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

Percentage Accurate: 68.3% → 91.6%

Time: 23.2s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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-264)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (if (<= t_2 5e+304)
           (+
            (* x (- (+ 1.0 (/ t (- a t))) (/ z (- a t))))
            (/ (* y (- z t)) (- a t)))
           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-264) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	} 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-264) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	} 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-264:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	elif t_2 <= 5e+304:
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t))
	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-264)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+304)
		tmp = Float64(Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) - Float64(z / Float64(a - t)))) + Float64(Float64(y * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 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-264)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	elseif (t_2 <= 5e+304)
		tmp = (x * ((1.0 + (t / (a - t))) - (z / (a - t)))) + ((y * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(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-264], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], N[(N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 46.5%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-264

   1. Initial program 98.0%

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

   if -2e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.7%

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

   3. Simplified 3.7%

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

      1. *-commutative 3.7%

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

      2. clear-num 3.9%

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

      3. un-div-inv 3.7%

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

   5. Applied egg-rr 3.7%

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

   6. Taylor expanded in t around -inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. associate-*r* 99.6%

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

      4. mul-1-neg 99.6%

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

      5. neg-sub0 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]

      6. associate--r- 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]

      7. neg-sub0 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

   8. Simplified 99.6%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 96.1%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around -inf 99.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-264}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) - \frac{z}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 2: 91.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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-264)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (if (<= t_2 5e+304) 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-264) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		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-264) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 5e+304) {
		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-264:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	elif t_2 <= 5e+304:
		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-264)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	elseif (t_2 <= 5e+304)
		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-264)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	elseif (t_2 <= 5e+304)
		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-264], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], 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 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 46.5%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-264 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 96.9%

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

   if -2e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.7%

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

   3. Simplified 3.7%

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

      1. *-commutative 3.7%

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

      2. clear-num 3.9%

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

      3. un-div-inv 3.7%

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

   5. Applied egg-rr 3.7%

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

   6. Taylor expanded in t around -inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. associate-*r* 99.6%

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

      4. mul-1-neg 99.6%

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

      5. neg-sub0 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]

      6. associate--r- 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]

      7. neg-sub0 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-264}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 3: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

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) (/ (- y x) (- a t))))
     (if (<= t_1 -2e-264)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (- x (/ (- x y) (/ (- a t) (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else if (t_1 <= -2e-264) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - 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) * ((y - x) / (a - t)));
	} else if (t_1 <= -2e-264) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	elif t_1 <= -2e-264:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	else:
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t_1 <= -2e-264)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	elseif (t_1 <= -2e-264)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	else
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-264], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - 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 47.8%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-264

   1. Initial program 98.0%

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

   if -2e-264 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

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

      1. associate-*l/ 3.7%

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

   3. Simplified 3.7%

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

      1. *-commutative 3.7%

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

      2. clear-num 3.9%

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

      3. un-div-inv 3.7%

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

   5. Applied egg-rr 3.7%

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

   6. Taylor expanded in t around -inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. associate-*r* 99.6%

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

      4. mul-1-neg 99.6%

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

      5. neg-sub0 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]

      6. associate--r- 99.6%

         \[\leadsto y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]

      7. neg-sub0 99.6%

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

      8. +-commutative 99.6%

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

      9. sub-neg 99.6%

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

   8. Simplified 99.6%

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

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

   1. Initial program 75.5%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-264}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 4: 55.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (+ x (* y (/ z a))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= t -6.5e+94)
     t_1
     (if (<= t -7.6e-85)
       (- x (* x (/ z a)))
       (if (<= t 4.6e-242)
         t_2
         (if (<= t 4e-130)
           t_3
           (if (<= t 5e-72)
             (+ x (/ (* y z) a))
             (if (<= t 2.9e-10)
               t_1
               (if (<= t 4.8e+48) t_2 (if (<= t 2.2e+90) t_3 t_1))))))))))

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 + (y * (z / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= -7.6e-85) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.6e-242) {
		tmp = t_2;
	} else if (t <= 4e-130) {
		tmp = t_3;
	} else if (t <= 5e-72) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.9e-10) {
		tmp = t_1;
	} else if (t <= 4.8e+48) {
		tmp = t_2;
	} else if (t <= 2.2e+90) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y * (z / a))
    t_3 = z * ((y - x) / (a - t))
    if (t <= (-6.5d+94)) then
        tmp = t_1
    else if (t <= (-7.6d-85)) then
        tmp = x - (x * (z / a))
    else if (t <= 4.6d-242) then
        tmp = t_2
    else if (t <= 4d-130) then
        tmp = t_3
    else if (t <= 5d-72) then
        tmp = x + ((y * z) / a)
    else if (t <= 2.9d-10) then
        tmp = t_1
    else if (t <= 4.8d+48) then
        tmp = t_2
    else if (t <= 2.2d+90) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y * (z / a));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= -7.6e-85) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.6e-242) {
		tmp = t_2;
	} else if (t <= 4e-130) {
		tmp = t_3;
	} else if (t <= 5e-72) {
		tmp = x + ((y * z) / a);
	} else if (t <= 2.9e-10) {
		tmp = t_1;
	} else if (t <= 4.8e+48) {
		tmp = t_2;
	} else if (t <= 2.2e+90) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y * (z / a))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_1
	elif t <= -7.6e-85:
		tmp = x - (x * (z / a))
	elif t <= 4.6e-242:
		tmp = t_2
	elif t <= 4e-130:
		tmp = t_3
	elif t <= 5e-72:
		tmp = x + ((y * z) / a)
	elif t <= 2.9e-10:
		tmp = t_1
	elif t <= 4.8e+48:
		tmp = t_2
	elif t <= 2.2e+90:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = t_1;
	elseif (t <= -7.6e-85)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 4.6e-242)
		tmp = t_2;
	elseif (t <= 4e-130)
		tmp = t_3;
	elseif (t <= 5e-72)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 2.9e-10)
		tmp = t_1;
	elseif (t <= 4.8e+48)
		tmp = t_2;
	elseif (t <= 2.2e+90)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y * (z / a));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = t_1;
	elseif (t <= -7.6e-85)
		tmp = x - (x * (z / a));
	elseif (t <= 4.6e-242)
		tmp = t_2;
	elseif (t <= 4e-130)
		tmp = t_3;
	elseif (t <= 5e-72)
		tmp = x + ((y * z) / a);
	elseif (t <= 2.9e-10)
		tmp = t_1;
	elseif (t <= 4.8e+48)
		tmp = t_2;
	elseif (t <= 2.2e+90)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+94], t$95$1, If[LessEqual[t, -7.6e-85], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-242], t$95$2, If[LessEqual[t, 4e-130], t$95$3, If[LessEqual[t, 5e-72], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-10], t$95$1, If[LessEqual[t, 4.8e+48], t$95$2, If[LessEqual[t, 2.2e+90], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.49999999999999976e94 or 4.9999999999999996e-72 < t < 2.89999999999999981e-10 or 2.1999999999999999e90 < t

   1. Initial program 41.9%

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

      1. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in x around 0 46.6%

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

      1. associate-*r/ 73.9%

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

   6. Simplified 73.9%

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

   if -6.49999999999999976e94 < t < -7.5999999999999997e-85

   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* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around 0 67.7%

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

   5. Taylor expanded in y around 0 54.3%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. neg-sub0 59.2%

         \[\leadsto x + \color{blue}{\left(0 - x \cdot \frac{z}{a}\right)} \]

      4. associate-+r- 59.2%

         \[\leadsto \color{blue}{\left(x + 0\right) - x \cdot \frac{z}{a}} \]

      5. +-rgt-identity 59.2%

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

   7. Simplified 59.2%

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

   if -7.5999999999999997e-85 < t < 4.59999999999999969e-242 or 2.89999999999999981e-10 < t < 4.8000000000000002e48

   1. Initial program 90.5%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around 0 83.2%

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

   5. Taylor expanded in y around inf 73.7%

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

      1. associate-*r/ 76.1%

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

   7. Simplified 76.1%

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

   if 4.59999999999999969e-242 < t < 4.0000000000000003e-130 or 4.8000000000000002e48 < t < 2.1999999999999999e90

   1. Initial program 84.4%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 69.4%

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

      1. div-sub 69.4%

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

   6. Simplified 69.4%

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

   if 4.0000000000000003e-130 < t < 4.9999999999999996e-72

   1. Initial program 93.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 75.6%

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

   5. Taylor expanded in y around inf 75.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-242}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 5: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 0.0071 \lor \neg \left(t \leq 5.6 \cdot 10^{+48}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a))))
        (t_2 (* y (/ (- z t) (- a t))))
        (t_3 (+ x (* y (/ z a)))))
   (if (<= t -6.5e+94)
     t_2
     (if (<= t -7.6e-85)
       t_1
       (if (<= t 8.5e-174)
         t_3
         (if (<= t 1.35e-116)
           t_1
           (if (<= t 1.6e-58)
             (+ x (/ y (/ a z)))
             (if (or (<= t 0.0071) (not (<= t 5.6e+48))) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (y * (z / a));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -7.6e-85) {
		tmp = t_1;
	} else if (t <= 8.5e-174) {
		tmp = t_3;
	} else if (t <= 1.35e-116) {
		tmp = t_1;
	} else if (t <= 1.6e-58) {
		tmp = x + (y / (a / z));
	} else if ((t <= 0.0071) || !(t <= 5.6e+48)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x - (x * (z / a))
    t_2 = y * ((z - t) / (a - t))
    t_3 = x + (y * (z / a))
    if (t <= (-6.5d+94)) then
        tmp = t_2
    else if (t <= (-7.6d-85)) then
        tmp = t_1
    else if (t <= 8.5d-174) then
        tmp = t_3
    else if (t <= 1.35d-116) then
        tmp = t_1
    else if (t <= 1.6d-58) then
        tmp = x + (y / (a / z))
    else if ((t <= 0.0071d0) .or. (.not. (t <= 5.6d+48))) then
        tmp = t_2
    else
        tmp = t_3
    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 - (x * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (y * (z / a));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -7.6e-85) {
		tmp = t_1;
	} else if (t <= 8.5e-174) {
		tmp = t_3;
	} else if (t <= 1.35e-116) {
		tmp = t_1;
	} else if (t <= 1.6e-58) {
		tmp = x + (y / (a / z));
	} else if ((t <= 0.0071) || !(t <= 5.6e+48)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	t_2 = y * ((z - t) / (a - t))
	t_3 = x + (y * (z / a))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_2
	elif t <= -7.6e-85:
		tmp = t_1
	elif t <= 8.5e-174:
		tmp = t_3
	elif t <= 1.35e-116:
		tmp = t_1
	elif t <= 1.6e-58:
		tmp = x + (y / (a / z))
	elif (t <= 0.0071) or not (t <= 5.6e+48):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_3 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -7.6e-85)
		tmp = t_1;
	elseif (t <= 8.5e-174)
		tmp = t_3;
	elseif (t <= 1.35e-116)
		tmp = t_1;
	elseif (t <= 1.6e-58)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif ((t <= 0.0071) || !(t <= 5.6e+48))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	t_2 = y * ((z - t) / (a - t));
	t_3 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -7.6e-85)
		tmp = t_1;
	elseif (t <= 8.5e-174)
		tmp = t_3;
	elseif (t <= 1.35e-116)
		tmp = t_1;
	elseif (t <= 1.6e-58)
		tmp = x + (y / (a / z));
	elseif ((t <= 0.0071) || ~((t <= 5.6e+48)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+94], t$95$2, If[LessEqual[t, -7.6e-85], t$95$1, If[LessEqual[t, 8.5e-174], t$95$3, If[LessEqual[t, 1.35e-116], t$95$1, If[LessEqual[t, 1.6e-58], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 0.0071], N[Not[LessEqual[t, 5.6e+48]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999976e94 or 1.6e-58 < t < 0.0071000000000000004 or 5.60000000000000025e48 < t

   1. Initial program 44.2%

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

      1. associate-*l/ 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -6.49999999999999976e94 < t < -7.5999999999999997e-85 or 8.4999999999999996e-174 < t < 1.35e-116

   1. Initial program 84.5%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in y around 0 58.9%

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

      1. associate-*r/ 64.1%

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

      2. mul-1-neg 64.1%

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

      3. neg-sub0 64.1%

         \[\leadsto x + \color{blue}{\left(0 - x \cdot \frac{z}{a}\right)} \]

      4. associate-+r- 64.1%

         \[\leadsto \color{blue}{\left(x + 0\right) - x \cdot \frac{z}{a}} \]

      5. +-rgt-identity 64.1%

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

   7. Simplified 64.1%

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

   if -7.5999999999999997e-85 < t < 8.4999999999999996e-174 or 0.0071000000000000004 < t < 5.60000000000000025e48

   1. Initial program 89.0%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around 0 80.1%

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

   5. Taylor expanded in y around inf 69.2%

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

      1. associate-*r/ 72.5%

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

   7. Simplified 72.5%

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

   if 1.35e-116 < t < 1.6e-58

   1. Initial program 92.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 72.1%

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

   5. Taylor expanded in y around inf 72.1%

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

      1. associate-*r/ 72.0%

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

   7. Simplified 72.0%

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

      1. associate-*r/ 72.1%

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

      2. associate-/l* 72.1%

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

   9. Applied egg-rr 72.1%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 0.0071 \lor \neg \left(t \leq 5.6 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 6: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ (* (- x y) (- a z)) t))))
   (if (<= a -3.5e-40)
     (- x (/ (- t z) (/ a (- y x))))
     (if (<= a 1.16e-213)
       t_1
       (if (<= a 2.8e-112)
         (* y (/ (- z t) (- a t)))
         (if (<= a 9.5e-14)
           t_1
           (if (<= a 2.4e+54)
             (+ x (/ (- y x) (/ (- a t) z)))
             (+ x (* (- z t) (/ y (- a t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (((x - y) * (a - z)) / t);
	double tmp;
	if (a <= -3.5e-40) {
		tmp = x - ((t - z) / (a / (y - x)));
	} else if (a <= 1.16e-213) {
		tmp = t_1;
	} else if (a <= 2.8e-112) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.5e-14) {
		tmp = t_1;
	} else if (a <= 2.4e+54) {
		tmp = x + ((y - x) / ((a - 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) :: t_1
    real(8) :: tmp
    t_1 = y - (((x - y) * (a - z)) / t)
    if (a <= (-3.5d-40)) then
        tmp = x - ((t - z) / (a / (y - x)))
    else if (a <= 1.16d-213) then
        tmp = t_1
    else if (a <= 2.8d-112) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 9.5d-14) then
        tmp = t_1
    else if (a <= 2.4d+54) then
        tmp = x + ((y - x) / ((a - 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 t_1 = y - (((x - y) * (a - z)) / t);
	double tmp;
	if (a <= -3.5e-40) {
		tmp = x - ((t - z) / (a / (y - x)));
	} else if (a <= 1.16e-213) {
		tmp = t_1;
	} else if (a <= 2.8e-112) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 9.5e-14) {
		tmp = t_1;
	} else if (a <= 2.4e+54) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (((x - y) * (a - z)) / t)
	tmp = 0
	if a <= -3.5e-40:
		tmp = x - ((t - z) / (a / (y - x)))
	elif a <= 1.16e-213:
		tmp = t_1
	elif a <= 2.8e-112:
		tmp = y * ((z - t) / (a - t))
	elif a <= 9.5e-14:
		tmp = t_1
	elif a <= 2.4e+54:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t))
	tmp = 0.0
	if (a <= -3.5e-40)
		tmp = Float64(x - Float64(Float64(t - z) / Float64(a / Float64(y - x))));
	elseif (a <= 1.16e-213)
		tmp = t_1;
	elseif (a <= 2.8e-112)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 9.5e-14)
		tmp = t_1;
	elseif (a <= 2.4e+54)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - 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)
	t_1 = y - (((x - y) * (a - z)) / t);
	tmp = 0.0;
	if (a <= -3.5e-40)
		tmp = x - ((t - z) / (a / (y - x)));
	elseif (a <= 1.16e-213)
		tmp = t_1;
	elseif (a <= 2.8e-112)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 9.5e-14)
		tmp = t_1;
	elseif (a <= 2.4e+54)
		tmp = x + ((y - x) / ((a - t) / z));
	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[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-40], N[(x - N[(N[(t - z), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e-213], t$95$1, If[LessEqual[a, 2.8e-112], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-14], t$95$1, If[LessEqual[a, 2.4e+54], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / 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 5 regimes

2. if a < -3.5000000000000002e-40

   1. Initial program 76.2%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-/l* 80.6%

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

   6. Simplified 80.6%

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

   if -3.5000000000000002e-40 < a < 1.15999999999999994e-213 or 2.80000000000000023e-112 < a < 9.4999999999999999e-14

   1. Initial program 63.3%

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

      1. associate-*l/ 65.3%

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

   3. Simplified 65.3%

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

      1. *-commutative 65.3%

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

      2. clear-num 65.1%

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

      3. un-div-inv 66.4%

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

   5. Applied egg-rr 66.4%

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

   6. Taylor expanded in t around -inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. distribute-rgt-out-- 84.9%

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

      3. associate-*r* 84.9%

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

      4. mul-1-neg 84.9%

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

      5. neg-sub0 84.9%

         \[\leadsto y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]

      6. associate--r- 84.9%

         \[\leadsto y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]

      7. neg-sub0 84.9%

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

      8. +-commutative 84.9%

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

      9. sub-neg 84.9%

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

   8. Simplified 84.9%

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

   if 1.15999999999999994e-213 < a < 2.80000000000000023e-112

   1. Initial program 65.9%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around 0 79.5%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

   if 9.4999999999999999e-14 < a < 2.39999999999999998e54

   1. Initial program 88.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 94.2%

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

   if 2.39999999999999998e54 < a

   1. Initial program 67.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 84.8%

      \[\leadsto x + \color{blue}{\frac{y}{a - t}} \cdot \left(z - t\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{t - z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-213}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 7: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a - t}{z}}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;y - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ (- a t) z))))
        (t_2 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -6.5e+94)
     t_2
     (if (<= t -2.1e-22)
       t_1
       (if (<= t -2.8e-45)
         (- y (* x (/ z (- a t))))
         (if (<= t -2e-68)
           (+ x (/ y (/ t (- t z))))
           (if (<= t 4.1e+74) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / ((a - t) / z));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -2.1e-22) {
		tmp = t_1;
	} else if (t <= -2.8e-45) {
		tmp = y - (x * (z / (a - t)));
	} else if (t <= -2e-68) {
		tmp = x + (y / (t / (t - z)));
	} else if (t <= 4.1e+74) {
		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 + ((y - x) / ((a - t) / z))
    t_2 = y + ((x - y) / (t / (z - a)))
    if (t <= (-6.5d+94)) then
        tmp = t_2
    else if (t <= (-2.1d-22)) then
        tmp = t_1
    else if (t <= (-2.8d-45)) then
        tmp = y - (x * (z / (a - t)))
    else if (t <= (-2d-68)) then
        tmp = x + (y / (t / (t - z)))
    else if (t <= 4.1d+74) 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 + ((y - x) / ((a - t) / z));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -2.1e-22) {
		tmp = t_1;
	} else if (t <= -2.8e-45) {
		tmp = y - (x * (z / (a - t)));
	} else if (t <= -2e-68) {
		tmp = x + (y / (t / (t - z)));
	} else if (t <= 4.1e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / ((a - t) / z))
	t_2 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_2
	elif t <= -2.1e-22:
		tmp = t_1
	elif t <= -2.8e-45:
		tmp = y - (x * (z / (a - t)))
	elif t <= -2e-68:
		tmp = x + (y / (t / (t - z)))
	elif t <= 4.1e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -2.1e-22)
		tmp = t_1;
	elseif (t <= -2.8e-45)
		tmp = Float64(y - Float64(x * Float64(z / Float64(a - t))));
	elseif (t <= -2e-68)
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	elseif (t <= 4.1e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / ((a - t) / z));
	t_2 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -2.1e-22)
		tmp = t_1;
	elseif (t <= -2.8e-45)
		tmp = y - (x * (z / (a - t)));
	elseif (t <= -2e-68)
		tmp = x + (y / (t / (t - z)));
	elseif (t <= 4.1e+74)
		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[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $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, -6.5e+94], t$95$2, If[LessEqual[t, -2.1e-22], t$95$1, If[LessEqual[t, -2.8e-45], N[(y - N[(x * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-68], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+74], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999976e94 or 4.1e74 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. distribute-rgt-out-- 73.6%

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

      3. associate-/l* 86.2%

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

   6. Simplified 86.2%

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

   if -6.49999999999999976e94 < t < -2.10000000000000008e-22 or -2.00000000000000013e-68 < t < 4.1e74

   1. Initial program 85.7%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -2.10000000000000008e-22 < t < -2.8000000000000001e-45

   1. Initial program 77.3%

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

      1. associate-*l/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in x around -inf 99.6%

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

   5. Taylor expanded in z around inf 99.3%

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

      1. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in t around inf 93.3%

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

   if -2.8000000000000001e-45 < t < -2.00000000000000013e-68

   1. Initial program 100.0%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in y around inf 53.4%

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

   5. Taylor expanded in a around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

      3. *-commutative 76.3%

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

      4. distribute-lft-neg-in 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in y around 0 76.3%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;y - x \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 8: 45.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= a -3.5e-6)
     x
     (if (<= a -3.2e-293)
       t_2
       (if (<= a 8.6e-299)
         t_1
         (if (<= a 4.2e-277)
           t_2
           (if (<= a 1.2e-213) t_1 (if (<= a 3.05e+140) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.5e-6) {
		tmp = x;
	} else if (a <= -3.2e-293) {
		tmp = t_2;
	} else if (a <= 8.6e-299) {
		tmp = t_1;
	} else if (a <= 4.2e-277) {
		tmp = t_2;
	} else if (a <= 1.2e-213) {
		tmp = t_1;
	} else if (a <= 3.05e+140) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z / t)
    t_2 = y * (1.0d0 - (z / t))
    if (a <= (-3.5d-6)) then
        tmp = x
    else if (a <= (-3.2d-293)) then
        tmp = t_2
    else if (a <= 8.6d-299) then
        tmp = t_1
    else if (a <= 4.2d-277) then
        tmp = t_2
    else if (a <= 1.2d-213) then
        tmp = t_1
    else if (a <= 3.05d+140) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.5e-6) {
		tmp = x;
	} else if (a <= -3.2e-293) {
		tmp = t_2;
	} else if (a <= 8.6e-299) {
		tmp = t_1;
	} else if (a <= 4.2e-277) {
		tmp = t_2;
	} else if (a <= 1.2e-213) {
		tmp = t_1;
	} else if (a <= 3.05e+140) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if a <= -3.5e-6:
		tmp = x
	elif a <= -3.2e-293:
		tmp = t_2
	elif a <= 8.6e-299:
		tmp = t_1
	elif a <= 4.2e-277:
		tmp = t_2
	elif a <= 1.2e-213:
		tmp = t_1
	elif a <= 3.05e+140:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (a <= -3.5e-6)
		tmp = x;
	elseif (a <= -3.2e-293)
		tmp = t_2;
	elseif (a <= 8.6e-299)
		tmp = t_1;
	elseif (a <= 4.2e-277)
		tmp = t_2;
	elseif (a <= 1.2e-213)
		tmp = t_1;
	elseif (a <= 3.05e+140)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (a <= -3.5e-6)
		tmp = x;
	elseif (a <= -3.2e-293)
		tmp = t_2;
	elseif (a <= 8.6e-299)
		tmp = t_1;
	elseif (a <= 4.2e-277)
		tmp = t_2;
	elseif (a <= 1.2e-213)
		tmp = t_1;
	elseif (a <= 3.05e+140)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-6], x, If[LessEqual[a, -3.2e-293], t$95$2, If[LessEqual[a, 8.6e-299], t$95$1, If[LessEqual[a, 4.2e-277], t$95$2, If[LessEqual[a, 1.2e-213], t$95$1, If[LessEqual[a, 3.05e+140], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.49999999999999995e-6 or 3.0499999999999998e140 < a

   1. Initial program 76.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 55.7%

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

   if -3.49999999999999995e-6 < a < -3.20000000000000005e-293 or 8.59999999999999959e-299 < a < 4.1999999999999999e-277 or 1.19999999999999998e-213 < a < 3.0499999999999998e140

   1. Initial program 65.1%

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

      1. associate-*l/ 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in a around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-/l* 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in y around inf 54.0%

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

   if -3.20000000000000005e-293 < a < 8.59999999999999959e-299 or 4.1999999999999999e-277 < a < 1.19999999999999998e-213

   1. Initial program 70.0%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in a around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. *-commutative 57.5%

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

      3. associate-/l* 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x around -inf 78.4%

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

      1. associate-/l* 78.5%

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

   9. Simplified 78.5%

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

       1. div-inv 78.6%

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

       2. *-commutative 78.6%

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

       3. clear-num 78.6%

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

   11. Applied egg-rr 78.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-295}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= a -3.5e-6)
     x
     (if (<= a -8.2e-200)
       t_1
       (if (<= a 2.2e-295)
         (* z (/ (- x y) t))
         (if (<= a 4.2e-277)
           t_1
           (if (<= a 3.5e-213) (* x (/ z t)) (if (<= a 1.7e+140) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.5e-6) {
		tmp = x;
	} else if (a <= -8.2e-200) {
		tmp = t_1;
	} else if (a <= 2.2e-295) {
		tmp = z * ((x - y) / t);
	} else if (a <= 4.2e-277) {
		tmp = t_1;
	} else if (a <= 3.5e-213) {
		tmp = x * (z / t);
	} else if (a <= 1.7e+140) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (1.0d0 - (z / t))
    if (a <= (-3.5d-6)) then
        tmp = x
    else if (a <= (-8.2d-200)) then
        tmp = t_1
    else if (a <= 2.2d-295) then
        tmp = z * ((x - y) / t)
    else if (a <= 4.2d-277) then
        tmp = t_1
    else if (a <= 3.5d-213) then
        tmp = x * (z / t)
    else if (a <= 1.7d+140) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (a <= -3.5e-6) {
		tmp = x;
	} else if (a <= -8.2e-200) {
		tmp = t_1;
	} else if (a <= 2.2e-295) {
		tmp = z * ((x - y) / t);
	} else if (a <= 4.2e-277) {
		tmp = t_1;
	} else if (a <= 3.5e-213) {
		tmp = x * (z / t);
	} else if (a <= 1.7e+140) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if a <= -3.5e-6:
		tmp = x
	elif a <= -8.2e-200:
		tmp = t_1
	elif a <= 2.2e-295:
		tmp = z * ((x - y) / t)
	elif a <= 4.2e-277:
		tmp = t_1
	elif a <= 3.5e-213:
		tmp = x * (z / t)
	elif a <= 1.7e+140:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (a <= -3.5e-6)
		tmp = x;
	elseif (a <= -8.2e-200)
		tmp = t_1;
	elseif (a <= 2.2e-295)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 4.2e-277)
		tmp = t_1;
	elseif (a <= 3.5e-213)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.7e+140)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (a <= -3.5e-6)
		tmp = x;
	elseif (a <= -8.2e-200)
		tmp = t_1;
	elseif (a <= 2.2e-295)
		tmp = z * ((x - y) / t);
	elseif (a <= 4.2e-277)
		tmp = t_1;
	elseif (a <= 3.5e-213)
		tmp = x * (z / t);
	elseif (a <= 1.7e+140)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-6], x, If[LessEqual[a, -8.2e-200], t$95$1, If[LessEqual[a, 2.2e-295], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-277], t$95$1, If[LessEqual[a, 3.5e-213], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+140], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.49999999999999995e-6 or 1.7e140 < a

   1. Initial program 76.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 55.7%

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

   if -3.49999999999999995e-6 < a < -8.19999999999999974e-200 or 2.2000000000000002e-295 < a < 4.1999999999999999e-277 or 3.50000000000000017e-213 < a < 1.7e140

   1. Initial program 67.2%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in a around 0 40.5%

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

      1. mul-1-neg 40.5%

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

      2. *-commutative 40.5%

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

      3. associate-/l* 48.8%

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

   6. Simplified 48.8%

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

   7. Taylor expanded in y around inf 55.3%

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

   if -8.19999999999999974e-200 < a < 2.2000000000000002e-295

   1. Initial program 58.7%

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

      1. associate-*l/ 59.1%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in a around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. *-commutative 54.2%

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

      3. associate-/l* 54.6%

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

   6. Simplified 54.6%

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

   7. Taylor expanded in z around -inf 60.9%

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

      1. associate-*r/ 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 56.8%

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

      4. neg-mul-1 56.8%

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

      5. distribute-neg-frac 56.8%

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

      6. neg-sub0 56.8%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{t} \cdot z \]

      7. associate--r- 56.8%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + x}}{t} \cdot z \]

      8. neg-sub0 56.8%

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

      9. +-commutative 56.8%

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

      10. sub-neg 56.8%

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

   9. Simplified 56.8%

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

   if 4.1999999999999999e-277 < a < 3.50000000000000017e-213

   1. Initial program 65.5%

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

      1. associate-*l/ 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in a around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 46.8%

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

   6. Simplified 46.8%

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

   7. Taylor expanded in x around -inf 68.9%

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

      1. associate-/l* 69.0%

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

   9. Simplified 69.0%

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

       1. div-inv 69.0%

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

       2. *-commutative 69.0%

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

       3. clear-num 69.0%

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

   11. Applied egg-rr 69.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-295}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* (- z t) (/ y a)))))
   (if (<= t -6.5e+94)
     t_1
     (if (<= t -4.6e-85)
       (- x (* x (/ z a)))
       (if (<= t 4.6e-242)
         t_2
         (if (<= t 6.5e-116)
           (* z (/ (- y x) (- a t)))
           (if (<= t 3.8e+49) t_2 t_1)))))))

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 + ((z - t) * (y / a));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= -4.6e-85) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.6e-242) {
		tmp = t_2;
	} else if (t <= 6.5e-116) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 3.8e+49) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + ((z - t) * (y / a))
    if (t <= (-6.5d+94)) then
        tmp = t_1
    else if (t <= (-4.6d-85)) then
        tmp = x - (x * (z / a))
    else if (t <= 4.6d-242) then
        tmp = t_2
    else if (t <= 6.5d-116) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 3.8d+49) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= -4.6e-85) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.6e-242) {
		tmp = t_2;
	} else if (t <= 6.5e-116) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 3.8e+49) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + ((z - t) * (y / a))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_1
	elif t <= -4.6e-85:
		tmp = x - (x * (z / a))
	elif t <= 4.6e-242:
		tmp = t_2
	elif t <= 6.5e-116:
		tmp = z * ((y - x) / (a - t))
	elif t <= 3.8e+49:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = t_1;
	elseif (t <= -4.6e-85)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 4.6e-242)
		tmp = t_2;
	elseif (t <= 6.5e-116)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 3.8e+49)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + ((z - t) * (y / a));
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = t_1;
	elseif (t <= -4.6e-85)
		tmp = x - (x * (z / a));
	elseif (t <= 4.6e-242)
		tmp = t_2;
	elseif (t <= 6.5e-116)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 3.8e+49)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+94], t$95$1, If[LessEqual[t, -4.6e-85], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-242], t$95$2, If[LessEqual[t, 6.5e-116], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+49], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999976e94 or 3.7999999999999999e49 < t

   1. Initial program 42.2%

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

      1. associate-*l/ 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in x around 0 44.0%

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

      1. associate-*r/ 71.1%

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

   6. Simplified 71.1%

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

   if -6.49999999999999976e94 < t < -4.6000000000000001e-85

   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* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around 0 67.7%

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

   5. Taylor expanded in y around 0 54.3%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. neg-sub0 59.2%

         \[\leadsto x + \color{blue}{\left(0 - x \cdot \frac{z}{a}\right)} \]

      4. associate-+r- 59.2%

         \[\leadsto \color{blue}{\left(x + 0\right) - x \cdot \frac{z}{a}} \]

      5. +-rgt-identity 59.2%

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

   7. Simplified 59.2%

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

   if -4.6000000000000001e-85 < t < 4.59999999999999969e-242 or 6.5000000000000001e-116 < t < 3.7999999999999999e49

   1. Initial program 87.1%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 78.6%

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

   5. Taylor expanded in a around inf 72.6%

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

   if 4.59999999999999969e-242 < t < 6.5000000000000001e-116

   1. Initial program 91.7%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 72.2%

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

      1. div-sub 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-242}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 11: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -6.5e+94)
     t_2
     (if (<= t -5e-85)
       t_1
       (if (<= t 3.3e-171)
         (+ x (* y (/ z a)))
         (if (<= t 9.8e-117)
           t_1
           (if (<= t 1.85e+78) (+ x (/ y (/ a z))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -5e-85) {
		tmp = t_1;
	} else if (t <= 3.3e-171) {
		tmp = x + (y * (z / a));
	} else if (t <= 9.8e-117) {
		tmp = t_1;
	} else if (t <= 1.85e+78) {
		tmp = x + (y / (a / z));
	} 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 - (x * (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-6.5d+94)) then
        tmp = t_2
    else if (t <= (-5d-85)) then
        tmp = t_1
    else if (t <= 3.3d-171) then
        tmp = x + (y * (z / a))
    else if (t <= 9.8d-117) then
        tmp = t_1
    else if (t <= 1.85d+78) then
        tmp = x + (y / (a / z))
    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 - (x * (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -6.5e+94) {
		tmp = t_2;
	} else if (t <= -5e-85) {
		tmp = t_1;
	} else if (t <= 3.3e-171) {
		tmp = x + (y * (z / a));
	} else if (t <= 9.8e-117) {
		tmp = t_1;
	} else if (t <= 1.85e+78) {
		tmp = x + (y / (a / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_2
	elif t <= -5e-85:
		tmp = t_1
	elif t <= 3.3e-171:
		tmp = x + (y * (z / a))
	elif t <= 9.8e-117:
		tmp = t_1
	elif t <= 1.85e+78:
		tmp = x + (y / (a / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -5e-85)
		tmp = t_1;
	elseif (t <= 3.3e-171)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 9.8e-117)
		tmp = t_1;
	elseif (t <= 1.85e+78)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = t_2;
	elseif (t <= -5e-85)
		tmp = t_1;
	elseif (t <= 3.3e-171)
		tmp = x + (y * (z / a));
	elseif (t <= 9.8e-117)
		tmp = t_1;
	elseif (t <= 1.85e+78)
		tmp = x + (y / (a / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+94], t$95$2, If[LessEqual[t, -5e-85], t$95$1, If[LessEqual[t, 3.3e-171], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-117], t$95$1, If[LessEqual[t, 1.85e+78], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999976e94 or 1.84999999999999992e78 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in a around 0 33.1%

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

      1. mul-1-neg 33.1%

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

      2. *-commutative 33.1%

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

      3. associate-/l* 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in y around inf 67.5%

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

   if -6.49999999999999976e94 < t < -5.0000000000000002e-85 or 3.3000000000000002e-171 < t < 9.7999999999999995e-117

   1. Initial program 84.5%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in y around 0 58.9%

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

      1. associate-*r/ 64.1%

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

      2. mul-1-neg 64.1%

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

      3. neg-sub0 64.1%

         \[\leadsto x + \color{blue}{\left(0 - x \cdot \frac{z}{a}\right)} \]

      4. associate-+r- 64.1%

         \[\leadsto \color{blue}{\left(x + 0\right) - x \cdot \frac{z}{a}} \]

      5. +-rgt-identity 64.1%

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

   7. Simplified 64.1%

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

   if -5.0000000000000002e-85 < t < 3.3000000000000002e-171

   1. Initial program 91.3%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in t around 0 82.2%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. associate-*r/ 73.3%

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

   7. Simplified 73.3%

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

   if 9.7999999999999995e-117 < t < 1.84999999999999992e78

   1. Initial program 78.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around 0 56.7%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. associate-*r/ 54.5%

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

   7. Simplified 54.5%

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

      1. associate-*r/ 50.0%

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

      2. associate-/l* 54.5%

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

   9. Applied egg-rr 54.5%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-117}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 12: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 0.021 \lor \neg \left(t \leq 5.2 \cdot 10^{+48}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.25e+95)
     t_1
     (if (<= t 1.95e-64)
       (+ x (/ z (/ a (- y x))))
       (if (or (<= t 0.021) (not (<= t 5.2e+48)))
         t_1
         (+ x (* (- z t) (/ 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 <= -1.25e+95) {
		tmp = t_1;
	} else if (t <= 1.95e-64) {
		tmp = x + (z / (a / (y - x)));
	} else if ((t <= 0.021) || !(t <= 5.2e+48)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (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 <= (-1.25d+95)) then
        tmp = t_1
    else if (t <= 1.95d-64) then
        tmp = x + (z / (a / (y - x)))
    else if ((t <= 0.021d0) .or. (.not. (t <= 5.2d+48))) then
        tmp = t_1
    else
        tmp = x + ((z - t) * (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 <= -1.25e+95) {
		tmp = t_1;
	} else if (t <= 1.95e-64) {
		tmp = x + (z / (a / (y - x)));
	} else if ((t <= 0.021) || !(t <= 5.2e+48)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.25e+95:
		tmp = t_1
	elif t <= 1.95e-64:
		tmp = x + (z / (a / (y - x)))
	elif (t <= 0.021) or not (t <= 5.2e+48):
		tmp = t_1
	else:
		tmp = x + ((z - t) * (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 <= -1.25e+95)
		tmp = t_1;
	elseif (t <= 1.95e-64)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif ((t <= 0.021) || !(t <= 5.2e+48))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(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 <= -1.25e+95)
		tmp = t_1;
	elseif (t <= 1.95e-64)
		tmp = x + (z / (a / (y - x)));
	elseif ((t <= 0.021) || ~((t <= 5.2e+48)))
		tmp = t_1;
	else
		tmp = x + ((z - t) * (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, -1.25e+95], t$95$1, If[LessEqual[t, 1.95e-64], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 0.021], N[Not[LessEqual[t, 5.2e+48]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000006e95 or 1.9499999999999998e-64 < t < 0.0210000000000000013 or 5.1999999999999999e48 < t

   1. Initial program 44.2%

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

      1. associate-*l/ 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -1.25000000000000006e95 < t < 1.9499999999999998e-64

   1. Initial program 88.8%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around 0 73.5%

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

      1. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

   if 0.0210000000000000013 < t < 5.1999999999999999e48

   1. Initial program 75.7%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in a around inf 67.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 0.021 \lor \neg \left(t \leq 5.2 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-11} \lor \neg \left(t \leq 2.2 \cdot 10^{+49}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -6.5e+94)
     t_1
     (if (<= t 4.2e-63)
       (+ x (/ (- y x) (/ a z)))
       (if (or (<= t 3.4e-11) (not (<= t 2.2e+49)))
         t_1
         (+ x (* (- z t) (/ 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 <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= 4.2e-63) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 3.4e-11) || !(t <= 2.2e+49)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (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 <= (-6.5d+94)) then
        tmp = t_1
    else if (t <= 4.2d-63) then
        tmp = x + ((y - x) / (a / z))
    else if ((t <= 3.4d-11) .or. (.not. (t <= 2.2d+49))) then
        tmp = t_1
    else
        tmp = x + ((z - t) * (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 <= -6.5e+94) {
		tmp = t_1;
	} else if (t <= 4.2e-63) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 3.4e-11) || !(t <= 2.2e+49)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -6.5e+94:
		tmp = t_1
	elif t <= 4.2e-63:
		tmp = x + ((y - x) / (a / z))
	elif (t <= 3.4e-11) or not (t <= 2.2e+49):
		tmp = t_1
	else:
		tmp = x + ((z - t) * (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 <= -6.5e+94)
		tmp = t_1;
	elseif (t <= 4.2e-63)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif ((t <= 3.4e-11) || !(t <= 2.2e+49))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(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 <= -6.5e+94)
		tmp = t_1;
	elseif (t <= 4.2e-63)
		tmp = x + ((y - x) / (a / z));
	elseif ((t <= 3.4e-11) || ~((t <= 2.2e+49)))
		tmp = t_1;
	else
		tmp = x + ((z - t) * (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, -6.5e+94], t$95$1, If[LessEqual[t, 4.2e-63], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.4e-11], N[Not[LessEqual[t, 2.2e+49]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.49999999999999976e94 or 4.2e-63 < t < 3.3999999999999999e-11 or 2.2000000000000001e49 < t

   1. Initial program 44.2%

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

      1. associate-*l/ 63.4%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 70.7%

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

   6. Simplified 70.7%

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

   if -6.49999999999999976e94 < t < 4.2e-63

   1. Initial program 88.8%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around 0 77.3%

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

   if 3.3999999999999999e-11 < t < 2.2000000000000001e49

   1. Initial program 75.7%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in a around inf 67.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-11} \lor \neg \left(t \leq 2.2 \cdot 10^{+49}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-8} \lor \neg \left(t \leq 5 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+95)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 1.4e-50)
     (+ x (/ (- y x) (/ a z)))
     (if (or (<= t 4.3e-8) (not (<= t 5e+48)))
       (* y (/ (- z t) (- a t)))
       (+ x (* (- z t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+95) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.4e-50) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 4.3e-8) || !(t <= 5e+48)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d+95)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 1.4d-50) then
        tmp = x + ((y - x) / (a / z))
    else if ((t <= 4.3d-8) .or. (.not. (t <= 5d+48))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + ((z - t) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+95) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.4e-50) {
		tmp = x + ((y - x) / (a / z));
	} else if ((t <= 4.3e-8) || !(t <= 5e+48)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+95:
		tmp = y / ((a - t) / (z - t))
	elif t <= 1.4e-50:
		tmp = x + ((y - x) / (a / z))
	elif (t <= 4.3e-8) or not (t <= 5e+48):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+95)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 1.4e-50)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif ((t <= 4.3e-8) || !(t <= 5e+48))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+95)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 1.4e-50)
		tmp = x + ((y - x) / (a / z));
	elseif ((t <= 4.3e-8) || ~((t <= 5e+48)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+95], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-50], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.3e-8], N[Not[LessEqual[t, 5e+48]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4e95

   1. Initial program 37.9%

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

      1. associate-*l/ 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 45.8%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -2.4e95 < t < 1.3999999999999999e-50

   1. Initial program 88.8%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in t around 0 77.3%

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

   if 1.3999999999999999e-50 < t < 4.3000000000000001e-8 or 4.99999999999999973e48 < t

   1. Initial program 47.7%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in x around 0 45.6%

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

      1. associate-*r/ 68.7%

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

   6. Simplified 68.7%

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

   if 4.3000000000000001e-8 < t < 4.99999999999999973e48

   1. Initial program 75.7%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in a around inf 67.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-8} \lor \neg \left(t \leq 5 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 15: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+165}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+94)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 1.35e-116)
     (+ x (/ (- y x) (/ a z)))
     (if (<= t 8e+165)
       (+ x (* (- z t) (/ y (- a t))))
       (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+94) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.35e-116) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 8e+165) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d+94)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 1.35d-116) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 8d+165) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+94) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 1.35e-116) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 8e+165) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+94:
		tmp = y / ((a - t) / (z - t))
	elif t <= 1.35e-116:
		tmp = x + ((y - x) / (a / z))
	elif t <= 8e+165:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+94)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 1.35e-116)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 8e+165)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+94)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 1.35e-116)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 8e+165)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+94], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-116], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+165], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999976e94

   1. Initial program 37.9%

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

      1. associate-*l/ 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 45.8%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -6.49999999999999976e94 < t < 1.35e-116

   1. Initial program 88.4%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around 0 77.9%

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

   if 1.35e-116 < t < 7.9999999999999992e165

   1. Initial program 68.4%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in y around inf 73.3%

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

   if 7.9999999999999992e165 < t

   1. Initial program 35.9%

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

      1. associate-*l/ 56.8%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in x around 0 41.2%

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

      1. associate-*r/ 77.4%

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

   6. Simplified 77.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+165}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 16: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-102} \lor \neg \left(a \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.1e-102) (not (<= a 1.35e-139)))
   (+ x (* (- z t) (/ (- y x) (- a t))))
   (- y (/ (* (- x y) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.1e-102) || !(a <= 1.35e-139)) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.1d-102)) .or. (.not. (a <= 1.35d-139))) then
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    else
        tmp = y - (((x - y) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.1e-102) || !(a <= 1.35e-139)) {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	} else {
		tmp = y - (((x - y) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.1e-102) or not (a <= 1.35e-139):
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	else:
		tmp = y - (((x - y) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.1e-102) || !(a <= 1.35e-139))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.1e-102) || ~((a <= 1.35e-139)))
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	else
		tmp = y - (((x - y) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.1e-102], N[Not[LessEqual[a, 1.35e-139]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.0999999999999997e-102 or 1.3499999999999999e-139 < a

   1. Initial program 74.1%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   if -6.0999999999999997e-102 < a < 1.3499999999999999e-139

   1. Initial program 59.8%

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

      1. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

      1. *-commutative 59.3%

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

      2. clear-num 59.1%

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

      3. un-div-inv 59.7%

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

   5. Applied egg-rr 59.7%

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

   6. Taylor expanded in t around -inf 90.0%

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

      1. associate-*r/ 90.0%

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

      2. distribute-rgt-out-- 90.0%

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

      3. associate-*r* 90.0%

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

      4. mul-1-neg 90.0%

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

      5. neg-sub0 90.0%

         \[\leadsto y + \frac{\color{blue}{\left(0 - \left(y - x\right)\right)} \cdot \left(z - a\right)}{t} \]

      6. associate--r- 90.0%

         \[\leadsto y + \frac{\color{blue}{\left(\left(0 - y\right) + x\right)} \cdot \left(z - a\right)}{t} \]

      7. neg-sub0 90.0%

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

      8. +-commutative 90.0%

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

      9. sub-neg 90.0%

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

   8. Simplified 90.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-102} \lor \neg \left(a \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 17: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+95)
   (/ y (/ (- a t) (- z t)))
   (if (<= t 4.5e+90)
     (+ x (/ (- y x) (/ (- a t) z)))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+95) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 4.5e+90) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.3d+95)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 4.5d+90) then
        tmp = x + ((y - x) / ((a - t) / z))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+95) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 4.5e+90) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+95:
		tmp = y / ((a - t) / (z - t))
	elif t <= 4.5e+90:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+95)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 4.5e+90)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+95)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 4.5e+90)
		tmp = x + ((y - x) / ((a - t) / z));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+95], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+90], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.29999999999999997e95

   1. Initial program 37.9%

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

      1. associate-*l/ 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 45.8%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -2.29999999999999997e95 < t < 4.5e90

   1. Initial program 84.8%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around inf 81.4%

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

   if 4.5e90 < t

   1. Initial program 40.8%

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

      1. associate-*l/ 66.1%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in x around 0 44.1%

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

      1. associate-*r/ 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 18: 55.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+95} \lor \neg \left(t \leq 1.15 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.16e+95) (not (<= t 1.15e+76)))
   (* y (- 1.0 (/ z t)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.16e+95) || !(t <= 1.15e+76)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.16d+95)) .or. (.not. (t <= 1.15d+76))) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.16e+95) || !(t <= 1.15e+76)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.16e+95) or not (t <= 1.15e+76):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.16e+95) || !(t <= 1.15e+76))
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.16e+95) || ~((t <= 1.15e+76)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.16e+95], N[Not[LessEqual[t, 1.15e+76]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1599999999999999e95 or 1.15000000000000001e76 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in a around 0 33.1%

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

      1. mul-1-neg 33.1%

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

      2. *-commutative 33.1%

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

      3. associate-/l* 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in y around inf 67.5%

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

   if -1.1599999999999999e95 < t < 1.15000000000000001e76

   1. Initial program 85.7%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around 0 72.3%

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

   5. Taylor expanded in y around inf 57.6%

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

      1. associate-*r/ 59.4%

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

   7. Simplified 59.4%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+95} \lor \neg \left(t \leq 1.15 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 19: 38.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+229} \lor \neg \left(z \leq 5.5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.22e+229) (not (<= z 5.5e+82))) (* y (/ z a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+229) || !(z <= 5.5e+82)) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.22d+229)) .or. (.not. (z <= 5.5d+82))) then
        tmp = y * (z / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.22e+229) || !(z <= 5.5e+82)) {
		tmp = y * (z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.22e+229) or not (z <= 5.5e+82):
		tmp = y * (z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.22e+229) || !(z <= 5.5e+82))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.22e+229) || ~((z <= 5.5e+82)))
		tmp = y * (z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.22e+229], N[Not[LessEqual[z, 5.5e+82]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2200000000000001e229 or 5.49999999999999997e82 < z

   1. Initial program 72.8%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around 0 62.0%

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

   5. Taylor expanded in y around inf 43.0%

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

   6. Taylor expanded in x around 0 37.4%

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

      1. associate-*r/ 41.9%

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

   8. Simplified 41.9%

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

   if -1.2200000000000001e229 < z < 5.49999999999999997e82

   1. Initial program 68.4%

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

      1. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in y around inf 65.9%

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

   5. Taylor expanded in t around inf 45.8%

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

      1. +-commutative 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+229} \lor \neg \left(z \leq 5.5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 20: 38.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e+96) y (if (<= t 3.2e+77) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+96) {
		tmp = y;
	} else if (t <= 3.2e+77) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d+96)) then
        tmp = y
    else if (t <= 3.2d+77) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e+96) {
		tmp = y;
	} else if (t <= 3.2e+77) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e+96:
		tmp = y
	elif t <= 3.2e+77:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e+96)
		tmp = y;
	elseif (t <= 3.2e+77)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e+96)
		tmp = y;
	elseif (t <= 3.2e+77)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e+96], y, If[LessEqual[t, 3.2e+77], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999993e96 or 3.2000000000000002e77 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around inf 56.4%

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

   if -2.39999999999999993e96 < t < 3.2000000000000002e77

   1. Initial program 85.7%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in a around inf 36.4%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 25.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. associate-*l/ 78.1%

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

3. Simplified 78.1%

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

4. Taylor expanded in a around inf 27.2%

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

5. Final simplification 27.2%

   \[\leadsto x \]

Developer target: 86.8% accurate, 0.7× 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 2023301 
(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))))