (- z t) (/ y (- a t))))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-17) || !(a <= 1.95e-84)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.2d-17)) .or. (.not. (a <= 1.95d-84))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.2e-17) || !(a <= 1.95e-84)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.2e-17) or not (a <= 1.95e-84):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.2e-17) || !(a <= 1.95e-84))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.2e-17) || ~((a <= 1.95e-84)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.2e-17], N[Not[LessEqual[a, 1.95e-84]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2000000000000002e-17 or 1.95000000000000011e-84 < a

   1. Initial program 77.9%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 81.1%

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

      2. associate-/r/ 79.0%

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

   7. Simplified 79.0%

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

   if -3.2000000000000002e-17 < a < 1.95000000000000011e-84

   1. Initial program 71.4%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in t around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. associate-*r/ 71.8%

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

      3. associate-*r/ 71.8%

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

      4. div-sub 72.8%

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

      5. distribute-lft-out-- 72.8%

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

      6. mul-1-neg 72.8%

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

      7. distribute-neg-frac 72.8%

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

      8. unsub-neg 72.8%

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

      9. distribute-rgt-out-- 72.8%

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

      10. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around inf 77.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-17} \lor \neg \left(a \leq 1.95 \cdot 10^{-84}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+21)
   (- x (/ (- x y) (/ a (- z t))))
   (if (<= a 2.9e-84)
     (+ y (/ (- x y) (/ t z)))
     (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (a <= 2.9e-84) {
		tmp = y + ((x - y) / (t / z));
	} 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 <= (-2.05d+21)) then
        tmp = x - ((x - y) / (a / (z - t)))
    else if (a <= 2.9d-84) then
        tmp = y + ((x - y) / (t / z))
    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 <= -2.05e+21) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else if (a <= 2.9e-84) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+21:
		tmp = x - ((x - y) / (a / (z - t)))
	elif a <= 2.9e-84:
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+21)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	elseif (a <= 2.9e-84)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	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 <= -2.05e+21)
		tmp = x - ((x - y) / (a / (z - t)));
	elseif (a <= 2.9e-84)
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+21], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-84], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $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 < -2.05e21

   1. Initial program 82.2%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around inf 74.8%

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

      1. associate-/l* 85.5%

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

   7. Simplified 85.5%

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

   if -2.05e21 < a < 2.90000000000000019e-84

   1. Initial program 69.9%

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

      1. associate-*l/ 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in t around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. associate-*r/ 71.0%

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

      3. associate-*r/ 71.0%

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

      4. div-sub 71.9%

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

      5. distribute-lft-out-- 71.9%

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

      6. mul-1-neg 71.9%

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

      7. distribute-neg-frac 71.9%

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

      8. unsub-neg 71.9%

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

      9. distribute-rgt-out-- 71.9%

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

      10. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in z around inf 76.9%

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

   if 2.90000000000000019e-84 < a

   1. Initial program 77.7%

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

      1. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. associate-/l* 80.6%

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

      2. associate-/r/ 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+21)
   (* x (- 1.0 (/ z a)))
   (if (<= a 1.25e-73) (/ (- y) (/ t (- z t))) (+ x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 1.25e-73) {
		tmp = -y / (t / (z - t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d+21)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= 1.25d-73) then
        tmp = -y / (t / (z - t))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 1.25e-73) {
		tmp = -y / (t / (z - t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+21:
		tmp = x * (1.0 - (z / a))
	elif a <= 1.25e-73:
		tmp = -y / (t / (z - t))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+21)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= 1.25e-73)
		tmp = Float64(Float64(-y) / Float64(t / Float64(z - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+21)
		tmp = x * (1.0 - (z / a));
	elseif (a <= 1.25e-73)
		tmp = -y / (t / (z - t));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+21], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-73], N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.05e21

   1. Initial program 82.2%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around 0 66.1%

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

   6. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   8. Simplified 68.5%

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

   if -2.05e21 < a < 1.25e-73

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-*l/ 69.9%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

      1. fma-udef 69.9%

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

      2. associate-/r/ 80.7%

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

      3. div-inv 80.7%

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

      4. clear-num 80.8%

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

   6. Applied egg-rr 80.8%

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

   7. Taylor expanded in y around -inf 56.6%

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

   8. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. associate-/l* 58.0%

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

      3. distribute-neg-frac 58.0%

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

   10. Simplified 58.0%

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

   if 1.25e-73 < a

   1. Initial program 76.6%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around 0 60.8%

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

   6. Taylor expanded in y around inf 55.0%

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

      1. associate-/l* 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+49) y (if (<= t 7e+135) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+49) {
		tmp = y;
	} else if (t <= 7e+135) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.6d+49)) then
        tmp = y
    else if (t <= 7d+135) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+49) {
		tmp = y;
	} else if (t <= 7e+135) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+49:
		tmp = y
	elif t <= 7e+135:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+49)
		tmp = y;
	elseif (t <= 7e+135)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+49)
		tmp = y;
	elseif (t <= 7e+135)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+49], y, If[LessEqual[t, 7e+135], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999996e49 or 7.0000000000000005e135 < t

   1. Initial program 45.4%

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

      1. associate-*l/ 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in t around inf 59.6%

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

   if -5.5999999999999996e49 < t < 7.0000000000000005e135

   1. Initial program 88.3%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around 0 62.3%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

   8. Simplified 50.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+21)
   (* x (- 1.0 (/ z a)))
   (if (<= a 1.2e-73) (- y (* z (/ y t))) (+ x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+21) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 1.2e-73) {
		tmp = y - (z * (y / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d+21)) then
        tmp = x * (1.0d0 - (z / a))
    else if (a <= 1.2d-73) then
        tmp = y - (z * (y / t))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+21) {
		tmp = x * (1.0 - (z / a));
	} else if (a <= 1.2e-73) {
		tmp = y - (z * (y / t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+21:
		tmp = x * (1.0 - (z / a))
	elif a <= 1.2e-73:
		tmp = y - (z * (y / t))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+21)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (a <= 1.2e-73)
		tmp = Float64(y - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+21)
		tmp = x * (1.0 - (z / a));
	elseif (a <= 1.2e-73)
		tmp = y - (z * (y / t));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+21], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-73], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e21

   1. Initial program 82.2%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around 0 66.1%

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

   6. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   8. Simplified 68.5%

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

   if -2e21 < a < 1.20000000000000003e-73

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-*l/ 69.9%

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

      3. fma-def 70.0%

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

   3. Simplified 70.0%

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

      1. fma-udef 69.9%

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

      2. associate-/r/ 80.7%

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

      3. div-inv 80.7%

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

      4. clear-num 80.8%

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

   6. Applied egg-rr 80.8%

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

   7. Taylor expanded in y around -inf 56.6%

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

   8. Taylor expanded in a around 0 47.2%

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

      1. associate-*r/ 47.2%

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

      2. neg-mul-1 47.2%

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

      3. distribute-lft-neg-in 47.2%

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

   10. Simplified 47.2%

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

   11. Taylor expanded in z around 0 53.4%

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

       1. mul-1-neg 53.4%

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

       2. unsub-neg 53.4%

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

       3. associate-/l* 58.0%

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

       4. associate-/r/ 54.1%

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

   13. Simplified 54.1%

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

   if 1.20000000000000003e-73 < a

   1. Initial program 76.6%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in t around 0 60.8%

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

   6. Taylor expanded in y around inf 55.0%

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

      1. associate-/l* 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e-96) y (if (<= t 1.3e+138) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e-96) {
		tmp = y;
	} else if (t <= 1.3e+138) {
		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 <= (-4d-96)) then
        tmp = y
    else if (t <= 1.3d+138) 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 <= -4e-96) {
		tmp = y;
	} else if (t <= 1.3e+138) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e-96:
		tmp = y
	elif t <= 1.3e+138:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e-96)
		tmp = y;
	elseif (t <= 1.3e+138)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4e-96)
		tmp = y;
	elseif (t <= 1.3e+138)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e-96], y, If[LessEqual[t, 1.3e+138], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9999999999999996e-96 or 1.3e138 < t

   1. Initial program 53.9%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in t around inf 50.7%

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

   if -3.9999999999999996e-96 < t < 1.3e138

   1. Initial program 89.6%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around inf 37.2%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 24.2% 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 75.1%

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

   1. associate-*l/ 79.9%

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

3. Simplified 79.9%

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

5. Taylor expanded in a around inf 26.8%

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

6. Final simplification 26.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.9% 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 2024031 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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