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

Percentage Accurate: 68.2% → 88.3%

Time: 21.5s

Alternatives: 26

Speedup: 0.8×

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: 68.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+205} \lor \neg \left(t \leq 4 \cdot 10^{+207}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+205) (not (<= t 4e+207)))
   (+ y (/ (- x y) (/ t (- z a))))
   (fma (/ (- z t) (- a t)) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+205) || !(t <= 4e+207)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+205) || !(t <= 4e+207))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+205], N[Not[LessEqual[t, 4e+207]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999998e205 or 4.0000000000000002e207 < t

   1. Initial program 21.3%

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

      1. +-commutative 21.3%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. fma-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in t around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. cancel-sign-sub-inv 62.5%

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

      3. metadata-eval 62.5%

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

      4. *-lft-identity 62.5%

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

      5. distribute-lft-in 62.3%

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

      6. mul-1-neg 62.3%

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

      7. distribute-rgt-neg-in 62.3%

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

      8. mul-1-neg 62.3%

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

      9. *-commutative 62.3%

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

      10. cancel-sign-sub 62.3%

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

      11. mul-1-neg 62.3%

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

      12. associate-*r* 62.3%

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

      13. distribute-lft-out-- 62.3%

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

      14. associate-*r/ 62.3%

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

      15. mul-1-neg 62.3%

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

   6. Simplified 93.6%

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

   if -3.4999999999999998e205 < t < 4.0000000000000002e207

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. associate-*r/ 92.7%

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

      3. *-commutative 92.7%

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

      4. fma-def 92.7%

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

   3. Simplified 92.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+205} \lor \neg \left(t \leq 4 \cdot 10^{+207}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-258} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- z t) (- x y)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (- t z) (/ (- a t) y)))
     (if (or (<= t_1 -1e-258) (and (not (<= t_1 0.0)) (<= t_1 2e+299)))
       t_1
       (- y (/ (- y x) (/ t (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if ((t_1 <= -1e-258) || (!(t_1 <= 0.0) && (t_1 <= 2e+299))) {
		tmp = t_1;
	} else {
		tmp = y - ((y - x) / (t / (z - a)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((z - t) * (x - y)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((t - z) / ((a - t) / y));
	} else if ((t_1 <= -1e-258) || (!(t_1 <= 0.0) && (t_1 <= 2e+299))) {
		tmp = t_1;
	} else {
		tmp = y - ((y - x) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((z - t) * (x - y)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((t - z) / ((a - t) / y))
	elif (t_1 <= -1e-258) or (not (t_1 <= 0.0) and (t_1 <= 2e+299)):
		tmp = t_1
	else:
		tmp = y - ((y - x) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(z - t) * Float64(x - y)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)));
	elseif ((t_1 <= -1e-258) || (!(t_1 <= 0.0) && (t_1 <= 2e+299)))
		tmp = t_1;
	else
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((z - t) * (x - y)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((t - z) / ((a - t) / y));
	elseif ((t_1 <= -1e-258) || (~((t_1 <= 0.0)) && (t_1 <= 2e+299)))
		tmp = t_1;
	else
		tmp = y - ((y - x) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(z - t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-258], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+299]]], t$95$1, N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 31.4%

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

      1. *-commutative 31.4%

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

      2. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.99999999999999954e-259 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.0000000000000001e299

   1. Initial program 98.5%

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

   if -9.99999999999999954e-259 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0 or 2.0000000000000001e299 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 22.6%

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

      1. +-commutative 22.6%

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

      2. associate-*r/ 64.4%

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

      3. *-commutative 64.4%

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

      4. fma-def 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. cancel-sign-sub-inv 51.5%

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

      3. metadata-eval 51.5%

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

      4. *-lft-identity 51.5%

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

      5. distribute-lft-in 51.4%

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

      6. mul-1-neg 51.4%

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

      7. distribute-rgt-neg-in 51.4%

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

      8. mul-1-neg 51.4%

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

      9. *-commutative 51.4%

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

      10. cancel-sign-sub 51.4%

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

      11. mul-1-neg 51.4%

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

      12. associate-*r* 51.4%

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

      13. distribute-lft-out-- 51.4%

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

      14. associate-*r/ 51.4%

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

      15. mul-1-neg 51.4%

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

   6. Simplified 70.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq -\infty:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq -1 \cdot 10^{-258} \lor \neg \left(x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq 0\right) \land x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot \left(x - y\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := x - \frac{t - z}{\frac{a - t}{y}}\\ t_3 := y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-101}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x)))))
        (t_2 (- x (/ (- t z) (/ (- a t) y))))
        (t_3 (- y (/ (- y x) (/ t (- z a))))))
   (if (<= a -6e+132)
     t_2
     (if (<= a -1.45e-21)
       t_1
       (if (<= a -4.4e-81)
         t_3
         (if (<= a -1.65e-101)
           (/ (- y x) (/ (- a t) z))
           (if (<= a -8.6e-138)
             (* y (/ (- z t) (- a t)))
             (if (<= a 1.02e+18)
               t_3
               (if (<= a 1.8e+45) t_1 (if (<= a 2.1e+54) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x - ((t - z) / ((a - t) / y));
	double t_3 = y - ((y - x) / (t / (z - a)));
	double tmp;
	if (a <= -6e+132) {
		tmp = t_2;
	} else if (a <= -1.45e-21) {
		tmp = t_1;
	} else if (a <= -4.4e-81) {
		tmp = t_3;
	} else if (a <= -1.65e-101) {
		tmp = (y - x) / ((a - t) / z);
	} else if (a <= -8.6e-138) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.02e+18) {
		tmp = t_3;
	} else if (a <= 1.8e+45) {
		tmp = t_1;
	} else if (a <= 2.1e+54) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = x - ((t - z) / ((a - t) / y))
    t_3 = y - ((y - x) / (t / (z - a)))
    if (a <= (-6d+132)) then
        tmp = t_2
    else if (a <= (-1.45d-21)) then
        tmp = t_1
    else if (a <= (-4.4d-81)) then
        tmp = t_3
    else if (a <= (-1.65d-101)) then
        tmp = (y - x) / ((a - t) / z)
    else if (a <= (-8.6d-138)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1.02d+18) then
        tmp = t_3
    else if (a <= 1.8d+45) then
        tmp = t_1
    else if (a <= 2.1d+54) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = x - ((t - z) / ((a - t) / y));
	double t_3 = y - ((y - x) / (t / (z - a)));
	double tmp;
	if (a <= -6e+132) {
		tmp = t_2;
	} else if (a <= -1.45e-21) {
		tmp = t_1;
	} else if (a <= -4.4e-81) {
		tmp = t_3;
	} else if (a <= -1.65e-101) {
		tmp = (y - x) / ((a - t) / z);
	} else if (a <= -8.6e-138) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.02e+18) {
		tmp = t_3;
	} else if (a <= 1.8e+45) {
		tmp = t_1;
	} else if (a <= 2.1e+54) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = x - ((t - z) / ((a - t) / y))
	t_3 = y - ((y - x) / (t / (z - a)))
	tmp = 0
	if a <= -6e+132:
		tmp = t_2
	elif a <= -1.45e-21:
		tmp = t_1
	elif a <= -4.4e-81:
		tmp = t_3
	elif a <= -1.65e-101:
		tmp = (y - x) / ((a - t) / z)
	elif a <= -8.6e-138:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1.02e+18:
		tmp = t_3
	elif a <= 1.8e+45:
		tmp = t_1
	elif a <= 2.1e+54:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)))
	t_3 = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (a <= -6e+132)
		tmp = t_2;
	elseif (a <= -1.45e-21)
		tmp = t_1;
	elseif (a <= -4.4e-81)
		tmp = t_3;
	elseif (a <= -1.65e-101)
		tmp = Float64(Float64(y - x) / Float64(Float64(a - t) / z));
	elseif (a <= -8.6e-138)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1.02e+18)
		tmp = t_3;
	elseif (a <= 1.8e+45)
		tmp = t_1;
	elseif (a <= 2.1e+54)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = x - ((t - z) / ((a - t) / y));
	t_3 = y - ((y - x) / (t / (z - a)));
	tmp = 0.0;
	if (a <= -6e+132)
		tmp = t_2;
	elseif (a <= -1.45e-21)
		tmp = t_1;
	elseif (a <= -4.4e-81)
		tmp = t_3;
	elseif (a <= -1.65e-101)
		tmp = (y - x) / ((a - t) / z);
	elseif (a <= -8.6e-138)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1.02e+18)
		tmp = t_3;
	elseif (a <= 1.8e+45)
		tmp = t_1;
	elseif (a <= 2.1e+54)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+132], t$95$2, If[LessEqual[a, -1.45e-21], t$95$1, If[LessEqual[a, -4.4e-81], t$95$3, If[LessEqual[a, -1.65e-101], N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.6e-138], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+18], t$95$3, If[LessEqual[a, 1.8e+45], t$95$1, If[LessEqual[a, 2.1e+54], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.9999999999999996e132 or 2.09999999999999986e54 < a

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 87.7%

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

   if -5.9999999999999996e132 < a < -1.45e-21 or 1.02e18 < a < 1.8e45

   1. Initial program 79.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. div-inv 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in t around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-/l* 88.0%

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

   8. Simplified 88.0%

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

   if -1.45e-21 < a < -4.3999999999999998e-81 or -8.6000000000000001e-138 < a < 1.02e18 or 1.8e45 < a < 2.09999999999999986e54

   1. Initial program 60.8%

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

      1. +-commutative 60.8%

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

      2. associate-*r/ 75.2%

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

      3. *-commutative 75.2%

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

      4. fma-def 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in t around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. cancel-sign-sub-inv 75.6%

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

      3. metadata-eval 75.6%

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

      4. *-lft-identity 75.6%

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

      5. distribute-lft-in 75.6%

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

      6. mul-1-neg 75.6%

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

      7. distribute-rgt-neg-in 75.6%

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

      8. mul-1-neg 75.6%

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

      9. *-commutative 75.6%

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

      10. cancel-sign-sub 75.6%

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

      11. mul-1-neg 75.6%

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

      12. associate-*r* 75.6%

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

      13. distribute-lft-out-- 75.6%

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

      14. associate-*r/ 75.6%

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

      15. mul-1-neg 75.6%

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

   6. Simplified 84.8%

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

   if -4.3999999999999998e-81 < a < -1.64999999999999992e-101

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-*r/ 96.2%

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

      3. *-commutative 96.2%

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

      4. fma-def 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around inf 90.7%

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

      1. div-sub 90.7%

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

      2. *-commutative 90.7%

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

      3. associate-*l/ 65.5%

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

      4. associate-/l* 91.1%

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

   6. Simplified 91.1%

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

   if -1.64999999999999992e-101 < a < -8.6000000000000001e-138

   1. Initial program 62.1%

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

      1. +-commutative 62.1%

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

      2. associate-*r/ 80.8%

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

      3. *-commutative 80.8%

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

      4. fma-def 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in y around inf 72.6%

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

      1. div-sub 72.6%

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

      2. *-commutative 72.6%

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

   6. Simplified 72.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+132}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-81}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-101}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 4: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x + \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (+ x (/ z (/ a y)))))
   (if (<= a -4.1e+98)
     t_2
     (if (<= a -1.5e-21)
       (* z (/ (- y x) a))
       (if (<= a -1.04e-162)
         t_1
         (if (<= a -2.8e-190)
           (/ (- x) (/ t (- a z)))
           (if (<= a 9.2e-237)
             t_1
             (if (<= a 2.35e-157)
               (/ z (/ t (- x y)))
               (if (<= a 1e+18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -4.1e+98) {
		tmp = t_2;
	} else if (a <= -1.5e-21) {
		tmp = z * ((y - x) / a);
	} else if (a <= -1.04e-162) {
		tmp = t_1;
	} else if (a <= -2.8e-190) {
		tmp = -x / (t / (a - z));
	} else if (a <= 9.2e-237) {
		tmp = t_1;
	} else if (a <= 2.35e-157) {
		tmp = z / (t / (x - y));
	} else if (a <= 1e+18) {
		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 = y * (1.0d0 - (z / t))
    t_2 = x + (z / (a / y))
    if (a <= (-4.1d+98)) then
        tmp = t_2
    else if (a <= (-1.5d-21)) then
        tmp = z * ((y - x) / a)
    else if (a <= (-1.04d-162)) then
        tmp = t_1
    else if (a <= (-2.8d-190)) then
        tmp = -x / (t / (a - z))
    else if (a <= 9.2d-237) then
        tmp = t_1
    else if (a <= 2.35d-157) then
        tmp = z / (t / (x - y))
    else if (a <= 1d+18) 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 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -4.1e+98) {
		tmp = t_2;
	} else if (a <= -1.5e-21) {
		tmp = z * ((y - x) / a);
	} else if (a <= -1.04e-162) {
		tmp = t_1;
	} else if (a <= -2.8e-190) {
		tmp = -x / (t / (a - z));
	} else if (a <= 9.2e-237) {
		tmp = t_1;
	} else if (a <= 2.35e-157) {
		tmp = z / (t / (x - y));
	} else if (a <= 1e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x + (z / (a / y))
	tmp = 0
	if a <= -4.1e+98:
		tmp = t_2
	elif a <= -1.5e-21:
		tmp = z * ((y - x) / a)
	elif a <= -1.04e-162:
		tmp = t_1
	elif a <= -2.8e-190:
		tmp = -x / (t / (a - z))
	elif a <= 9.2e-237:
		tmp = t_1
	elif a <= 2.35e-157:
		tmp = z / (t / (x - y))
	elif a <= 1e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x + Float64(z / Float64(a / y)))
	tmp = 0.0
	if (a <= -4.1e+98)
		tmp = t_2;
	elseif (a <= -1.5e-21)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= -1.04e-162)
		tmp = t_1;
	elseif (a <= -2.8e-190)
		tmp = Float64(Float64(-x) / Float64(t / Float64(a - z)));
	elseif (a <= 9.2e-237)
		tmp = t_1;
	elseif (a <= 2.35e-157)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 1e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x + (z / (a / y));
	tmp = 0.0;
	if (a <= -4.1e+98)
		tmp = t_2;
	elseif (a <= -1.5e-21)
		tmp = z * ((y - x) / a);
	elseif (a <= -1.04e-162)
		tmp = t_1;
	elseif (a <= -2.8e-190)
		tmp = -x / (t / (a - z));
	elseif (a <= 9.2e-237)
		tmp = t_1;
	elseif (a <= 2.35e-157)
		tmp = z / (t / (x - y));
	elseif (a <= 1e+18)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+98], t$95$2, If[LessEqual[a, -1.5e-21], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.04e-162], t$95$1, If[LessEqual[a, -2.8e-190], N[((-x) / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-237], t$95$1, If[LessEqual[a, 2.35e-157], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+18], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.1e98 or 1e18 < a

   1. Initial program 65.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. div-inv 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in t around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-/l* 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in y around inf 65.1%

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

   if -4.1e98 < a < -1.49999999999999996e-21

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

      4. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in t around 0 80.6%

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

      1. div-sub 80.6%

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

   7. Simplified 80.6%

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

   if -1.49999999999999996e-21 < a < -1.04000000000000001e-162 or -2.80000000000000005e-190 < a < 9.20000000000000046e-237 or 2.3500000000000001e-157 < a < 1e18

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-*r/ 81.5%

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

      3. *-commutative 81.5%

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

      4. fma-def 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in a around 0 43.7%

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

      1. +-commutative 43.7%

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

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

      4. associate-/l* 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in y around inf 60.6%

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

   if -1.04000000000000001e-162 < a < -2.80000000000000005e-190

   1. Initial program 59.9%

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

      1. associate-/l* 61.1%

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

   3. Simplified 61.1%

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

      1. div-inv 60.5%

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

   5. Applied egg-rr 60.5%

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

   6. Taylor expanded in x around inf 61.1%

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

      1. div-sub 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. div-sub 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in t around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. *-commutative 99.7%

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

       3. mul-1-neg 99.7%

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

       4. +-commutative 99.7%

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

       5. sub-neg 99.7%

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

       6. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if 9.20000000000000046e-237 < a < 2.3500000000000001e-157

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*r/ 62.5%

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

      3. *-commutative 62.5%

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

      4. fma-def 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in a around 0 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. div-sub 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*r/ 62.8%

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

      5. neg-mul-1 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in z around 0 57.5%

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

      1. associate-/l* 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 10^{+18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x + \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (+ x (/ z (/ a y)))))
   (if (<= a -1.1e+103)
     t_2
     (if (<= a -5e-22)
       (* z (/ (- y x) a))
       (if (<= a -4.1e-156)
         t_1
         (if (<= a -2.8e-190)
           (/ (- x) (/ t (- a z)))
           (if (<= a 1.42e-236)
             t_1
             (if (<= a 3.6e-158)
               (* z (/ (- x y) t))
               (if (<= a 8.8e+17) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -1.1e+103) {
		tmp = t_2;
	} else if (a <= -5e-22) {
		tmp = z * ((y - x) / a);
	} else if (a <= -4.1e-156) {
		tmp = t_1;
	} else if (a <= -2.8e-190) {
		tmp = -x / (t / (a - z));
	} else if (a <= 1.42e-236) {
		tmp = t_1;
	} else if (a <= 3.6e-158) {
		tmp = z * ((x - y) / t);
	} else if (a <= 8.8e+17) {
		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 = y * (1.0d0 - (z / t))
    t_2 = x + (z / (a / y))
    if (a <= (-1.1d+103)) then
        tmp = t_2
    else if (a <= (-5d-22)) then
        tmp = z * ((y - x) / a)
    else if (a <= (-4.1d-156)) then
        tmp = t_1
    else if (a <= (-2.8d-190)) then
        tmp = -x / (t / (a - z))
    else if (a <= 1.42d-236) then
        tmp = t_1
    else if (a <= 3.6d-158) then
        tmp = z * ((x - y) / t)
    else if (a <= 8.8d+17) 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 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -1.1e+103) {
		tmp = t_2;
	} else if (a <= -5e-22) {
		tmp = z * ((y - x) / a);
	} else if (a <= -4.1e-156) {
		tmp = t_1;
	} else if (a <= -2.8e-190) {
		tmp = -x / (t / (a - z));
	} else if (a <= 1.42e-236) {
		tmp = t_1;
	} else if (a <= 3.6e-158) {
		tmp = z * ((x - y) / t);
	} else if (a <= 8.8e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x + (z / (a / y))
	tmp = 0
	if a <= -1.1e+103:
		tmp = t_2
	elif a <= -5e-22:
		tmp = z * ((y - x) / a)
	elif a <= -4.1e-156:
		tmp = t_1
	elif a <= -2.8e-190:
		tmp = -x / (t / (a - z))
	elif a <= 1.42e-236:
		tmp = t_1
	elif a <= 3.6e-158:
		tmp = z * ((x - y) / t)
	elif a <= 8.8e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x + Float64(z / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.1e+103)
		tmp = t_2;
	elseif (a <= -5e-22)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= -4.1e-156)
		tmp = t_1;
	elseif (a <= -2.8e-190)
		tmp = Float64(Float64(-x) / Float64(t / Float64(a - z)));
	elseif (a <= 1.42e-236)
		tmp = t_1;
	elseif (a <= 3.6e-158)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (a <= 8.8e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x + (z / (a / y));
	tmp = 0.0;
	if (a <= -1.1e+103)
		tmp = t_2;
	elseif (a <= -5e-22)
		tmp = z * ((y - x) / a);
	elseif (a <= -4.1e-156)
		tmp = t_1;
	elseif (a <= -2.8e-190)
		tmp = -x / (t / (a - z));
	elseif (a <= 1.42e-236)
		tmp = t_1;
	elseif (a <= 3.6e-158)
		tmp = z * ((x - y) / t);
	elseif (a <= 8.8e+17)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+103], t$95$2, If[LessEqual[a, -5e-22], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.1e-156], t$95$1, If[LessEqual[a, -2.8e-190], N[((-x) / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-236], t$95$1, If[LessEqual[a, 3.6e-158], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+17], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.09999999999999996e103 or 8.8e17 < a

   1. Initial program 65.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. div-inv 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in t around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-/l* 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in y around inf 65.1%

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

   if -1.09999999999999996e103 < a < -4.99999999999999954e-22

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

      4. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in t around 0 80.6%

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

      1. div-sub 80.6%

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

   7. Simplified 80.6%

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

   if -4.99999999999999954e-22 < a < -4.1000000000000002e-156 or -2.80000000000000005e-190 < a < 1.41999999999999996e-236 or 3.59999999999999991e-158 < a < 8.8e17

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-*r/ 81.5%

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

      3. *-commutative 81.5%

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

      4. fma-def 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in a around 0 43.7%

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

      1. +-commutative 43.7%

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

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

      4. associate-/l* 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in y around inf 60.6%

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

   if -4.1000000000000002e-156 < a < -2.80000000000000005e-190

   1. Initial program 59.9%

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

      1. associate-/l* 61.1%

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

   3. Simplified 61.1%

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

      1. div-inv 60.5%

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

   5. Applied egg-rr 60.5%

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

   6. Taylor expanded in x around inf 61.1%

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

      1. div-sub 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. div-sub 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in t around inf 99.7%

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

       1. mul-1-neg 99.7%

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

       2. *-commutative 99.7%

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

       3. mul-1-neg 99.7%

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

       4. +-commutative 99.7%

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

       5. sub-neg 99.7%

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

       6. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if 1.41999999999999996e-236 < a < 3.59999999999999991e-158

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*r/ 62.5%

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

      3. *-commutative 62.5%

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

      4. fma-def 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in a around 0 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. div-sub 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*r/ 62.8%

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

      5. neg-mul-1 62.8%

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

   7. Simplified 62.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+103}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{-x}{\frac{t}{a - z}}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- t z) (/ (- a t) y)))))
   (if (<= a -2.7e+132)
     t_1
     (if (<= a -2.5e-22)
       (+ x (/ z (/ a (- y x))))
       (if (<= a -3e-68)
         t_1
         (if (<= a -5.5e-106)
           (/ (- y x) (/ (- a t) z))
           (if (<= a 9.5e+17) (+ y (/ (* (- y x) (- a z)) t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - z) / ((a - t) / y));
	double tmp;
	if (a <= -2.7e+132) {
		tmp = t_1;
	} else if (a <= -2.5e-22) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -3e-68) {
		tmp = t_1;
	} else if (a <= -5.5e-106) {
		tmp = (y - x) / ((a - t) / z);
	} else if (a <= 9.5e+17) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t - z) / ((a - t) / y))
    if (a <= (-2.7d+132)) then
        tmp = t_1
    else if (a <= (-2.5d-22)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= (-3d-68)) then
        tmp = t_1
    else if (a <= (-5.5d-106)) then
        tmp = (y - x) / ((a - t) / z)
    else if (a <= 9.5d+17) then
        tmp = y + (((y - x) * (a - z)) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - z) / ((a - t) / y));
	double tmp;
	if (a <= -2.7e+132) {
		tmp = t_1;
	} else if (a <= -2.5e-22) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= -3e-68) {
		tmp = t_1;
	} else if (a <= -5.5e-106) {
		tmp = (y - x) / ((a - t) / z);
	} else if (a <= 9.5e+17) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t - z) / ((a - t) / y))
	tmp = 0
	if a <= -2.7e+132:
		tmp = t_1
	elif a <= -2.5e-22:
		tmp = x + (z / (a / (y - x)))
	elif a <= -3e-68:
		tmp = t_1
	elif a <= -5.5e-106:
		tmp = (y - x) / ((a - t) / z)
	elif a <= 9.5e+17:
		tmp = y + (((y - x) * (a - z)) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (a <= -2.7e+132)
		tmp = t_1;
	elseif (a <= -2.5e-22)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= -3e-68)
		tmp = t_1;
	elseif (a <= -5.5e-106)
		tmp = Float64(Float64(y - x) / Float64(Float64(a - t) / z));
	elseif (a <= 9.5e+17)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t - z) / ((a - t) / y));
	tmp = 0.0;
	if (a <= -2.7e+132)
		tmp = t_1;
	elseif (a <= -2.5e-22)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= -3e-68)
		tmp = t_1;
	elseif (a <= -5.5e-106)
		tmp = (y - x) / ((a - t) / z);
	elseif (a <= 9.5e+17)
		tmp = y + (((y - x) * (a - z)) / 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[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+132], t$95$1, If[LessEqual[a, -2.5e-22], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-68], t$95$1, If[LessEqual[a, -5.5e-106], N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+17], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7e132 or -2.49999999999999977e-22 < a < -3e-68 or 9.5e17 < a

   1. Initial program 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in y around inf 82.7%

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

   if -2.7e132 < a < -2.49999999999999977e-22

   1. Initial program 77.1%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

      1. div-inv 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in t around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 84.7%

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

   8. Simplified 84.7%

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

   if -3e-68 < a < -5.5000000000000001e-106

   1. Initial program 58.6%

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

      1. +-commutative 58.6%

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

      2. associate-*r/ 96.9%

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

      3. *-commutative 96.9%

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

      4. fma-def 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around inf 81.1%

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

      1. div-sub 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*l/ 52.3%

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

      4. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

   if -5.5000000000000001e-106 < a < 9.5e17

   1. Initial program 62.5%

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

      1. associate-/l* 73.7%

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

   3. Simplified 73.7%

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

      1. div-inv 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in t around -inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. div-sub 75.8%

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

      4. *-commutative 75.8%

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

      5. div-sub 75.9%

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

      6. distribute-rgt-out-- 75.9%

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

   8. Simplified 75.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 7: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{if}\;x \leq -12:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+70} \lor \neg \left(x \leq 3.9 \cdot 10^{+123}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (/ (- t z) (- a t)) 1.0))))
   (if (<= x -12.0)
     t_1
     (if (<= x 1.05e-27)
       (* y (/ (- z t) (- a t)))
       (if (or (<= x 1.6e+70) (not (<= x 3.9e+123)))
         t_1
         (* (- z t) (/ y (- a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (((t - z) / (a - t)) + 1.0);
	double tmp;
	if (x <= -12.0) {
		tmp = t_1;
	} else if (x <= 1.05e-27) {
		tmp = y * ((z - t) / (a - t));
	} else if ((x <= 1.6e+70) || !(x <= 3.9e+123)) {
		tmp = t_1;
	} else {
		tmp = (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 = x * (((t - z) / (a - t)) + 1.0d0)
    if (x <= (-12.0d0)) then
        tmp = t_1
    else if (x <= 1.05d-27) then
        tmp = y * ((z - t) / (a - t))
    else if ((x <= 1.6d+70) .or. (.not. (x <= 3.9d+123))) then
        tmp = t_1
    else
        tmp = (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 = x * (((t - z) / (a - t)) + 1.0);
	double tmp;
	if (x <= -12.0) {
		tmp = t_1;
	} else if (x <= 1.05e-27) {
		tmp = y * ((z - t) / (a - t));
	} else if ((x <= 1.6e+70) || !(x <= 3.9e+123)) {
		tmp = t_1;
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (((t - z) / (a - t)) + 1.0)
	tmp = 0
	if x <= -12.0:
		tmp = t_1
	elif x <= 1.05e-27:
		tmp = y * ((z - t) / (a - t))
	elif (x <= 1.6e+70) or not (x <= 3.9e+123):
		tmp = t_1
	else:
		tmp = (z - t) * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0))
	tmp = 0.0
	if (x <= -12.0)
		tmp = t_1;
	elseif (x <= 1.05e-27)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif ((x <= 1.6e+70) || !(x <= 3.9e+123))
		tmp = t_1;
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (((t - z) / (a - t)) + 1.0);
	tmp = 0.0;
	if (x <= -12.0)
		tmp = t_1;
	elseif (x <= 1.05e-27)
		tmp = y * ((z - t) / (a - t));
	elseif ((x <= 1.6e+70) || ~((x <= 3.9e+123)))
		tmp = t_1;
	else
		tmp = (z - t) * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -12.0], t$95$1, If[LessEqual[x, 1.05e-27], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.6e+70], N[Not[LessEqual[x, 3.9e+123]], $MachinePrecision]], t$95$1, N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -12 or 1.05000000000000008e-27 < x < 1.6000000000000001e70 or 3.89999999999999993e123 < x

   1. Initial program 60.3%

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

      1. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

      1. div-inv 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. div-sub 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. div-sub 67.4%

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

   8. Simplified 67.4%

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

   if -12 < x < 1.05000000000000008e-27

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-*r/ 91.0%

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

      3. *-commutative 91.0%

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

      4. fma-def 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. div-sub 75.7%

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

      2. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   if 1.6000000000000001e70 < x < 3.89999999999999993e123

   1. Initial program 39.2%

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

      1. +-commutative 39.2%

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

      2. associate-*r/ 73.4%

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

      3. *-commutative 73.4%

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

      4. fma-def 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

      2. *-commutative 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in y around 0 38.6%

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

      1. associate-*l/ 72.9%

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

   9. Simplified 72.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+70} \lor \neg \left(x \leq 3.9 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 8: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{-x}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-244}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+99)
   x
   (if (<= a -1.65e-21)
     (* z (/ (- x) a))
     (if (<= a -1.55e-49)
       y
       (if (<= a -1.8e-117)
         (* x (/ z t))
         (if (<= a 1.75e-244)
           y
           (if (<= a 4.4e-158) (/ z (/ t x)) (if (<= a 2.6e+51) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+99) {
		tmp = x;
	} else if (a <= -1.65e-21) {
		tmp = z * (-x / a);
	} else if (a <= -1.55e-49) {
		tmp = y;
	} else if (a <= -1.8e-117) {
		tmp = x * (z / t);
	} else if (a <= 1.75e-244) {
		tmp = y;
	} else if (a <= 4.4e-158) {
		tmp = z / (t / x);
	} else if (a <= 2.6e+51) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d+99)) then
        tmp = x
    else if (a <= (-1.65d-21)) then
        tmp = z * (-x / a)
    else if (a <= (-1.55d-49)) then
        tmp = y
    else if (a <= (-1.8d-117)) then
        tmp = x * (z / t)
    else if (a <= 1.75d-244) then
        tmp = y
    else if (a <= 4.4d-158) then
        tmp = z / (t / x)
    else if (a <= 2.6d+51) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+99) {
		tmp = x;
	} else if (a <= -1.65e-21) {
		tmp = z * (-x / a);
	} else if (a <= -1.55e-49) {
		tmp = y;
	} else if (a <= -1.8e-117) {
		tmp = x * (z / t);
	} else if (a <= 1.75e-244) {
		tmp = y;
	} else if (a <= 4.4e-158) {
		tmp = z / (t / x);
	} else if (a <= 2.6e+51) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+99:
		tmp = x
	elif a <= -1.65e-21:
		tmp = z * (-x / a)
	elif a <= -1.55e-49:
		tmp = y
	elif a <= -1.8e-117:
		tmp = x * (z / t)
	elif a <= 1.75e-244:
		tmp = y
	elif a <= 4.4e-158:
		tmp = z / (t / x)
	elif a <= 2.6e+51:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+99)
		tmp = x;
	elseif (a <= -1.65e-21)
		tmp = Float64(z * Float64(Float64(-x) / a));
	elseif (a <= -1.55e-49)
		tmp = y;
	elseif (a <= -1.8e-117)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.75e-244)
		tmp = y;
	elseif (a <= 4.4e-158)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 2.6e+51)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+99)
		tmp = x;
	elseif (a <= -1.65e-21)
		tmp = z * (-x / a);
	elseif (a <= -1.55e-49)
		tmp = y;
	elseif (a <= -1.8e-117)
		tmp = x * (z / t);
	elseif (a <= 1.75e-244)
		tmp = y;
	elseif (a <= 4.4e-158)
		tmp = z / (t / x);
	elseif (a <= 2.6e+51)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+99], x, If[LessEqual[a, -1.65e-21], N[(z * N[((-x) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-49], y, If[LessEqual[a, -1.8e-117], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-244], y, If[LessEqual[a, 4.4e-158], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+51], y, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.50000000000000007e99 or 2.6000000000000001e51 < a

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. associate-*r/ 93.9%

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

      3. *-commutative 93.9%

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

      4. fma-def 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 53.5%

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

   if -1.50000000000000007e99 < a < -1.65000000000000004e-21

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

      4. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in t around 0 80.6%

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

      1. div-sub 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in y around 0 48.8%

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

      1. neg-mul-1 48.8%

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

      2. distribute-neg-frac 48.8%

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

   10. Simplified 48.8%

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

   if -1.65000000000000004e-21 < a < -1.55e-49 or -1.8e-117 < a < 1.74999999999999996e-244 or 4.4000000000000002e-158 < a < 2.6000000000000001e51

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-*r/ 79.8%

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

      3. *-commutative 79.8%

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

      4. fma-def 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in t around inf 44.5%

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

   if -1.55e-49 < a < -1.8e-117

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-*r/ 88.5%

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

      3. *-commutative 88.5%

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

      4. fma-def 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in a around 0 34.4%

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

      1. +-commutative 34.4%

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

      2. mul-1-neg 34.4%

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

      3. unsub-neg 34.4%

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

      4. associate-/l* 56.0%

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

   6. Simplified 56.0%

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

   7. Taylor expanded in x around -inf 26.1%

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

      1. associate-/l* 38.0%

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

   9. Simplified 38.0%

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

       1. associate-/r/ 38.0%

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

   11. Applied egg-rr 38.0%

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

   if 1.74999999999999996e-244 < a < 4.4000000000000002e-158

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*r/ 62.5%

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

      3. *-commutative 62.5%

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

      4. fma-def 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in a around 0 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. associate-/l* 45.6%

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

   6. Simplified 45.6%

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

   7. Taylor expanded in x around -inf 36.4%

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

      1. associate-/l* 46.7%

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

   9. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{-x}{a}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-49}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-244}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 41.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= t -4.6e+136)
     y
     (if (<= t -1.7e-5)
       t_1
       (if (<= t -4.2e-52)
         x
         (if (<= t -1.18e-60)
           t_1
           (if (<= t 2.2e-120)
             (* z (/ (- y x) a))
             (if (<= t 8.5e+103) x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -4.6e+136) {
		tmp = y;
	} else if (t <= -1.7e-5) {
		tmp = t_1;
	} else if (t <= -4.2e-52) {
		tmp = x;
	} else if (t <= -1.18e-60) {
		tmp = t_1;
	} else if (t <= 2.2e-120) {
		tmp = z * ((y - x) / a);
	} else if (t <= 8.5e+103) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (t <= (-4.6d+136)) then
        tmp = y
    else if (t <= (-1.7d-5)) then
        tmp = t_1
    else if (t <= (-4.2d-52)) then
        tmp = x
    else if (t <= (-1.18d-60)) then
        tmp = t_1
    else if (t <= 2.2d-120) then
        tmp = z * ((y - x) / a)
    else if (t <= 8.5d+103) 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 t_1 = x * (z / t);
	double tmp;
	if (t <= -4.6e+136) {
		tmp = y;
	} else if (t <= -1.7e-5) {
		tmp = t_1;
	} else if (t <= -4.2e-52) {
		tmp = x;
	} else if (t <= -1.18e-60) {
		tmp = t_1;
	} else if (t <= 2.2e-120) {
		tmp = z * ((y - x) / a);
	} else if (t <= 8.5e+103) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if t <= -4.6e+136:
		tmp = y
	elif t <= -1.7e-5:
		tmp = t_1
	elif t <= -4.2e-52:
		tmp = x
	elif t <= -1.18e-60:
		tmp = t_1
	elif t <= 2.2e-120:
		tmp = z * ((y - x) / a)
	elif t <= 8.5e+103:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (t <= -4.6e+136)
		tmp = y;
	elseif (t <= -1.7e-5)
		tmp = t_1;
	elseif (t <= -4.2e-52)
		tmp = x;
	elseif (t <= -1.18e-60)
		tmp = t_1;
	elseif (t <= 2.2e-120)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 8.5e+103)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (t <= -4.6e+136)
		tmp = y;
	elseif (t <= -1.7e-5)
		tmp = t_1;
	elseif (t <= -4.2e-52)
		tmp = x;
	elseif (t <= -1.18e-60)
		tmp = t_1;
	elseif (t <= 2.2e-120)
		tmp = z * ((y - x) / a);
	elseif (t <= 8.5e+103)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+136], y, If[LessEqual[t, -1.7e-5], t$95$1, If[LessEqual[t, -4.2e-52], x, If[LessEqual[t, -1.18e-60], t$95$1, If[LessEqual[t, 2.2e-120], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+103], x, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.6e136 or 8.4999999999999992e103 < t

   1. Initial program 23.1%

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

      1. +-commutative 23.1%

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

      2. associate-*r/ 68.9%

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

      3. *-commutative 68.9%

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

      4. fma-def 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around inf 51.8%

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

   if -4.6e136 < t < -1.7e-5 or -4.1999999999999997e-52 < t < -1.17999999999999994e-60

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-*r/ 83.7%

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

      3. *-commutative 83.7%

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

      4. fma-def 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in a around 0 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

      4. associate-/l* 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in x around -inf 39.3%

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

      1. associate-/l* 42.2%

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

   9. Simplified 42.2%

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

       1. associate-/r/ 44.9%

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

   11. Applied egg-rr 44.9%

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

   if -1.7e-5 < t < -4.1999999999999997e-52 or 2.20000000000000012e-120 < t < 8.4999999999999992e103

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-*r/ 97.2%

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

      3. *-commutative 97.2%

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

      4. fma-def 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around inf 47.4%

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

   if -1.17999999999999994e-60 < t < 2.20000000000000012e-120

   1. Initial program 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-*r/ 97.6%

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

      3. *-commutative 97.6%

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

      4. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 62.9%

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

   5. Taylor expanded in t around 0 54.6%

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

      1. div-sub 55.7%

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

   7. Simplified 55.7%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.18 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ t_2 := x + \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 2.32 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))) (t_2 (+ x (/ z (/ a y)))))
   (if (<= a -1.12e+98)
     t_2
     (if (<= a -1e-21)
       (* z (/ (- y x) a))
       (if (<= a 2.32e-237)
         t_1
         (if (<= a 3.8e-154)
           (/ z (/ t (- x y)))
           (if (<= a 1.02e+18) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -1.12e+98) {
		tmp = t_2;
	} else if (a <= -1e-21) {
		tmp = z * ((y - x) / a);
	} else if (a <= 2.32e-237) {
		tmp = t_1;
	} else if (a <= 3.8e-154) {
		tmp = z / (t / (x - y));
	} else if (a <= 1.02e+18) {
		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 = y * (1.0d0 - (z / t))
    t_2 = x + (z / (a / y))
    if (a <= (-1.12d+98)) then
        tmp = t_2
    else if (a <= (-1d-21)) then
        tmp = z * ((y - x) / a)
    else if (a <= 2.32d-237) then
        tmp = t_1
    else if (a <= 3.8d-154) then
        tmp = z / (t / (x - y))
    else if (a <= 1.02d+18) 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 = y * (1.0 - (z / t));
	double t_2 = x + (z / (a / y));
	double tmp;
	if (a <= -1.12e+98) {
		tmp = t_2;
	} else if (a <= -1e-21) {
		tmp = z * ((y - x) / a);
	} else if (a <= 2.32e-237) {
		tmp = t_1;
	} else if (a <= 3.8e-154) {
		tmp = z / (t / (x - y));
	} else if (a <= 1.02e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	t_2 = x + (z / (a / y))
	tmp = 0
	if a <= -1.12e+98:
		tmp = t_2
	elif a <= -1e-21:
		tmp = z * ((y - x) / a)
	elif a <= 2.32e-237:
		tmp = t_1
	elif a <= 3.8e-154:
		tmp = z / (t / (x - y))
	elif a <= 1.02e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	t_2 = Float64(x + Float64(z / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.12e+98)
		tmp = t_2;
	elseif (a <= -1e-21)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= 2.32e-237)
		tmp = t_1;
	elseif (a <= 3.8e-154)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 1.02e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	t_2 = x + (z / (a / y));
	tmp = 0.0;
	if (a <= -1.12e+98)
		tmp = t_2;
	elseif (a <= -1e-21)
		tmp = z * ((y - x) / a);
	elseif (a <= 2.32e-237)
		tmp = t_1;
	elseif (a <= 3.8e-154)
		tmp = z / (t / (x - y));
	elseif (a <= 1.02e+18)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e+98], t$95$2, If[LessEqual[a, -1e-21], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.32e-237], t$95$1, If[LessEqual[a, 3.8e-154], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+18], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.12e98 or 1.02e18 < a

   1. Initial program 65.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. div-inv 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in t around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-/l* 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in y around inf 65.1%

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

   if -1.12e98 < a < -9.99999999999999908e-22

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

      4. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in t around 0 80.6%

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

      1. div-sub 80.6%

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

   7. Simplified 80.6%

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

   if -9.99999999999999908e-22 < a < 2.3199999999999999e-237 or 3.8000000000000001e-154 < a < 1.02e18

   1. Initial program 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-*r/ 80.5%

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

      3. *-commutative 80.5%

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

      4. fma-def 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. associate-/l* 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in y around inf 58.0%

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

   if 2.3199999999999999e-237 < a < 3.8000000000000001e-154

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*r/ 62.5%

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

      3. *-commutative 62.5%

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

      4. fma-def 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in a around 0 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. div-sub 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*r/ 62.8%

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

      5. neg-mul-1 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in z around 0 57.5%

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

      1. associate-/l* 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 2.32 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.55e+143)
     t_2
     (if (<= t -2.65e+114)
       t_1
       (if (<= t -1.15e-5) (/ z (/ t (- x y))) (if (<= t 2e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = t_2;
	} else if (t <= -2.65e+114) {
		tmp = t_1;
	} else if (t <= -1.15e-5) {
		tmp = z / (t / (x - y));
	} else if (t <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-2.55d+143)) then
        tmp = t_2
    else if (t <= (-2.65d+114)) then
        tmp = t_1
    else if (t <= (-1.15d-5)) then
        tmp = z / (t / (x - y))
    else if (t <= 2d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = t_2;
	} else if (t <= -2.65e+114) {
		tmp = t_1;
	} else if (t <= -1.15e-5) {
		tmp = z / (t / (x - y));
	} else if (t <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.55e+143:
		tmp = t_2
	elif t <= -2.65e+114:
		tmp = t_1
	elif t <= -1.15e-5:
		tmp = z / (t / (x - y))
	elif t <= 2e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.55e+143)
		tmp = t_2;
	elseif (t <= -2.65e+114)
		tmp = t_1;
	elseif (t <= -1.15e-5)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= 2e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.55e+143)
		tmp = t_2;
	elseif (t <= -2.65e+114)
		tmp = t_1;
	elseif (t <= -1.15e-5)
		tmp = z / (t / (x - y));
	elseif (t <= 2e+69)
		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[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+143], t$95$2, If[LessEqual[t, -2.65e+114], t$95$1, If[LessEqual[t, -1.15e-5], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.55000000000000019e143 or 2.0000000000000001e69 < t

   1. Initial program 27.3%

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

      1. +-commutative 27.3%

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

      2. associate-*r/ 70.6%

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

      3. *-commutative 70.6%

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

      4. fma-def 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. div-sub 67.2%

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

      2. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -2.55000000000000019e143 < t < -2.65e114 or -1.15e-5 < t < 2.0000000000000001e69

   1. Initial program 87.8%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

      1. div-inv 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in t around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. *-commutative 65.2%

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

      3. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if -2.65e114 < t < -1.15e-5

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*r/ 80.7%

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

      3. *-commutative 80.7%

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

      4. fma-def 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 60.5%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. distribute-lft-out-- 59.7%

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

      2. div-sub 59.7%

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

      3. *-commutative 59.7%

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

      4. associate-*r/ 59.7%

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

      5. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around 0 47.3%

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

      1. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 12: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.55e+143)
     t_1
     (if (<= t -8.6e+113)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -2.9e-6)
         (/ z (/ t (- x y)))
         (if (<= t 2.3e+98) (- x (/ (- x y) (/ a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = t_1;
	} else if (t <= -8.6e+113) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -2.9e-6) {
		tmp = z / (t / (x - y));
	} else if (t <= 2.3e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-2.55d+143)) then
        tmp = t_1
    else if (t <= (-8.6d+113)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-2.9d-6)) then
        tmp = z / (t / (x - y))
    else if (t <= 2.3d+98) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = t_1;
	} else if (t <= -8.6e+113) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -2.9e-6) {
		tmp = z / (t / (x - y));
	} else if (t <= 2.3e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.55e+143:
		tmp = t_1
	elif t <= -8.6e+113:
		tmp = x + (z / (a / (y - x)))
	elif t <= -2.9e-6:
		tmp = z / (t / (x - y))
	elif t <= 2.3e+98:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.55e+143)
		tmp = t_1;
	elseif (t <= -8.6e+113)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -2.9e-6)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= 2.3e+98)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.55e+143)
		tmp = t_1;
	elseif (t <= -8.6e+113)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -2.9e-6)
		tmp = z / (t / (x - y));
	elseif (t <= 2.3e+98)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+143], t$95$1, If[LessEqual[t, -8.6e+113], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-6], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+98], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.55000000000000019e143 or 2.30000000000000013e98 < t

   1. Initial program 24.2%

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

      1. +-commutative 24.2%

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

      2. associate-*r/ 68.9%

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

      3. *-commutative 68.9%

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

      4. fma-def 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in y around inf 68.6%

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

      1. div-sub 68.6%

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

      2. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   if -2.55000000000000019e143 < t < -8.6000000000000007e113

   1. Initial program 61.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

      1. div-inv 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in t around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. *-commutative 52.4%

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

      3. associate-/l* 70.7%

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

   8. Simplified 70.7%

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

   if -8.6000000000000007e113 < t < -2.9000000000000002e-6

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*r/ 80.7%

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

      3. *-commutative 80.7%

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

      4. fma-def 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 60.5%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. distribute-lft-out-- 59.7%

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

      2. div-sub 59.7%

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

      3. *-commutative 59.7%

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

      4. associate-*r/ 59.7%

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

      5. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around 0 47.3%

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

      1. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

   if -2.9000000000000002e-6 < t < 2.30000000000000013e98

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-*r/ 97.5%

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

      3. *-commutative 97.5%

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

      4. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+143)
   (* y (/ (- z t) (- a t)))
   (if (<= t -8.5e+113)
     (+ x (/ z (/ a (- y x))))
     (if (<= t -4.9e-6)
       (/ z (/ t (- x y)))
       (if (<= t 2e+98)
         (- x (/ (- x y) (/ a z)))
         (/ y (/ (- a t) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+143) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -8.5e+113) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -4.9e-6) {
		tmp = z / (t / (x - y));
	} else if (t <= 2e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.55d+143)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-8.5d+113)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-4.9d-6)) then
        tmp = z / (t / (x - y))
    else if (t <= 2d+98) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y / ((a - t) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+143) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -8.5e+113) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -4.9e-6) {
		tmp = z / (t / (x - y));
	} else if (t <= 2e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+143:
		tmp = y * ((z - t) / (a - t))
	elif t <= -8.5e+113:
		tmp = x + (z / (a / (y - x)))
	elif t <= -4.9e-6:
		tmp = z / (t / (x - y))
	elif t <= 2e+98:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+143)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -8.5e+113)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -4.9e-6)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= 2e+98)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.55e+143)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -8.5e+113)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -4.9e-6)
		tmp = z / (t / (x - y));
	elseif (t <= 2e+98)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+143], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e+113], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.9e-6], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+98], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.55000000000000019e143

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. associate-*r/ 64.4%

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

      3. *-commutative 64.4%

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

      4. fma-def 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.2%

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

      2. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -2.55000000000000019e143 < t < -8.5000000000000001e113

   1. Initial program 61.7%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

      1. div-inv 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in t around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. *-commutative 52.4%

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

      3. associate-/l* 70.7%

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

   8. Simplified 70.7%

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

   if -8.5000000000000001e113 < t < -4.89999999999999967e-6

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*r/ 80.7%

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

      3. *-commutative 80.7%

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

      4. fma-def 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 60.5%

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

   5. Taylor expanded in a around 0 59.7%

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

      1. distribute-lft-out-- 59.7%

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

      2. div-sub 59.7%

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

      3. *-commutative 59.7%

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

      4. associate-*r/ 59.7%

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

      5. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around 0 47.3%

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

      1. associate-/l* 60.0%

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

   10. Simplified 60.0%

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

   if -4.89999999999999967e-6 < t < 2e98

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-*r/ 97.5%

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

      3. *-commutative 97.5%

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

      4. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

   if 2e98 < t

   1. Initial program 20.0%

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

      1. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

      1. div-inv 71.7%

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

   5. Applied egg-rr 71.7%

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

   6. Taylor expanded in x around 0 27.9%

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

      1. associate-/l* 71.1%

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

   8. Simplified 71.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 14: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- t z) (/ (- a t) y)))))
   (if (<= y -3.7e-44)
     t_1
     (if (<= y 2.5e-125)
       (* x (+ (/ (- t z) (- a t)) 1.0))
       (if (<= y 2.7e-24) (* (- y x) (/ z (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - z) / ((a - t) / y));
	double tmp;
	if (y <= -3.7e-44) {
		tmp = t_1;
	} else if (y <= 2.5e-125) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (y <= 2.7e-24) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t - z) / ((a - t) / y))
    if (y <= (-3.7d-44)) then
        tmp = t_1
    else if (y <= 2.5d-125) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (y <= 2.7d-24) then
        tmp = (y - x) * (z / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - z) / ((a - t) / y));
	double tmp;
	if (y <= -3.7e-44) {
		tmp = t_1;
	} else if (y <= 2.5e-125) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (y <= 2.7e-24) {
		tmp = (y - x) * (z / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t - z) / ((a - t) / y))
	tmp = 0
	if y <= -3.7e-44:
		tmp = t_1
	elif y <= 2.5e-125:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif y <= 2.7e-24:
		tmp = (y - x) * (z / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t - z) / Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (y <= -3.7e-44)
		tmp = t_1;
	elseif (y <= 2.5e-125)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (y <= 2.7e-24)
		tmp = Float64(Float64(y - x) * Float64(z / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t - z) / ((a - t) / y));
	tmp = 0.0;
	if (y <= -3.7e-44)
		tmp = t_1;
	elseif (y <= 2.5e-125)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (y <= 2.7e-24)
		tmp = (y - x) * (z / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e-44], t$95$1, If[LessEqual[y, 2.5e-125], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-24], N[(N[(y - x), $MachinePrecision] * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e-44 or 2.70000000000000007e-24 < y

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around inf 77.0%

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

   if -3.7e-44 < y < 2.49999999999999983e-125

   1. Initial program 68.1%

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

      1. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

      1. div-inv 74.5%

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

   5. Applied egg-rr 74.5%

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

   6. Taylor expanded in x around inf 66.2%

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

      1. div-sub 66.2%

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

      2. mul-1-neg 66.2%

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

      3. unsub-neg 66.2%

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

      4. div-sub 66.2%

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

   8. Simplified 66.2%

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

   if 2.49999999999999983e-125 < y < 2.70000000000000007e-24

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-*r/ 85.1%

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

      3. *-commutative 85.1%

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

      4. fma-def 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in z around inf 79.2%

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

      1. div-sub 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l/ 72.1%

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

   6. Simplified 72.1%

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

      1. *-un-lft-identity 72.1%

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

      2. times-frac 79.3%

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

   8. Applied egg-rr 79.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-44}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 15: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+206} \lor \neg \left(t \leq 4.6 \cdot 10^{+207}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+206) (not (<= t 4.6e+207)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+206) || !(t <= 4.6e+207)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.15d+206)) .or. (.not. (t <= 4.6d+207))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+206) || !(t <= 4.6e+207)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+206) or not (t <= 4.6e+207):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+206) || !(t <= 4.6e+207))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+206) || ~((t <= 4.6e+207)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+206], N[Not[LessEqual[t, 4.6e+207]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15000000000000008e206 or 4.59999999999999989e207 < t

   1. Initial program 21.3%

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

      1. +-commutative 21.3%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. fma-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in t around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. cancel-sign-sub-inv 62.5%

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

      3. metadata-eval 62.5%

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

      4. *-lft-identity 62.5%

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

      5. distribute-lft-in 62.3%

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

      6. mul-1-neg 62.3%

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

      7. distribute-rgt-neg-in 62.3%

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

      8. mul-1-neg 62.3%

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

      9. *-commutative 62.3%

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

      10. cancel-sign-sub 62.3%

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

      11. mul-1-neg 62.3%

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

      12. associate-*r* 62.3%

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

      13. distribute-lft-out-- 62.3%

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

      14. associate-*r/ 62.3%

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

      15. mul-1-neg 62.3%

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

   6. Simplified 93.6%

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

   if -1.15000000000000008e206 < t < 4.59999999999999989e207

   1. Initial program 73.6%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+206} \lor \neg \left(t \leq 4.6 \cdot 10^{+207}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 16: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -2.55e+143)
     y
     (if (<= t -1.7e-235)
       t_1
       (if (<= t 7e-260) (* z (/ (- y x) a)) (if (<= t 4.2e+100) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = y;
	} else if (t <= -1.7e-235) {
		tmp = t_1;
	} else if (t <= 7e-260) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.2e+100) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-2.55d+143)) then
        tmp = y
    else if (t <= (-1.7d-235)) then
        tmp = t_1
    else if (t <= 7d-260) then
        tmp = z * ((y - x) / a)
    else if (t <= 4.2d+100) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -2.55e+143) {
		tmp = y;
	} else if (t <= -1.7e-235) {
		tmp = t_1;
	} else if (t <= 7e-260) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.2e+100) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -2.55e+143:
		tmp = y
	elif t <= -1.7e-235:
		tmp = t_1
	elif t <= 7e-260:
		tmp = z * ((y - x) / a)
	elif t <= 4.2e+100:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -2.55e+143)
		tmp = y;
	elseif (t <= -1.7e-235)
		tmp = t_1;
	elseif (t <= 7e-260)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4.2e+100)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -2.55e+143)
		tmp = y;
	elseif (t <= -1.7e-235)
		tmp = t_1;
	elseif (t <= 7e-260)
		tmp = z * ((y - x) / a);
	elseif (t <= 4.2e+100)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e+143], y, If[LessEqual[t, -1.7e-235], t$95$1, If[LessEqual[t, 7e-260], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+100], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.55000000000000019e143 or 4.1999999999999997e100 < t

   1. Initial program 24.2%

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

      1. +-commutative 24.2%

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

      2. associate-*r/ 68.9%

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

      3. *-commutative 68.9%

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

      4. fma-def 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in t around inf 51.8%

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

   if -2.55000000000000019e143 < t < -1.69999999999999986e-235 or 6.9999999999999999e-260 < t < 4.1999999999999997e100

   1. Initial program 84.2%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

      1. div-inv 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in x around inf 57.9%

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

      1. div-sub 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. div-sub 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in t around 0 47.1%

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

   if -1.69999999999999986e-235 < t < 6.9999999999999999e-260

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-*r/ 95.5%

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

      3. *-commutative 95.5%

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

      4. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around inf 77.5%

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

   5. Taylor expanded in t around 0 76.2%

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

      1. div-sub 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-7}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.1e+145)
   (* y (/ (- z t) (- a t)))
   (if (<= t -9e-7)
     (/ (- y x) (/ (- a t) z))
     (if (<= t 1.4e+98) (- x (/ (- x y) (/ a z))) (/ y (/ (- a t) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.1e+145) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -9e-7) {
		tmp = (y - x) / ((a - t) / z);
	} else if (t <= 1.4e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8.1d+145)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-9d-7)) then
        tmp = (y - x) / ((a - t) / z)
    else if (t <= 1.4d+98) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y / ((a - t) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.1e+145) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -9e-7) {
		tmp = (y - x) / ((a - t) / z);
	} else if (t <= 1.4e+98) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y / ((a - t) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.1e+145:
		tmp = y * ((z - t) / (a - t))
	elif t <= -9e-7:
		tmp = (y - x) / ((a - t) / z)
	elif t <= 1.4e+98:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y / ((a - t) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.1e+145)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -9e-7)
		tmp = Float64(Float64(y - x) / Float64(Float64(a - t) / z));
	elseif (t <= 1.4e+98)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.1e+145)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -9e-7)
		tmp = (y - x) / ((a - t) / z);
	elseif (t <= 1.4e+98)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y / ((a - t) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.1e+145], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-7], N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+98], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.1000000000000001e145

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. associate-*r/ 64.4%

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

      3. *-commutative 64.4%

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

      4. fma-def 64.4%

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

   3. Simplified 64.4%

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

   4. Taylor expanded in y around inf 65.2%

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

      1. div-sub 65.2%

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

      2. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -8.1000000000000001e145 < t < -8.99999999999999959e-7

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-*r/ 83.7%

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

      3. *-commutative 83.7%

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

      4. fma-def 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in z around inf 54.9%

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

      1. div-sub 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*l/ 46.7%

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

      4. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   if -8.99999999999999959e-7 < t < 1.4e98

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-*r/ 97.5%

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

      3. *-commutative 97.5%

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

      4. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

   if 1.4e98 < t

   1. Initial program 20.0%

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

      1. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

      1. div-inv 71.7%

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

   5. Applied egg-rr 71.7%

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

   6. Taylor expanded in x around 0 27.9%

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

      1. associate-/l* 71.1%

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

   8. Simplified 71.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-7}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 18: 37.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-196}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+115)
   x
   (if (<= a -1.02e-21)
     (* z (/ y a))
     (if (<= a 3.35e-196)
       y
       (if (<= a 3.4e-152) (* x (/ z t)) (if (<= a 1.6e+52) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+115) {
		tmp = x;
	} else if (a <= -1.02e-21) {
		tmp = z * (y / a);
	} else if (a <= 3.35e-196) {
		tmp = y;
	} else if (a <= 3.4e-152) {
		tmp = x * (z / t);
	} else if (a <= 1.6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+115)) then
        tmp = x
    else if (a <= (-1.02d-21)) then
        tmp = z * (y / a)
    else if (a <= 3.35d-196) then
        tmp = y
    else if (a <= 3.4d-152) then
        tmp = x * (z / t)
    else if (a <= 1.6d+52) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+115) {
		tmp = x;
	} else if (a <= -1.02e-21) {
		tmp = z * (y / a);
	} else if (a <= 3.35e-196) {
		tmp = y;
	} else if (a <= 3.4e-152) {
		tmp = x * (z / t);
	} else if (a <= 1.6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+115:
		tmp = x
	elif a <= -1.02e-21:
		tmp = z * (y / a)
	elif a <= 3.35e-196:
		tmp = y
	elif a <= 3.4e-152:
		tmp = x * (z / t)
	elif a <= 1.6e+52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+115)
		tmp = x;
	elseif (a <= -1.02e-21)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 3.35e-196)
		tmp = y;
	elseif (a <= 3.4e-152)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 1.6e+52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+115)
		tmp = x;
	elseif (a <= -1.02e-21)
		tmp = z * (y / a);
	elseif (a <= 3.35e-196)
		tmp = y;
	elseif (a <= 3.4e-152)
		tmp = x * (z / t);
	elseif (a <= 1.6e+52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+115], x, If[LessEqual[a, -1.02e-21], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.35e-196], y, If[LessEqual[a, 3.4e-152], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+52], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1e115 or 1.6e52 < a

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-*r/ 93.6%

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

      3. *-commutative 93.6%

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

      4. fma-def 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 54.5%

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

   if -1.1e115 < a < -1.02000000000000004e-21

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

      4. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 79.2%

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

      1. div-sub 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l/ 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in a around inf 59.5%

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

   8. Taylor expanded in y around inf 29.8%

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

      1. associate-/l* 39.2%

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

      2. associate-/r/ 39.4%

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

   10. Simplified 39.4%

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

   if -1.02000000000000004e-21 < a < 3.3499999999999998e-196 or 3.39999999999999984e-152 < a < 1.6e52

   1. Initial program 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-*r/ 79.7%

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

      3. *-commutative 79.7%

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

      4. fma-def 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in t around inf 39.6%

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

   if 3.3499999999999998e-196 < a < 3.39999999999999984e-152

   1. Initial program 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-*r/ 70.9%

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

      3. *-commutative 70.9%

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

      4. fma-def 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in a around 0 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. associate-/l* 50.6%

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

   6. Simplified 50.6%

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

   7. Taylor expanded in x around -inf 31.8%

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

      1. associate-/l* 50.6%

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

   9. Simplified 50.6%

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

       1. associate-/r/ 50.8%

          \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]

   11. Applied egg-rr 50.8%

       \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{-196}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 37.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-237}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e+115)
   x
   (if (<= a -8e-22)
     (* z (/ y a))
     (if (<= a 4.2e-237)
       y
       (if (<= a 1.15e-157) (/ z (/ t x)) (if (<= a 4.6e+52) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+115) {
		tmp = x;
	} else if (a <= -8e-22) {
		tmp = z * (y / a);
	} else if (a <= 4.2e-237) {
		tmp = y;
	} else if (a <= 1.15e-157) {
		tmp = z / (t / x);
	} else if (a <= 4.6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d+115)) then
        tmp = x
    else if (a <= (-8d-22)) then
        tmp = z * (y / a)
    else if (a <= 4.2d-237) then
        tmp = y
    else if (a <= 1.15d-157) then
        tmp = z / (t / x)
    else if (a <= 4.6d+52) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+115) {
		tmp = x;
	} else if (a <= -8e-22) {
		tmp = z * (y / a);
	} else if (a <= 4.2e-237) {
		tmp = y;
	} else if (a <= 1.15e-157) {
		tmp = z / (t / x);
	} else if (a <= 4.6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e+115:
		tmp = x
	elif a <= -8e-22:
		tmp = z * (y / a)
	elif a <= 4.2e-237:
		tmp = y
	elif a <= 1.15e-157:
		tmp = z / (t / x)
	elif a <= 4.6e+52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e+115)
		tmp = x;
	elseif (a <= -8e-22)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 4.2e-237)
		tmp = y;
	elseif (a <= 1.15e-157)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 4.6e+52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e+115)
		tmp = x;
	elseif (a <= -8e-22)
		tmp = z * (y / a);
	elseif (a <= 4.2e-237)
		tmp = y;
	elseif (a <= 1.15e-157)
		tmp = z / (t / x);
	elseif (a <= 4.6e+52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e+115], x, If[LessEqual[a, -8e-22], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-237], y, If[LessEqual[a, 1.15e-157], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+52], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4e115 or 4.6e52 < a

   1. Initial program 62.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 54.5%

      \[\leadsto \color{blue}{x} \]

   if -2.4e115 < a < -8.0000000000000004e-22

   1. Initial program 80.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 79.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 79.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 79.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 59.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   6. Simplified 59.5%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   7. Taylor expanded in a around inf 59.5%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a}} \]

   8. Taylor expanded in y around inf 29.8%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 39.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

      2. associate-/r/ 39.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   10. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   if -8.0000000000000004e-22 < a < 4.2000000000000002e-237 or 1.14999999999999994e-157 < a < 4.6e52

   1. Initial program 63.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 39.6%

      \[\leadsto \color{blue}{y} \]

   if 4.2000000000000002e-237 < a < 1.14999999999999994e-157

   1. Initial program 57.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 62.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 62.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 62.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t} + x} \]
   5. Step-by-step derivation

      1. +-commutative 51.0%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 51.0%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(z - t\right) \cdot \left(y - x\right)}{t}\right)} \]

      3. unsub-neg 51.0%

         \[\leadsto \color{blue}{x - \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      4. associate-/l* 45.6%

         \[\leadsto x - \color{blue}{\frac{z - t}{\frac{t}{y - x}}} \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{x - \frac{z - t}{\frac{t}{y - x}}} \]

   7. Taylor expanded in x around -inf 36.4%

      \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 46.7%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   9. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-237}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-237}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+111)
   x
   (if (<= a -5e-23)
     (* y (/ (- z t) a))
     (if (<= a 7.6e-237)
       y
       (if (<= a 2.8e-158) (/ z (/ t x)) (if (<= a 2.15e+51) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+111) {
		tmp = x;
	} else if (a <= -5e-23) {
		tmp = y * ((z - t) / a);
	} else if (a <= 7.6e-237) {
		tmp = y;
	} else if (a <= 2.8e-158) {
		tmp = z / (t / x);
	} else if (a <= 2.15e+51) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d+111)) then
        tmp = x
    else if (a <= (-5d-23)) then
        tmp = y * ((z - t) / a)
    else if (a <= 7.6d-237) then
        tmp = y
    else if (a <= 2.8d-158) then
        tmp = z / (t / x)
    else if (a <= 2.15d+51) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+111) {
		tmp = x;
	} else if (a <= -5e-23) {
		tmp = y * ((z - t) / a);
	} else if (a <= 7.6e-237) {
		tmp = y;
	} else if (a <= 2.8e-158) {
		tmp = z / (t / x);
	} else if (a <= 2.15e+51) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+111:
		tmp = x
	elif a <= -5e-23:
		tmp = y * ((z - t) / a)
	elif a <= 7.6e-237:
		tmp = y
	elif a <= 2.8e-158:
		tmp = z / (t / x)
	elif a <= 2.15e+51:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+111)
		tmp = x;
	elseif (a <= -5e-23)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= 7.6e-237)
		tmp = y;
	elseif (a <= 2.8e-158)
		tmp = Float64(z / Float64(t / x));
	elseif (a <= 2.15e+51)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+111)
		tmp = x;
	elseif (a <= -5e-23)
		tmp = y * ((z - t) / a);
	elseif (a <= 7.6e-237)
		tmp = y;
	elseif (a <= 2.8e-158)
		tmp = z / (t / x);
	elseif (a <= 2.15e+51)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+111], x, If[LessEqual[a, -5e-23], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-237], y, If[LessEqual[a, 2.8e-158], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+51], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6e111 or 2.1499999999999999e51 < a

   1. Initial program 63.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 54.4%

      \[\leadsto \color{blue}{x} \]

   if -1.6e111 < a < -5.0000000000000002e-23

   1. Initial program 77.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 99.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 54.6%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 54.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 54.6%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 54.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in a around inf 49.0%

      \[\leadsto y \cdot \color{blue}{\frac{z - t}{a}} \]

   if -5.0000000000000002e-23 < a < 7.60000000000000047e-237 or 2.80000000000000002e-158 < a < 2.1499999999999999e51

   1. Initial program 63.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 39.6%

      \[\leadsto \color{blue}{y} \]

   if 7.60000000000000047e-237 < a < 2.80000000000000002e-158

   1. Initial program 57.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 62.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 62.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 62.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t} + x} \]
   5. Step-by-step derivation

      1. +-commutative 51.0%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 51.0%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(z - t\right) \cdot \left(y - x\right)}{t}\right)} \]

      3. unsub-neg 51.0%

         \[\leadsto \color{blue}{x - \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      4. associate-/l* 45.6%

         \[\leadsto x - \color{blue}{\frac{z - t}{\frac{t}{y - x}}} \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{x - \frac{z - t}{\frac{t}{y - x}}} \]

   7. Taylor expanded in x around -inf 36.4%

      \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 46.7%

         \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   9. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-237}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+51}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -1.2e+111)
     t_1
     (if (<= a -1.95e-22)
       (* z (/ (- y x) a))
       (if (<= a 1.02e+18) (* y (- 1.0 (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.2e+111) {
		tmp = t_1;
	} else if (a <= -1.95e-22) {
		tmp = z * ((y - x) / a);
	} else if (a <= 1.02e+18) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-1.2d+111)) then
        tmp = t_1
    else if (a <= (-1.95d-22)) then
        tmp = z * ((y - x) / a)
    else if (a <= 1.02d+18) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.2e+111) {
		tmp = t_1;
	} else if (a <= -1.95e-22) {
		tmp = z * ((y - x) / a);
	} else if (a <= 1.02e+18) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -1.2e+111:
		tmp = t_1
	elif a <= -1.95e-22:
		tmp = z * ((y - x) / a)
	elif a <= 1.02e+18:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -1.2e+111)
		tmp = t_1;
	elseif (a <= -1.95e-22)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= 1.02e+18)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -1.2e+111)
		tmp = t_1;
	elseif (a <= -1.95e-22)
		tmp = z * ((y - x) / a);
	elseif (a <= 1.02e+18)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e+111], t$95$1, If[LessEqual[a, -1.95e-22], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+18], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000003e111 or 1.02e18 < a

   1. Initial program 64.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 93.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
   4. Step-by-step derivation

      1. div-inv 93.4%

         \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   5. Applied egg-rr 93.4%

      \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   6. Taylor expanded in x around inf 58.1%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right) \cdot x} \]
   7. Step-by-step derivation

      1. div-sub 58.1%

         \[\leadsto \left(1 + -1 \cdot \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)}\right) \cdot x \]

      2. mul-1-neg 58.1%

         \[\leadsto \left(1 + \color{blue}{\left(-\left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)}\right) \cdot x \]

      3. unsub-neg 58.1%

         \[\leadsto \color{blue}{\left(1 - \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \cdot x \]

      4. div-sub 58.1%

         \[\leadsto \left(1 - \color{blue}{\frac{z - t}{a - t}}\right) \cdot x \]

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\left(1 - \frac{z - t}{a - t}\right) \cdot x} \]

   9. Taylor expanded in t around 0 56.4%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{a}\right)} \cdot x \]

   if -1.20000000000000003e111 < a < -1.94999999999999999e-22

   1. Initial program 77.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 99.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 82.5%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in t around 0 77.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   6. Step-by-step derivation

      1. div-sub 77.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -1.94999999999999999e-22 < a < 1.02e18

   1. Initial program 62.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 78.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 78.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around 0 45.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t} + x} \]
   5. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 45.3%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(z - t\right) \cdot \left(y - x\right)}{t}\right)} \]

      3. unsub-neg 45.3%

         \[\leadsto \color{blue}{x - \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      4. associate-/l* 54.1%

         \[\leadsto x - \color{blue}{\frac{z - t}{\frac{t}{y - x}}} \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{x - \frac{z - t}{\frac{t}{y - x}}} \]

   7. Taylor expanded in y around inf 55.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 22: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a y)))))
   (if (<= a -9.5e+97)
     t_1
     (if (<= a -9.5e-23)
       (* z (/ (- y x) a))
       (if (<= a 8.5e+17) (* y (- 1.0 (/ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double tmp;
	if (a <= -9.5e+97) {
		tmp = t_1;
	} else if (a <= -9.5e-23) {
		tmp = z * ((y - x) / a);
	} else if (a <= 8.5e+17) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (a / y))
    if (a <= (-9.5d+97)) then
        tmp = t_1
    else if (a <= (-9.5d-23)) then
        tmp = z * ((y - x) / a)
    else if (a <= 8.5d+17) then
        tmp = y * (1.0d0 - (z / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double tmp;
	if (a <= -9.5e+97) {
		tmp = t_1;
	} else if (a <= -9.5e-23) {
		tmp = z * ((y - x) / a);
	} else if (a <= 8.5e+17) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / y))
	tmp = 0
	if a <= -9.5e+97:
		tmp = t_1
	elif a <= -9.5e-23:
		tmp = z * ((y - x) / a)
	elif a <= 8.5e+17:
		tmp = y * (1.0 - (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / y)))
	tmp = 0.0
	if (a <= -9.5e+97)
		tmp = t_1;
	elseif (a <= -9.5e-23)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (a <= 8.5e+17)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / y));
	tmp = 0.0;
	if (a <= -9.5e+97)
		tmp = t_1;
	elseif (a <= -9.5e-23)
		tmp = z * ((y - x) / a);
	elseif (a <= 8.5e+17)
		tmp = y * (1.0 - (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e+97], t$95$1, If[LessEqual[a, -9.5e-23], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+17], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999975e97 or 8.5e17 < a

   1. Initial program 65.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 93.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
   4. Step-by-step derivation

      1. div-inv 93.5%

         \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   5. Applied egg-rr 93.5%

      \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   6. Taylor expanded in t around 0 60.1%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   7. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. *-commutative 60.1%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(y - x\right)}}{a} \]

      3. associate-/l* 69.9%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   8. Simplified 69.9%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]

   9. Taylor expanded in y around inf 65.1%

      \[\leadsto x + \frac{z}{\color{blue}{\frac{a}{y}}} \]

   if -9.49999999999999975e97 < a < -9.50000000000000058e-23

   1. Initial program 75.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 75.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 86.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]

   5. Taylor expanded in t around 0 80.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   6. Step-by-step derivation

      1. div-sub 80.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

   7. Simplified 80.6%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -9.50000000000000058e-23 < a < 8.5e17

   1. Initial program 62.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 78.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 78.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around 0 45.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t} + x} \]
   5. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 45.3%

         \[\leadsto x + \color{blue}{\left(-\frac{\left(z - t\right) \cdot \left(y - x\right)}{t}\right)} \]

      3. unsub-neg 45.3%

         \[\leadsto \color{blue}{x - \frac{\left(z - t\right) \cdot \left(y - x\right)}{t}} \]

      4. associate-/l* 54.1%

         \[\leadsto x - \color{blue}{\frac{z - t}{\frac{t}{y - x}}} \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{x - \frac{z - t}{\frac{t}{y - x}}} \]

   7. Taylor expanded in y around inf 55.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 23: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1600 \lor \neg \left(x \leq 1.1 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1600.0) (not (<= x 1.1e+136)))
   (* x (- 1.0 (/ z a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1600.0) || !(x <= 1.1e+136)) {
		tmp = x * (1.0 - (z / a));
	} 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 ((x <= (-1600.0d0)) .or. (.not. (x <= 1.1d+136))) then
        tmp = x * (1.0d0 - (z / a))
    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 ((x <= -1600.0) || !(x <= 1.1e+136)) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1600.0) or not (x <= 1.1e+136):
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1600.0) || !(x <= 1.1e+136))
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	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 ((x <= -1600.0) || ~((x <= 1.1e+136)))
		tmp = x * (1.0 - (z / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1600.0], N[Not[LessEqual[x, 1.1e+136]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1600 or 1.1e136 < x

   1. Initial program 60.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]
   4. Step-by-step derivation

      1. div-inv 81.7%

         \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   5. Applied egg-rr 81.7%

      \[\leadsto x + \frac{y - x}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}} \]

   6. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z - t}{a - t}\right) \cdot x} \]
   7. Step-by-step derivation

      1. div-sub 68.1%

         \[\leadsto \left(1 + -1 \cdot \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right)}\right) \cdot x \]

      2. mul-1-neg 68.1%

         \[\leadsto \left(1 + \color{blue}{\left(-\left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)}\right) \cdot x \]

      3. unsub-neg 68.1%

         \[\leadsto \color{blue}{\left(1 - \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\right)} \cdot x \]

      4. div-sub 68.1%

         \[\leadsto \left(1 - \color{blue}{\frac{z - t}{a - t}}\right) \cdot x \]

   8. Simplified 68.1%

      \[\leadsto \color{blue}{\left(1 - \frac{z - t}{a - t}\right) \cdot x} \]

   9. Taylor expanded in t around 0 56.1%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{a}\right)} \cdot x \]

   if -1600 < x < 1.1e136

   1. Initial program 66.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 66.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 89.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 89.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 69.3%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 69.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 69.3%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 69.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1600 \lor \neg \left(x \leq 1.1 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 24: 37.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+115)
   x
   (if (<= a -1.05e-21) (* z (/ y a)) (if (<= a 6e+52) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+115) {
		tmp = x;
	} else if (a <= -1.05e-21) {
		tmp = z * (y / a);
	} else if (a <= 6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d+115)) then
        tmp = x
    else if (a <= (-1.05d-21)) then
        tmp = z * (y / a)
    else if (a <= 6d+52) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+115) {
		tmp = x;
	} else if (a <= -1.05e-21) {
		tmp = z * (y / a);
	} else if (a <= 6e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+115:
		tmp = x
	elif a <= -1.05e-21:
		tmp = z * (y / a)
	elif a <= 6e+52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+115)
		tmp = x;
	elseif (a <= -1.05e-21)
		tmp = Float64(z * Float64(y / a));
	elseif (a <= 6e+52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+115)
		tmp = x;
	elseif (a <= -1.05e-21)
		tmp = z * (y / a);
	elseif (a <= 6e+52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+115], x, If[LessEqual[a, -1.05e-21], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+52], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000004e115 or 6e52 < a

   1. Initial program 62.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 54.5%

      \[\leadsto \color{blue}{x} \]

   if -2.30000000000000004e115 < a < -1.05000000000000006e-21

   1. Initial program 80.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 79.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 79.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 79.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 59.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   6. Simplified 59.5%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   7. Taylor expanded in a around inf 59.5%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a}} \]

   8. Taylor expanded in y around inf 29.8%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 39.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

      2. associate-/r/ 39.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   10. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   if -1.05000000000000006e-21 < a < 6e52

   1. Initial program 63.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 37.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 38.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-22) x (if (<= a 1.3e+52) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-22) {
		tmp = x;
	} else if (a <= 1.3e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.95d-22)) then
        tmp = x
    else if (a <= 1.3d+52) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-22) {
		tmp = x;
	} else if (a <= 1.3e+52) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e-22:
		tmp = x
	elif a <= 1.3e+52:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-22)
		tmp = x;
	elseif (a <= 1.3e+52)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e-22)
		tmp = x;
	elseif (a <= 1.3e+52)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-22], x, If[LessEqual[a, 1.3e+52], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.94999999999999999e-22 or 1.3e52 < a

   1. Initial program 65.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{x} \]

   if -1.94999999999999999e-22 < a < 1.3e52

   1. Initial program 63.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 37.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+52}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 24.9% 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 64.2%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. +-commutative 64.2%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

   2. associate-*r/ 86.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

   3. *-commutative 86.2%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

   4. fma-def 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

3. Simplified 86.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

4. Taylor expanded in a around inf 25.4%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 25.4%

   \[\leadsto x \]

Developer target: 86.3% 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 2023185 
(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))))