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

Percentage Accurate: 68.4% → 90.3%

Time: 17.6s

Alternatives: 21

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) * (t - x)) / (a - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-234}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-269)
       t_2
       (if (<= t_2 1e-234)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 2e+306) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-269) {
		tmp = t_2;
	} else if (t_2 <= 1e-234) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-269) {
		tmp = t_2;
	} else if (t_2 <= 1e-234) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-269:
		tmp = t_2
	elif t_2 <= 1e-234:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 2e+306:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-269)
		tmp = t_2;
	elseif (t_2 <= 1e-234)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-269)
		tmp = t_2;
	elseif (t_2 <= 1e-234)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-269], t$95$2, If[LessEqual[t$95$2, 1e-234], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 2.00000000000000003e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 45.7%

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

      1. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-269 or 9.9999999999999996e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 2.00000000000000003e306

   1. Initial program 97.5%

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

   if -1.9999999999999999e-269 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999996e-235

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. *-commutative 4.3%

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

      3. associate-/l* 10.9%

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

      4. fma-define 10.9%

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

   3. Simplified 10.9%

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

   5. Taylor expanded in z around inf 96.0%

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

      1. associate--l+ 96.0%

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

      2. associate-*r/ 96.0%

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

      3. associate-*r/ 96.0%

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

      4. mul-1-neg 96.0%

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

      5. div-sub 95.9%

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

      6. mul-1-neg 95.9%

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

      7. distribute-lft-out-- 95.9%

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

      8. associate-*r/ 95.9%

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

      9. mul-1-neg 95.9%

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

      10. unsub-neg 95.9%

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

      11. distribute-rgt-out-- 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-269}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-234}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-269} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-269}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -2e-269) (not (<= t_1 5e-269)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-269) || !(t_1 <= 5e-269)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-2d-269)) .or. (.not. (t_1 <= 5d-269))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-269) || !(t_1 <= 5e-269)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-269) or not (t_1 <= 5e-269):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-269) || !(t_1 <= 5e-269))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-269) || ~((t_1 <= 5e-269)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-269], N[Not[LessEqual[t$95$1, 5e-269]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.9999999999999999e-269 or 4.99999999999999979e-269 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 74.1%

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

      1. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-/l* 79.7%

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

      3. distribute-lft-neg-out 79.7%

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

      4. +-commutative 79.7%

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

      5. div-sub 81.0%

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

      6. distribute-rgt-out 84.6%

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

      7. sub-neg 84.6%

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

      8. associate-/r/ 90.4%

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

   7. Simplified 90.4%

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

   if -1.9999999999999999e-269 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.99999999999999979e-269

   1. Initial program 4.2%

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

      1. +-commutative 4.2%

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

      2. *-commutative 4.2%

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

      3. associate-/l* 7.3%

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

      4. fma-define 7.3%

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

   3. Simplified 7.3%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-269} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{-269}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -96000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -96000000000000.0)
   (* x (- 1.0 (/ y a)))
   (if (<= a -1.55e-54)
     t
     (if (<= a 5.2e-131)
       (/ (* x y) (- z a))
       (if (<= a 6.4e+68) t (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -96000000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.55e-54) {
		tmp = t;
	} else if (a <= 5.2e-131) {
		tmp = (x * y) / (z - a);
	} else if (a <= 6.4e+68) {
		tmp = t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-96000000000000.0d0)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-1.55d-54)) then
        tmp = t
    else if (a <= 5.2d-131) then
        tmp = (x * y) / (z - a)
    else if (a <= 6.4d+68) then
        tmp = t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -96000000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.55e-54) {
		tmp = t;
	} else if (a <= 5.2e-131) {
		tmp = (x * y) / (z - a);
	} else if (a <= 6.4e+68) {
		tmp = t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -96000000000000.0:
		tmp = x * (1.0 - (y / a))
	elif a <= -1.55e-54:
		tmp = t
	elif a <= 5.2e-131:
		tmp = (x * y) / (z - a)
	elif a <= 6.4e+68:
		tmp = t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -96000000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -1.55e-54)
		tmp = t;
	elseif (a <= 5.2e-131)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	elseif (a <= 6.4e+68)
		tmp = t;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -96000000000000.0)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -1.55e-54)
		tmp = t;
	elseif (a <= 5.2e-131)
		tmp = (x * y) / (z - a);
	elseif (a <= 6.4e+68)
		tmp = t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -96000000000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-54], t, If[LessEqual[a, 5.2e-131], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+68], t, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.6e13

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   10. Simplified 61.7%

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

   if -9.6e13 < a < -1.55000000000000002e-54 or 5.19999999999999993e-131 < a < 6.39999999999999989e68

   1. Initial program 57.4%

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

      1. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 46.2%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around inf 32.8%

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

   9. Taylor expanded in x around 0 44.0%

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

   if -1.55000000000000002e-54 < a < 5.19999999999999993e-131

   1. Initial program 66.7%

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

      1. +-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-/l* 73.3%

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

      4. fma-define 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around inf 63.9%

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

   6. Taylor expanded in t around 0 51.0%

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

      1. mul-1-neg 51.0%

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

   8. Simplified 51.0%

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

   if 6.39999999999999989e68 < a

   1. Initial program 73.2%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 72.3%

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

      1. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around 0 58.2%

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

      1. associate-/l* 63.7%

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

   10. Simplified 63.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -96000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -29000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -29000000000000.0)
   (* x (- 1.0 (/ y a)))
   (if (<= a -8.2e-55)
     t
     (if (<= a 4e-131)
       (* x (/ y z))
       (if (<= a 9.5e+63) t (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -29000000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -8.2e-55) {
		tmp = t;
	} else if (a <= 4e-131) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+63) {
		tmp = t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-29000000000000.0d0)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-8.2d-55)) then
        tmp = t
    else if (a <= 4d-131) then
        tmp = x * (y / z)
    else if (a <= 9.5d+63) then
        tmp = t
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -29000000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -8.2e-55) {
		tmp = t;
	} else if (a <= 4e-131) {
		tmp = x * (y / z);
	} else if (a <= 9.5e+63) {
		tmp = t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -29000000000000.0:
		tmp = x * (1.0 - (y / a))
	elif a <= -8.2e-55:
		tmp = t
	elif a <= 4e-131:
		tmp = x * (y / z)
	elif a <= 9.5e+63:
		tmp = t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -29000000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -8.2e-55)
		tmp = t;
	elseif (a <= 4e-131)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 9.5e+63)
		tmp = t;
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -29000000000000.0)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -8.2e-55)
		tmp = t;
	elseif (a <= 4e-131)
		tmp = x * (y / z);
	elseif (a <= 9.5e+63)
		tmp = t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -29000000000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-55], t, If[LessEqual[a, 4e-131], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+63], t, N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9e13

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   10. Simplified 61.7%

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

   if -2.9e13 < a < -8.1999999999999996e-55 or 3.9999999999999999e-131 < a < 9.5000000000000003e63

   1. Initial program 57.4%

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

      1. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 46.2%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around inf 32.8%

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

   9. Taylor expanded in x around 0 44.0%

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

   if -8.1999999999999996e-55 < a < 3.9999999999999999e-131

   1. Initial program 66.7%

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

      1. +-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-/l* 73.3%

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

      4. fma-define 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around inf 63.9%

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

   6. Taylor expanded in t around 0 51.0%

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

      1. mul-1-neg 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in a around 0 47.4%

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

       1. associate-/l* 50.1%

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

   11. Simplified 50.1%

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

   if 9.5000000000000003e63 < a

   1. Initial program 73.2%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 72.3%

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

      1. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around 0 58.2%

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

      1. associate-/l* 63.7%

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

   10. Simplified 63.7%

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

Alternative 5: 41.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -85000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -85000000000000.0)
     t_1
     (if (<= a -7e-55)
       t
       (if (<= a 2e-131) (* x (/ y z)) (if (<= a 1.9e+61) t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -85000000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-55) {
		tmp = t;
	} else if (a <= 2e-131) {
		tmp = x * (y / z);
	} else if (a <= 1.9e+61) {
		tmp = 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 - (y / a))
    if (a <= (-85000000000000.0d0)) then
        tmp = t_1
    else if (a <= (-7d-55)) then
        tmp = t
    else if (a <= 2d-131) then
        tmp = x * (y / z)
    else if (a <= 1.9d+61) then
        tmp = 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 - (y / a));
	double tmp;
	if (a <= -85000000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-55) {
		tmp = t;
	} else if (a <= 2e-131) {
		tmp = x * (y / z);
	} else if (a <= 1.9e+61) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -85000000000000.0:
		tmp = t_1
	elif a <= -7e-55:
		tmp = t
	elif a <= 2e-131:
		tmp = x * (y / z)
	elif a <= 1.9e+61:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -85000000000000.0)
		tmp = t_1;
	elseif (a <= -7e-55)
		tmp = t;
	elseif (a <= 2e-131)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.9e+61)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -85000000000000.0)
		tmp = t_1;
	elseif (a <= -7e-55)
		tmp = t;
	elseif (a <= 2e-131)
		tmp = x * (y / z);
	elseif (a <= 1.9e+61)
		tmp = 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[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -85000000000000.0], t$95$1, If[LessEqual[a, -7e-55], t, If[LessEqual[a, 2e-131], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+61], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5e13 or 1.89999999999999998e61 < a

   1. Initial program 73.1%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around 0 63.0%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

   10. Simplified 56.4%

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

   if -8.5e13 < a < -7.00000000000000051e-55 or 2e-131 < a < 1.89999999999999998e61

   1. Initial program 58.4%

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

      1. associate-/l* 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in t around inf 47.1%

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

      1. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in z around inf 33.4%

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

   9. Taylor expanded in x around 0 44.8%

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

   if -7.00000000000000051e-55 < a < 2e-131

   1. Initial program 66.7%

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

      1. +-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-/l* 73.3%

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

      4. fma-define 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around inf 63.9%

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

   6. Taylor expanded in t around 0 51.0%

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

      1. mul-1-neg 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in a around 0 47.4%

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

       1. associate-/l* 50.1%

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

   11. Simplified 50.1%

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

Alternative 6: 55.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a y)))))
   (if (<= a -9500000000000.0)
     t_1
     (if (<= a -2.45e-36)
       (* z (/ t (- z a)))
       (if (<= a 2.4e-75) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = t_1;
	} else if (a <= -2.45e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.4e-75) {
		tmp = y * ((x - t) / 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 = x + ((t - x) / (a / y))
    if (a <= (-9500000000000.0d0)) then
        tmp = t_1
    else if (a <= (-2.45d-36)) then
        tmp = z * (t / (z - a))
    else if (a <= 2.4d-75) then
        tmp = y * ((x - t) / 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 = x + ((t - x) / (a / y));
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = t_1;
	} else if (a <= -2.45e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.4e-75) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / y))
	tmp = 0
	if a <= -9500000000000.0:
		tmp = t_1
	elif a <= -2.45e-36:
		tmp = z * (t / (z - a))
	elif a <= 2.4e-75:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / y)))
	tmp = 0.0
	if (a <= -9500000000000.0)
		tmp = t_1;
	elseif (a <= -2.45e-36)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= 2.4e-75)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / y));
	tmp = 0.0;
	if (a <= -9500000000000.0)
		tmp = t_1;
	elseif (a <= -2.45e-36)
		tmp = z * (t / (z - a));
	elseif (a <= 2.4e-75)
		tmp = y * ((x - t) / z);
	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 - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9500000000000.0], t$95$1, If[LessEqual[a, -2.45e-36], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-75], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5e12 or 2.40000000000000019e-75 < a

   1. Initial program 71.0%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. associate-/l* 87.4%

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

      3. distribute-lft-neg-out 87.4%

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

      4. +-commutative 87.4%

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

      5. div-sub 87.4%

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

      6. distribute-rgt-out 87.4%

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

      7. sub-neg 87.4%

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

      8. associate-/r/ 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in z around 0 69.4%

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

   if -9.5e12 < a < -2.4499999999999998e-36

   1. Initial program 62.3%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. mul-1-neg 41.8%

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

       2. unsub-neg 41.8%

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

       3. *-commutative 41.8%

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

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0 49.5%

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

       1. associate-*l/ 63.1%

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

       2. neg-mul-1 63.1%

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

       3. distribute-lft-neg-in 63.1%

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

       4. distribute-neg-frac2 63.1%

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

   16. Simplified 63.1%

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

   if -2.4499999999999998e-36 < a < 2.40000000000000019e-75

   1. Initial program 64.7%

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

      1. +-commutative 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-/l* 72.0%

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

      4. fma-define 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in y around inf 61.3%

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

   6. Taylor expanded in a around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. associate-*r/ 53.1%

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

      3. div-sub 56.5%

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

      4. distribute-lft-out-- 56.5%

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

      5. neg-mul-1 56.5%

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

   8. Simplified 56.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -16500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) a)))))
   (if (<= a -16500000000000.0)
     t_1
     (if (<= a -1.85e-35)
       (* z (/ t (- z a)))
       (if (<= a 2.1e-75) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -16500000000000.0) {
		tmp = t_1;
	} else if (a <= -1.85e-35) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.1e-75) {
		tmp = y * ((x - t) / 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 = x + (y * ((t - x) / a))
    if (a <= (-16500000000000.0d0)) then
        tmp = t_1
    else if (a <= (-1.85d-35)) then
        tmp = z * (t / (z - a))
    else if (a <= 2.1d-75) then
        tmp = y * ((x - t) / 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 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -16500000000000.0) {
		tmp = t_1;
	} else if (a <= -1.85e-35) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.1e-75) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -16500000000000.0:
		tmp = t_1
	elif a <= -1.85e-35:
		tmp = z * (t / (z - a))
	elif a <= 2.1e-75:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -16500000000000.0)
		tmp = t_1;
	elseif (a <= -1.85e-35)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= 2.1e-75)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -16500000000000.0)
		tmp = t_1;
	elseif (a <= -1.85e-35)
		tmp = z * (t / (z - a));
	elseif (a <= 2.1e-75)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -16500000000000.0], t$95$1, If[LessEqual[a, -1.85e-35], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-75], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e13 or 2.1000000000000001e-75 < a

   1. Initial program 71.0%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around 0 59.5%

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

      1. associate-/l* 67.1%

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

   7. Simplified 67.1%

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

   if -1.65e13 < a < -1.8499999999999999e-35

   1. Initial program 62.3%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. mul-1-neg 41.8%

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

       2. unsub-neg 41.8%

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

       3. *-commutative 41.8%

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

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0 49.5%

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

       1. associate-*l/ 63.1%

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

       2. neg-mul-1 63.1%

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

       3. distribute-lft-neg-in 63.1%

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

       4. distribute-neg-frac2 63.1%

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

   16. Simplified 63.1%

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

   if -1.8499999999999999e-35 < a < 2.1000000000000001e-75

   1. Initial program 64.7%

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

      1. +-commutative 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-/l* 72.0%

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

      4. fma-define 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in y around inf 61.3%

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

   6. Taylor expanded in a around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. associate-*r/ 53.1%

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

      3. div-sub 56.5%

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

      4. distribute-lft-out-- 56.5%

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

      5. neg-mul-1 56.5%

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

   8. Simplified 56.5%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -16500000000000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9500000000000.0)
   (+ x (* t (/ y (- a z))))
   (if (<= a -7.2e-36)
     (* z (/ t (- z a)))
     (if (<= a 2.75e-70) (* y (/ (- x t) z)) (+ x (* t (/ (- y z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = x + (t * (y / (a - z)));
	} else if (a <= -7.2e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.75e-70) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9500000000000.0d0)) then
        tmp = x + (t * (y / (a - z)))
    else if (a <= (-7.2d-36)) then
        tmp = z * (t / (z - a))
    else if (a <= 2.75d-70) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = x + (t * (y / (a - z)));
	} else if (a <= -7.2e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 2.75e-70) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9500000000000.0:
		tmp = x + (t * (y / (a - z)))
	elif a <= -7.2e-36:
		tmp = z * (t / (z - a))
	elif a <= 2.75e-70:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9500000000000.0)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	elseif (a <= -7.2e-36)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= 2.75e-70)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9500000000000.0)
		tmp = x + (t * (y / (a - z)));
	elseif (a <= -7.2e-36)
		tmp = z * (t / (z - a));
	elseif (a <= 2.75e-70)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9500000000000.0], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e-36], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e-70], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.5e12

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around inf 58.4%

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

      1. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in y around inf 56.2%

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

      1. associate-/l* 65.7%

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

   10. Simplified 65.7%

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

   if -9.5e12 < a < -7.20000000000000064e-36

   1. Initial program 62.3%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. mul-1-neg 41.8%

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

       2. unsub-neg 41.8%

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

       3. *-commutative 41.8%

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

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0 49.5%

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

       1. associate-*l/ 63.1%

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

       2. neg-mul-1 63.1%

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

       3. distribute-lft-neg-in 63.1%

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

       4. distribute-neg-frac2 63.1%

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

   16. Simplified 63.1%

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

   if -7.20000000000000064e-36 < a < 2.75e-70

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-/l* 72.2%

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

      4. fma-define 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in y around inf 61.6%

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

   6. Taylor expanded in a around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*r/ 53.5%

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

      3. div-sub 56.8%

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

      4. distribute-lft-out-- 56.8%

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

      5. neg-mul-1 56.8%

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

   8. Simplified 56.8%

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

   if 2.75e-70 < a

   1. Initial program 68.2%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in t around inf 63.4%

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

      1. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in a around inf 53.8%

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

      1. associate-/l* 57.8%

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

   10. Simplified 57.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -13000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y (- a z))))))
   (if (<= a -13000000000000.0)
     t_1
     (if (<= a -6e-36)
       (* z (/ t (- z a)))
       (if (<= a 1.32e-73) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (a - z)));
	double tmp;
	if (a <= -13000000000000.0) {
		tmp = t_1;
	} else if (a <= -6e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 1.32e-73) {
		tmp = y * ((x - t) / 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 = x + (t * (y / (a - z)))
    if (a <= (-13000000000000.0d0)) then
        tmp = t_1
    else if (a <= (-6d-36)) then
        tmp = z * (t / (z - a))
    else if (a <= 1.32d-73) then
        tmp = y * ((x - t) / 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 = x + (t * (y / (a - z)));
	double tmp;
	if (a <= -13000000000000.0) {
		tmp = t_1;
	} else if (a <= -6e-36) {
		tmp = z * (t / (z - a));
	} else if (a <= 1.32e-73) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / (a - z)))
	tmp = 0
	if a <= -13000000000000.0:
		tmp = t_1
	elif a <= -6e-36:
		tmp = z * (t / (z - a))
	elif a <= 1.32e-73:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / Float64(a - z))))
	tmp = 0.0
	if (a <= -13000000000000.0)
		tmp = t_1;
	elseif (a <= -6e-36)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= 1.32e-73)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / (a - z)));
	tmp = 0.0;
	if (a <= -13000000000000.0)
		tmp = t_1;
	elseif (a <= -6e-36)
		tmp = z * (t / (z - a));
	elseif (a <= 1.32e-73)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -13000000000000.0], t$95$1, If[LessEqual[a, -6e-36], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e-73], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e13 or 1.31999999999999998e-73 < a

   1. Initial program 70.7%

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

      1. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in y around inf 53.0%

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

      1. associate-/l* 59.9%

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

   10. Simplified 59.9%

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

   if -1.3e13 < a < -6.0000000000000003e-36

   1. Initial program 62.3%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. mul-1-neg 41.8%

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

       2. unsub-neg 41.8%

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

       3. *-commutative 41.8%

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

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0 49.5%

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

       1. associate-*l/ 63.1%

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

       2. neg-mul-1 63.1%

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

       3. distribute-lft-neg-in 63.1%

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

       4. distribute-neg-frac2 63.1%

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

   16. Simplified 63.1%

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

   if -6.0000000000000003e-36 < a < 1.31999999999999998e-73

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-/l* 72.2%

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

      4. fma-define 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in y around inf 61.6%

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

   6. Taylor expanded in a around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*r/ 53.5%

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

      3. div-sub 56.8%

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

      4. distribute-lft-out-- 56.8%

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

      5. neg-mul-1 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -13000000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-186} \lor \neg \left(a \leq 3.3 \cdot 10^{-52}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-186) (not (<= a 3.3e-52)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-186) || !(a <= 3.3e-52)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-186)) .or. (.not. (a <= 3.3d-52))) then
        tmp = x + ((y - z) * ((t - x) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-186) || !(a <= 3.3e-52)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-186) or not (a <= 3.3e-52):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-186) || !(a <= 3.3e-52))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-186) || ~((a <= 3.3e-52)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-186], N[Not[LessEqual[a, 3.3e-52]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000006e-186 or 3.29999999999999995e-52 < a

   1. Initial program 70.1%

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

      1. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   if -4.80000000000000006e-186 < a < 3.29999999999999995e-52

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-/l* 70.7%

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

      4. fma-define 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. associate--l+ 86.3%

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

      2. associate-*r/ 86.3%

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

      3. associate-*r/ 86.3%

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

      4. mul-1-neg 86.3%

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

      5. div-sub 87.4%

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

      6. mul-1-neg 87.4%

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

      7. distribute-lft-out-- 87.4%

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

      8. associate-*r/ 87.4%

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

      9. mul-1-neg 87.4%

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

      10. unsub-neg 87.4%

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

      11. distribute-rgt-out-- 87.4%

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

   7. Simplified 87.4%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-186} \lor \neg \left(a \leq 3.3 \cdot 10^{-52}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -16500000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -16500000000000.0)
   (* x (- 1.0 (/ y a)))
   (if (<= a -1.2e-35)
     (* z (/ t (- z a)))
     (if (<= a 3.8e-15) (* y (/ (- x t) z)) (+ x (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -16500000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.2e-35) {
		tmp = z * (t / (z - a));
	} else if (a <= 3.8e-15) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-16500000000000.0d0)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-1.2d-35)) then
        tmp = z * (t / (z - a))
    else if (a <= 3.8d-15) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -16500000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.2e-35) {
		tmp = z * (t / (z - a));
	} else if (a <= 3.8e-15) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -16500000000000.0:
		tmp = x * (1.0 - (y / a))
	elif a <= -1.2e-35:
		tmp = z * (t / (z - a))
	elif a <= 3.8e-15:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -16500000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -1.2e-35)
		tmp = Float64(z * Float64(t / Float64(z - a)));
	elseif (a <= 3.8e-15)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -16500000000000.0)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -1.2e-35)
		tmp = z * (t / (z - a));
	elseif (a <= 3.8e-15)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -16500000000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-35], N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-15], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.65e13

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   10. Simplified 61.7%

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

   if -1.65e13 < a < -1.2000000000000001e-35

   1. Initial program 62.3%

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

      1. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   10. Simplified 61.7%

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

   11. Taylor expanded in x around 0 41.8%

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

       1. mul-1-neg 41.8%

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

       2. unsub-neg 41.8%

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

       3. *-commutative 41.8%

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

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0 49.5%

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

       1. associate-*l/ 63.1%

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

       2. neg-mul-1 63.1%

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

       3. distribute-lft-neg-in 63.1%

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

       4. distribute-neg-frac2 63.1%

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

   16. Simplified 63.1%

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

   if -1.2000000000000001e-35 < a < 3.8000000000000002e-15

   1. Initial program 64.9%

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

      1. +-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-/l* 72.7%

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

      4. fma-define 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in y around inf 59.9%

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

   6. Taylor expanded in a around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. associate-*r/ 51.0%

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

      3. div-sub 54.0%

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

      4. distribute-lft-out-- 54.0%

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

      5. neg-mul-1 54.0%

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

   8. Simplified 54.0%

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

   if 3.8000000000000002e-15 < a

   1. Initial program 69.3%

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

      1. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in t around inf 67.0%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in z around 0 54.6%

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

      1. associate-/l* 59.3%

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

   10. Simplified 59.3%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -16500000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -17500000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -17500000000000.0)
   (* x (- 1.0 (/ y a)))
   (if (<= a -1.6e-34)
     t
     (if (<= a 5.2e-15) (* y (/ (- x t) z)) (+ x (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -17500000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.6e-34) {
		tmp = t;
	} else if (a <= 5.2e-15) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-17500000000000.0d0)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= (-1.6d-34)) then
        tmp = t
    else if (a <= 5.2d-15) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -17500000000000.0) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= -1.6e-34) {
		tmp = t;
	} else if (a <= 5.2e-15) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -17500000000000.0:
		tmp = x * (1.0 - (y / a))
	elif a <= -1.6e-34:
		tmp = t
	elif a <= 5.2e-15:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -17500000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= -1.6e-34)
		tmp = t;
	elseif (a <= 5.2e-15)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -17500000000000.0)
		tmp = x * (1.0 - (y / a));
	elseif (a <= -1.6e-34)
		tmp = t;
	elseif (a <= 5.2e-15)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -17500000000000.0], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-34], t, If[LessEqual[a, 5.2e-15], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.75e13

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   10. Simplified 61.7%

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

   if -1.75e13 < a < -1.60000000000000001e-34

   1. Initial program 59.1%

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

      1. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in t around inf 50.3%

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

      1. associate-/l* 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in z around inf 42.3%

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

   9. Taylor expanded in x around 0 59.6%

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

   if -1.60000000000000001e-34 < a < 5.20000000000000009e-15

   1. Initial program 65.1%

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

      1. +-commutative 65.1%

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

      2. *-commutative 65.1%

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

      3. associate-/l* 72.9%

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

      4. fma-define 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in y around inf 59.5%

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

   6. Taylor expanded in a around 0 50.7%

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

      1. associate-*r/ 50.7%

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

      2. associate-*r/ 50.7%

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

      3. div-sub 53.7%

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

      4. distribute-lft-out-- 53.7%

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

      5. neg-mul-1 53.7%

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

   8. Simplified 53.7%

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

   if 5.20000000000000009e-15 < a

   1. Initial program 69.3%

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

      1. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in t around inf 67.0%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in z around 0 54.6%

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

      1. associate-/l* 59.3%

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

   10. Simplified 59.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -17500000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+62} \lor \neg \left(z \leq 1.95 \cdot 10^{+81}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+62) (not (<= z 1.95e+81)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ (- t x) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+62) || !(z <= 1.95e+81)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+62)) .or. (.not. (z <= 1.95d+81))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) / ((a - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+62) || !(z <= 1.95e+81)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+62) or not (z <= 1.95e+81):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+62) || !(z <= 1.95e+81))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+62) || ~((z <= 1.95e+81)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+62], N[Not[LessEqual[z, 1.95e+81]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e62 or 1.95e81 < z

   1. Initial program 39.5%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

      1. *-commutative 64.7%

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

      2. sub-neg 64.7%

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

      3. distribute-lft-in 64.8%

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

   6. Applied egg-rr 64.8%

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

   7. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 71.2%

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

      2. *-commutative 71.2%

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

      3. neg-mul-1 71.2%

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

      4. distribute-lft-neg-in 71.2%

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

      5. neg-mul-1 71.2%

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

      6. distribute-lft-out-- 71.2%

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

      7. *-commutative 71.2%

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

      8. associate-/l* 79.1%

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

      9. distribute-lft-out-- 79.1%

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

      10. neg-mul-1 79.1%

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

   9. Simplified 79.1%

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

   if -4.2e62 < z < 1.95e81

   1. Initial program 84.4%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in y around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-/l* 77.7%

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

      3. distribute-lft-neg-out 77.7%

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

      4. +-commutative 77.7%

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

      5. div-sub 79.7%

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

      6. distribute-rgt-out 84.9%

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

      7. sub-neg 84.9%

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

      8. associate-/r/ 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in y around inf 81.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+62} \lor \neg \left(z \leq 1.95 \cdot 10^{+81}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+61} \lor \neg \left(z \leq 3 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+61) (not (<= z 3e+79)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ (* y (- t x)) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+61) || !(z <= 3e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((y * (t - x)) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4d+61)) .or. (.not. (z <= 3d+79))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((y * (t - x)) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+61) || !(z <= 3e+79)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((y * (t - x)) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+61) or not (z <= 3e+79):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((y * (t - x)) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+61) || !(z <= 3e+79))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+61) || ~((z <= 3e+79)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((y * (t - x)) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+61], N[Not[LessEqual[z, 3e+79]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999998e61 or 2.99999999999999974e79 < z

   1. Initial program 39.5%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

      1. *-commutative 64.7%

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

      2. sub-neg 64.7%

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

      3. distribute-lft-in 64.8%

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

   6. Applied egg-rr 64.8%

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

   7. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 71.2%

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

      2. *-commutative 71.2%

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

      3. neg-mul-1 71.2%

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

      4. distribute-lft-neg-in 71.2%

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

      5. neg-mul-1 71.2%

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

      6. distribute-lft-out-- 71.2%

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

      7. *-commutative 71.2%

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

      8. associate-/l* 79.1%

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

      9. distribute-lft-out-- 79.1%

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

      10. neg-mul-1 79.1%

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

   9. Simplified 79.1%

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

   if -3.9999999999999998e61 < z < 2.99999999999999974e79

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+61} \lor \neg \left(z \leq 3 \cdot 10^{+79}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-36} \lor \neg \left(a \leq 3.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e-36) (not (<= a 3.8e-17)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-36) || !(a <= 3.8e-17)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.3d-36)) .or. (.not. (a <= 3.8d-17))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-36) || !(a <= 3.8e-17)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e-36) or not (a <= 3.8e-17):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e-36) || !(a <= 3.8e-17))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e-36) || ~((a <= 3.8e-17)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e-36], N[Not[LessEqual[a, 3.8e-17]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.29999999999999996e-36 or 3.8000000000000001e-17 < a

   1. Initial program 70.1%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 61.8%

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

      1. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   if -2.29999999999999996e-36 < a < 3.8000000000000001e-17

   1. Initial program 65.3%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

      1. *-commutative 69.2%

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

      2. sub-neg 69.2%

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

      3. distribute-lft-in 63.0%

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

   6. Applied egg-rr 63.0%

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

   7. Taylor expanded in a around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. neg-mul-1 74.7%

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

      4. distribute-lft-neg-in 74.7%

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

      5. neg-mul-1 74.7%

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

      6. distribute-lft-out-- 74.7%

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

      7. *-commutative 74.7%

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

      8. associate-/l* 75.5%

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

      9. distribute-lft-out-- 75.5%

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

      10. neg-mul-1 75.5%

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

   9. Simplified 75.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-36} \lor \neg \left(a \leq 3.8 \cdot 10^{-17}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9500000000000.0)
   (+ x (/ (- t x) (/ (- a z) y)))
   (if (<= a 7.2e-52)
     (+ t (/ (* (- t x) (- a y)) z))
     (+ x (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (a <= 7.2e-52) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9500000000000.0d0)) then
        tmp = x + ((t - x) / ((a - z) / y))
    else if (a <= 7.2d-52) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9500000000000.0) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else if (a <= 7.2e-52) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9500000000000.0:
		tmp = x + ((t - x) / ((a - z) / y))
	elif a <= 7.2e-52:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9500000000000.0)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	elseif (a <= 7.2e-52)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9500000000000.0)
		tmp = x + ((t - x) / ((a - z) / y));
	elseif (a <= 7.2e-52)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9500000000000.0], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-52], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5e12

   1. Initial program 74.5%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. associate-/l* 90.0%

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

      3. distribute-lft-neg-out 90.0%

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

      4. +-commutative 90.0%

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

      5. div-sub 90.0%

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

      6. distribute-rgt-out 90.0%

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

      7. sub-neg 90.0%

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

      8. associate-/r/ 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in y around inf 85.6%

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

   if -9.5e12 < a < 7.19999999999999976e-52

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-/l* 72.5%

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

      4. fma-define 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in z around inf 79.9%

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

      1. associate--l+ 79.9%

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

      2. associate-*r/ 79.9%

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

      3. associate-*r/ 79.9%

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

      4. mul-1-neg 79.9%

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

      5. div-sub 81.4%

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

      6. mul-1-neg 81.4%

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

      7. distribute-lft-out-- 81.4%

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

      8. associate-*r/ 81.4%

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

      9. mul-1-neg 81.4%

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

      10. unsub-neg 81.4%

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

      11. distribute-rgt-out-- 81.4%

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

   7. Simplified 81.4%

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

   if 7.19999999999999976e-52 < a

   1. Initial program 69.7%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 64.7%

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

      1. associate-/l* 80.8%

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

   7. Simplified 80.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9500000000000:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-40} \lor \neg \left(y \leq 2.3 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.4e+255)
   (* x (/ y (- a)))
   (if (or (<= y -1.05e-40) (not (<= y 2.3e+89))) (* x (/ y z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.4e+255) {
		tmp = x * (y / -a);
	} else if ((y <= -1.05e-40) || !(y <= 2.3e+89)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.4d+255)) then
        tmp = x * (y / -a)
    else if ((y <= (-1.05d-40)) .or. (.not. (y <= 2.3d+89))) then
        tmp = x * (y / z)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.4e+255) {
		tmp = x * (y / -a);
	} else if ((y <= -1.05e-40) || !(y <= 2.3e+89)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.4e+255:
		tmp = x * (y / -a)
	elif (y <= -1.05e-40) or not (y <= 2.3e+89):
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.4e+255)
		tmp = Float64(x * Float64(y / Float64(-a)));
	elseif ((y <= -1.05e-40) || !(y <= 2.3e+89))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.4e+255)
		tmp = x * (y / -a);
	elseif ((y <= -1.05e-40) || ~((y <= 2.3e+89)))
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.4e+255], N[(x * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.05e-40], N[Not[LessEqual[y, 2.3e+89]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999979e255

   1. Initial program 78.5%

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

      1. +-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-/l* 99.8%

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

      4. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.1%

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

   6. Taylor expanded in t around 0 41.7%

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

      1. mul-1-neg 41.7%

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

   8. Simplified 41.7%

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

   9. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{a}} \]
   10. Step-by-step derivation

       1. mul-1-neg 42.8%

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

       2. associate-/l* 63.8%

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

       3. distribute-rgt-neg-in 63.8%

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

       4. mul-1-neg 63.8%

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

       5. associate-*r/ 63.8%

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

       6. neg-mul-1 63.8%

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

   11. Simplified 63.8%

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

   if -7.39999999999999979e255 < y < -1.05000000000000009e-40 or 2.2999999999999999e89 < y

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/l* 85.4%

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

      4. fma-define 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in y around inf 78.3%

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

   6. Taylor expanded in t around 0 44.8%

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

      1. mul-1-neg 44.8%

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

   8. Simplified 44.8%

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

   9. Taylor expanded in a around 0 39.9%

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

       1. associate-/l* 43.5%

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

   11. Simplified 43.5%

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

   if -1.05000000000000009e-40 < y < 2.2999999999999999e89

   1. Initial program 61.5%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in t around inf 53.2%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around inf 46.2%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+255}:\\ \;\;\;\;x \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-40} \lor \neg \left(y \leq 2.3 \cdot 10^{+89}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -13000000000000 \lor \neg \left(a \leq 1.85 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -13000000000000.0) (not (<= a 1.85e+61)))
   (+ x (/ (- t x) (/ a y)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -13000000000000.0) || !(a <= 1.85e+61)) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-13000000000000.0d0)) .or. (.not. (a <= 1.85d+61))) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -13000000000000.0) || !(a <= 1.85e+61)) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -13000000000000.0) or not (a <= 1.85e+61):
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -13000000000000.0) || !(a <= 1.85e+61))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -13000000000000.0) || ~((a <= 1.85e+61)))
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -13000000000000.0], N[Not[LessEqual[a, 1.85e+61]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e13 or 1.85000000000000001e61 < a

   1. Initial program 73.1%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/l* 88.5%

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

      3. distribute-lft-neg-out 88.5%

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

      4. +-commutative 88.5%

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

      5. div-sub 88.5%

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

      6. distribute-rgt-out 88.5%

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

      7. sub-neg 88.5%

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

      8. associate-/r/ 94.2%

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

   7. Simplified 94.2%

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

   8. Taylor expanded in z around 0 74.3%

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

   if -1.3e13 < a < 1.85000000000000001e61

   1. Initial program 64.0%

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

      1. associate-/l* 70.3%

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

   3. Simplified 70.3%

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

      1. *-commutative 70.3%

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

      2. sub-neg 70.3%

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

      3. distribute-lft-in 65.0%

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

   6. Applied egg-rr 65.0%

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

   7. Taylor expanded in a around 0 73.3%

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

      1. associate-*r/ 73.3%

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

      2. *-commutative 73.3%

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

      3. neg-mul-1 73.3%

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

      4. distribute-lft-neg-in 73.3%

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

      5. neg-mul-1 73.3%

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

      6. distribute-lft-out-- 73.3%

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

      7. *-commutative 73.3%

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

      8. associate-/l* 73.4%

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

      9. distribute-lft-out-- 73.4%

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

      10. neg-mul-1 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -13000000000000 \lor \neg \left(a \leq 1.85 \cdot 10^{+61}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-41} \lor \neg \left(y \leq 9.2 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.8e-41) (not (<= y 9.2e+92))) (* x (/ y z)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.8e-41) || !(y <= 9.2e+92)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8.8d-41)) .or. (.not. (y <= 9.2d+92))) then
        tmp = x * (y / z)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.8e-41) || !(y <= 9.2e+92)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.8e-41) or not (y <= 9.2e+92):
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.8e-41) || !(y <= 9.2e+92))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.8e-41) || ~((y <= 9.2e+92)))
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.8e-41], N[Not[LessEqual[y, 9.2e+92]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.7999999999999999e-41 or 9.19999999999999994e92 < y

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-/l* 86.8%

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

      4. fma-define 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in y around inf 79.0%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. mul-1-neg 44.5%

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

   8. Simplified 44.5%

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

   9. Taylor expanded in a around 0 38.4%

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

       1. associate-/l* 41.7%

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

   11. Simplified 41.7%

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

   if -8.7999999999999999e-41 < y < 9.19999999999999994e92

   1. Initial program 61.5%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in t around inf 53.2%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around inf 46.2%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-41} \lor \neg \left(y \leq 9.2 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+14) t (if (<= z 6.5e+82) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+14) {
		tmp = t;
	} else if (z <= 6.5e+82) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.8d+14)) then
        tmp = t
    else if (z <= 6.5d+82) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+14) {
		tmp = t;
	} else if (z <= 6.5e+82) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+14:
		tmp = t
	elif z <= 6.5e+82:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+14)
		tmp = t;
	elseif (z <= 6.5e+82)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+14)
		tmp = t;
	elseif (z <= 6.5e+82)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+14], t, If[LessEqual[z, 6.5e+82], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8e14 or 6.5000000000000003e82 < z

   1. Initial program 44.4%

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

      1. associate-/l* 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in t around inf 33.0%

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

      1. associate-/l* 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 39.7%

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

   9. Taylor expanded in x around 0 45.6%

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

   if -9.8e14 < z < 6.5000000000000003e82

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-/l* 89.3%

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

      4. fma-define 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around inf 27.1%

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

Alternative 21: 25.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.6%

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

   1. associate-/l* 77.3%

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

3. Simplified 77.3%

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

5. Taylor expanded in t around inf 49.5%

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

   1. associate-/l* 61.9%

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

7. Simplified 61.9%

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

8. Taylor expanded in z around inf 29.0%

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

9. Taylor expanded in x around 0 23.3%

   \[\leadsto \color{blue}{t} \]
10. Add Preprocessing

Developer Target 1: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - 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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))