Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.9%

Time: 23.5s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-306) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	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))))
	tmp = 0.0
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return 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]}, If[Or[LessEqual[t$95$1, -5e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. remove-double-neg 85.5%

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

      3. unsub-neg 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-*l/ 75.3%

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

      6. associate-/l* 92.4%

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

      7. fma-neg 92.4%

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

      8. remove-double-neg 92.4%

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

   3. Simplified 92.4%

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

   if -4.99999999999999998e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   3. Taylor expanded in z around inf 87.5%

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

      1. associate--l+ 87.5%

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

      2. distribute-lft-out-- 87.5%

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

      3. div-sub 87.5%

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

      4. mul-1-neg 87.5%

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

      5. unsub-neg 87.5%

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

      6. div-sub 87.5%

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

      7. associate-/l* 87.6%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := x \cdot \left(z - a\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;t\_2 \leq 10^{-69}:\\ \;\;\;\;x \cdot \left(t \cdot \left(\left(\frac{1}{t} + \left(\frac{z}{t \cdot \left(a - z\right)} - \frac{y}{t\_3}\right)\right) + \left(\frac{y}{t \cdot \left(z - a\right)} + \frac{z}{t\_3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (* x (- z a))))
   (if (<= t_2 -5e-249)
     t_1
     (if (<= t_2 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (if (<= t_2 1e-69)
         (*
          x
          (*
           t
           (+
            (+ (/ 1.0 t) (- (/ z (* t (- a z))) (/ y t_3)))
            (+ (/ y (* t (- z a))) (/ z t_3)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = x * (z - a);
	double tmp;
	if (t_2 <= -5e-249) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else if (t_2 <= 1e-69) {
		tmp = x * (t * (((1.0 / t) + ((z / (t * (a - z))) - (y / t_3))) + ((y / (t * (z - a))) + (z / t_3))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    t_3 = x * (z - a)
    if (t_2 <= (-5d-249)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) / z) * (a - y))
    else if (t_2 <= 1d-69) then
        tmp = x * (t * (((1.0d0 / t) + ((z / (t * (a - z))) - (y / t_3))) + ((y / (t * (z - a))) + (z / t_3))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = x * (z - a);
	double tmp;
	if (t_2 <= -5e-249) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else if (t_2 <= 1e-69) {
		tmp = x * (t * (((1.0 / t) + ((z / (t * (a - z))) - (y / t_3))) + ((y / (t * (z - a))) + (z / t_3))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	t_3 = x * (z - a)
	tmp = 0
	if t_2 <= -5e-249:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (((t - x) / z) * (a - y))
	elif t_2 <= 1e-69:
		tmp = x * (t * (((1.0 / t) + ((z / (t * (a - z))) - (y / t_3))) + ((y / (t * (z - a))) + (z / t_3))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = Float64(x * Float64(z - a))
	tmp = 0.0
	if (t_2 <= -5e-249)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	elseif (t_2 <= 1e-69)
		tmp = Float64(x * Float64(t * Float64(Float64(Float64(1.0 / t) + Float64(Float64(z / Float64(t * Float64(a - z))) - Float64(y / t_3))) + Float64(Float64(y / Float64(t * Float64(z - a))) + Float64(z / t_3)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	t_3 = x * (z - a);
	tmp = 0.0;
	if (t_2 <= -5e-249)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) / z) * (a - y));
	elseif (t_2 <= 1e-69)
		tmp = x * (t * (((1.0 / t) + ((z / (t * (a - z))) - (y / t_3))) + ((y / (t * (z - a))) + (z / t_3))));
	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[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-249], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-69], N[(x * N[(t * N[(N[(N[(1.0 / t), $MachinePrecision] + N[(N[(z / N[(t * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-249 or 9.9999999999999996e-70 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.9%

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

      1. clear-num 89.9%

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

      2. un-div-inv 90.3%

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

   4. Applied egg-rr 90.3%

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

   if -4.9999999999999999e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. div-sub 82.2%

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

      7. associate-/l* 82.2%

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

      8. associate-/l* 92.2%

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

      9. distribute-rgt-out-- 92.2%

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

   5. Simplified 92.2%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999996e-70

   1. Initial program 55.5%

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

      1. add-cube-cbrt 55.4%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}} \cdot \sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}} \]

      2. pow3 55.4%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}\right)}^{3}} \]

      3. *-commutative 55.4%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}}\right)}^{3} \]

      4. associate-*l/ 71.7%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}}\right)}^{3} \]

      5. associate-*r/ 71.7%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}}\right)}^{3} \]

   4. Applied egg-rr 71.7%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right)}^{3}} \]

   5. Taylor expanded in x around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. associate-/l* 72.2%

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

      5. *-commutative 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in t around inf 88.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-249}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-69}:\\ \;\;\;\;x \cdot \left(t \cdot \left(\left(\frac{1}{t} + \left(\frac{z}{t \cdot \left(a - z\right)} - \frac{y}{x \cdot \left(z - a\right)}\right)\right) + \left(\frac{y}{t \cdot \left(z - a\right)} + \frac{z}{x \cdot \left(z - a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-249) (not (<= t_1 0.0)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-249)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-249) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	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))))
	tmp = 0.0
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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 <= -5e-249) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	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]}, If[Or[LessEqual[t$95$1, -5e-249], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-249 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

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

   if -4.9999999999999999e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. div-sub 82.2%

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

      7. associate-/l* 82.2%

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

      8. associate-/l* 92.2%

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

      9. distribute-rgt-out-- 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-249} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-249) (not (<= t_1 0.0)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-249)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-249) or not (t_1 <= 0.0):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	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))))
	tmp = 0.0
	if ((t_1 <= -5e-249) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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 <= -5e-249) || ~((t_1 <= 0.0)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	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]}, If[Or[LessEqual[t$95$1, -5e-249], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-249 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

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

      1. clear-num 87.2%

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

      2. un-div-inv 87.6%

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

   4. Applied egg-rr 87.6%

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

   if -4.9999999999999999e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate--l+ 82.2%

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

      2. distribute-lft-out-- 82.2%

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

      3. div-sub 82.2%

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

      4. mul-1-neg 82.2%

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

      5. unsub-neg 82.2%

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

      6. div-sub 82.2%

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

      7. associate-/l* 82.2%

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

      8. associate-/l* 92.2%

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

      9. distribute-rgt-out-- 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-249} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 600000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -2.85e+29)
     x
     (if (<= a -9.4e-184)
       t
       (if (<= a 1.8e-210)
         (* x (/ y z))
         (if (<= a 1.55e-134)
           t
           (if (<= a 4.5e-43)
             t_1
             (if (<= a 600000.0) t (if (<= a 8.5e+175) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -2.85e+29) {
		tmp = x;
	} else if (a <= -9.4e-184) {
		tmp = t;
	} else if (a <= 1.8e-210) {
		tmp = x * (y / z);
	} else if (a <= 1.55e-134) {
		tmp = t;
	} else if (a <= 4.5e-43) {
		tmp = t_1;
	} else if (a <= 600000.0) {
		tmp = t;
	} else if (a <= 8.5e+175) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (a <= (-2.85d+29)) then
        tmp = x
    else if (a <= (-9.4d-184)) then
        tmp = t
    else if (a <= 1.8d-210) then
        tmp = x * (y / z)
    else if (a <= 1.55d-134) then
        tmp = t
    else if (a <= 4.5d-43) then
        tmp = t_1
    else if (a <= 600000.0d0) then
        tmp = t
    else if (a <= 8.5d+175) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -2.85e+29) {
		tmp = x;
	} else if (a <= -9.4e-184) {
		tmp = t;
	} else if (a <= 1.8e-210) {
		tmp = x * (y / z);
	} else if (a <= 1.55e-134) {
		tmp = t;
	} else if (a <= 4.5e-43) {
		tmp = t_1;
	} else if (a <= 600000.0) {
		tmp = t;
	} else if (a <= 8.5e+175) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -2.85e+29:
		tmp = x
	elif a <= -9.4e-184:
		tmp = t
	elif a <= 1.8e-210:
		tmp = x * (y / z)
	elif a <= 1.55e-134:
		tmp = t
	elif a <= 4.5e-43:
		tmp = t_1
	elif a <= 600000.0:
		tmp = t
	elif a <= 8.5e+175:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -2.85e+29)
		tmp = x;
	elseif (a <= -9.4e-184)
		tmp = t;
	elseif (a <= 1.8e-210)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.55e-134)
		tmp = t;
	elseif (a <= 4.5e-43)
		tmp = t_1;
	elseif (a <= 600000.0)
		tmp = t;
	elseif (a <= 8.5e+175)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -2.85e+29)
		tmp = x;
	elseif (a <= -9.4e-184)
		tmp = t;
	elseif (a <= 1.8e-210)
		tmp = x * (y / z);
	elseif (a <= 1.55e-134)
		tmp = t;
	elseif (a <= 4.5e-43)
		tmp = t_1;
	elseif (a <= 600000.0)
		tmp = t;
	elseif (a <= 8.5e+175)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e+29], x, If[LessEqual[a, -9.4e-184], t, If[LessEqual[a, 1.8e-210], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-134], t, If[LessEqual[a, 4.5e-43], t$95$1, If[LessEqual[a, 600000.0], t, If[LessEqual[a, 8.5e+175], t$95$1, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.85e29 or 8.50000000000000034e175 < a

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf 52.6%

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

   if -2.85e29 < a < -9.40000000000000039e-184 or 1.7999999999999999e-210 < a < 1.55000000000000003e-134 or 4.50000000000000025e-43 < a < 6e5

   1. Initial program 57.5%

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

   3. Taylor expanded in z around inf 48.9%

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

   if -9.40000000000000039e-184 < a < 1.7999999999999999e-210

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-neg-frac2 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in t around 0 50.7%

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

       1. associate-/l* 54.5%

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

   11. Simplified 54.5%

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

   if 1.55000000000000003e-134 < a < 4.50000000000000025e-43 or 6e5 < a < 8.50000000000000034e175

   1. Initial program 81.0%

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

   3. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in t around inf 39.0%

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

      1. associate-/l* 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 600000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 15000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -4.9e+27)
     x
     (if (<= a -1.75e-191)
       t
       (if (<= a 3.6e-209)
         t_1
         (if (<= a 4e-133)
           t
           (if (<= a 2.1e-42)
             t_1
             (if (<= a 15000000000000.0)
               t
               (if (<= a 8e+175) (* t (/ y a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -4.9e+27) {
		tmp = x;
	} else if (a <= -1.75e-191) {
		tmp = t;
	} else if (a <= 3.6e-209) {
		tmp = t_1;
	} else if (a <= 4e-133) {
		tmp = t;
	} else if (a <= 2.1e-42) {
		tmp = t_1;
	} else if (a <= 15000000000000.0) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-4.9d+27)) then
        tmp = x
    else if (a <= (-1.75d-191)) then
        tmp = t
    else if (a <= 3.6d-209) then
        tmp = t_1
    else if (a <= 4d-133) then
        tmp = t
    else if (a <= 2.1d-42) then
        tmp = t_1
    else if (a <= 15000000000000.0d0) then
        tmp = t
    else if (a <= 8d+175) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -4.9e+27) {
		tmp = x;
	} else if (a <= -1.75e-191) {
		tmp = t;
	} else if (a <= 3.6e-209) {
		tmp = t_1;
	} else if (a <= 4e-133) {
		tmp = t;
	} else if (a <= 2.1e-42) {
		tmp = t_1;
	} else if (a <= 15000000000000.0) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -4.9e+27:
		tmp = x
	elif a <= -1.75e-191:
		tmp = t
	elif a <= 3.6e-209:
		tmp = t_1
	elif a <= 4e-133:
		tmp = t
	elif a <= 2.1e-42:
		tmp = t_1
	elif a <= 15000000000000.0:
		tmp = t
	elif a <= 8e+175:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -4.9e+27)
		tmp = x;
	elseif (a <= -1.75e-191)
		tmp = t;
	elseif (a <= 3.6e-209)
		tmp = t_1;
	elseif (a <= 4e-133)
		tmp = t;
	elseif (a <= 2.1e-42)
		tmp = t_1;
	elseif (a <= 15000000000000.0)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -4.9e+27)
		tmp = x;
	elseif (a <= -1.75e-191)
		tmp = t;
	elseif (a <= 3.6e-209)
		tmp = t_1;
	elseif (a <= 4e-133)
		tmp = t;
	elseif (a <= 2.1e-42)
		tmp = t_1;
	elseif (a <= 15000000000000.0)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.9e+27], x, If[LessEqual[a, -1.75e-191], t, If[LessEqual[a, 3.6e-209], t$95$1, If[LessEqual[a, 4e-133], t, If[LessEqual[a, 2.1e-42], t$95$1, If[LessEqual[a, 15000000000000.0], t, If[LessEqual[a, 8e+175], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.90000000000000015e27 or 7.9999999999999995e175 < a

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf 52.6%

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

   if -4.90000000000000015e27 < a < -1.75000000000000003e-191 or 3.60000000000000016e-209 < a < 4.0000000000000003e-133 or 2.10000000000000006e-42 < a < 1.5e13

   1. Initial program 56.6%

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

   3. Taylor expanded in z around inf 48.2%

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

   if -1.75000000000000003e-191 < a < 3.60000000000000016e-209 or 4.0000000000000003e-133 < a < 2.10000000000000006e-42

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. div-sub 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in a around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-neg-frac2 51.9%

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

   8. Simplified 51.9%

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

   9. Taylor expanded in t around 0 43.5%

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

       1. associate-/l* 49.1%

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

   11. Simplified 49.1%

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

   if 1.5e13 < a < 7.9999999999999995e175

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 45.0%

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

   4. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 33.4%

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

   6. Simplified 33.4%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-191}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 15000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-190}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -1e+41)
     t_1
     (if (<= a -6.4e-76)
       (* y (/ (- t x) a))
       (if (<= a -1.65e-190)
         t
         (if (<= a 1.22e-213)
           (* x (/ y z))
           (if (<= a 1.05e-135)
             t
             (if (<= a 6.5e+18) (* x (/ (- y a) z)) 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 <= -1e+41) {
		tmp = t_1;
	} else if (a <= -6.4e-76) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.65e-190) {
		tmp = t;
	} else if (a <= 1.22e-213) {
		tmp = x * (y / z);
	} else if (a <= 1.05e-135) {
		tmp = t;
	} else if (a <= 6.5e+18) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-1d+41)) then
        tmp = t_1
    else if (a <= (-6.4d-76)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-1.65d-190)) then
        tmp = t
    else if (a <= 1.22d-213) then
        tmp = x * (y / z)
    else if (a <= 1.05d-135) then
        tmp = t
    else if (a <= 6.5d+18) then
        tmp = x * ((y - a) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1e+41) {
		tmp = t_1;
	} else if (a <= -6.4e-76) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.65e-190) {
		tmp = t;
	} else if (a <= 1.22e-213) {
		tmp = x * (y / z);
	} else if (a <= 1.05e-135) {
		tmp = t;
	} else if (a <= 6.5e+18) {
		tmp = x * ((y - a) / z);
	} 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 <= -1e+41:
		tmp = t_1
	elif a <= -6.4e-76:
		tmp = y * ((t - x) / a)
	elif a <= -1.65e-190:
		tmp = t
	elif a <= 1.22e-213:
		tmp = x * (y / z)
	elif a <= 1.05e-135:
		tmp = t
	elif a <= 6.5e+18:
		tmp = x * ((y - a) / z)
	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 <= -1e+41)
		tmp = t_1;
	elseif (a <= -6.4e-76)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -1.65e-190)
		tmp = t;
	elseif (a <= 1.22e-213)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.05e-135)
		tmp = t;
	elseif (a <= 6.5e+18)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	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 <= -1e+41)
		tmp = t_1;
	elseif (a <= -6.4e-76)
		tmp = y * ((t - x) / a);
	elseif (a <= -1.65e-190)
		tmp = t;
	elseif (a <= 1.22e-213)
		tmp = x * (y / z);
	elseif (a <= 1.05e-135)
		tmp = t;
	elseif (a <= 6.5e+18)
		tmp = x * ((y - a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+41], t$95$1, If[LessEqual[a, -6.4e-76], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-190], t, If[LessEqual[a, 1.22e-213], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-135], t, If[LessEqual[a, 6.5e+18], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.00000000000000001e41 or 6.5e18 < a

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 65.8%

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

   4. Taylor expanded in x around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   6. Simplified 58.5%

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

   if -1.00000000000000001e41 < a < -6.3999999999999995e-76

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. div-sub 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in a around inf 57.0%

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

   if -6.3999999999999995e-76 < a < -1.65000000000000009e-190 or 1.22e-213 < a < 1.05e-135

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf 54.6%

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

   if -1.65000000000000009e-190 < a < 1.22e-213

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-neg-frac2 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in t around 0 50.7%

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

       1. associate-/l* 54.5%

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

   11. Simplified 54.5%

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

   if 1.05e-135 < a < 6.5e18

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 59.3%

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

      1. associate--l+ 59.3%

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

      2. distribute-lft-out-- 59.3%

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

      3. div-sub 59.3%

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

      4. mul-1-neg 59.3%

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

      5. unsub-neg 59.3%

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

      6. div-sub 59.3%

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

      7. associate-/l* 61.9%

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

      8. associate-/l* 58.6%

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

      9. distribute-rgt-out-- 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in t around 0 29.2%

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

      1. associate-/l* 41.0%

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

   8. Simplified 41.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-190}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -6.8e+173)
     (* x (/ (- y a) z))
     (if (<= z -3.4e+91)
       (/ (* x t) x)
       (if (<= z -4e+14)
         t_1
         (if (<= z -5e-91)
           (* x (- 1.0 (/ y a)))
           (if (<= z -1.08e-150)
             (* y (/ (- t x) a))
             (if (<= z 6.2e+74) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.8e+173) {
		tmp = x * ((y - a) / z);
	} else if (z <= -3.4e+91) {
		tmp = (x * t) / x;
	} else if (z <= -4e+14) {
		tmp = t_1;
	} else if (z <= -5e-91) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -1.08e-150) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6.2e+74) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-6.8d+173)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-3.4d+91)) then
        tmp = (x * t) / x
    else if (z <= (-4d+14)) then
        tmp = t_1
    else if (z <= (-5d-91)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= (-1.08d-150)) then
        tmp = y * ((t - x) / a)
    else if (z <= 6.2d+74) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.8e+173) {
		tmp = x * ((y - a) / z);
	} else if (z <= -3.4e+91) {
		tmp = (x * t) / x;
	} else if (z <= -4e+14) {
		tmp = t_1;
	} else if (z <= -5e-91) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= -1.08e-150) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6.2e+74) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -6.8e+173:
		tmp = x * ((y - a) / z)
	elif z <= -3.4e+91:
		tmp = (x * t) / x
	elif z <= -4e+14:
		tmp = t_1
	elif z <= -5e-91:
		tmp = x * (1.0 - (y / a))
	elif z <= -1.08e-150:
		tmp = y * ((t - x) / a)
	elif z <= 6.2e+74:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -6.8e+173)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -3.4e+91)
		tmp = Float64(Float64(x * t) / x);
	elseif (z <= -4e+14)
		tmp = t_1;
	elseif (z <= -5e-91)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= -1.08e-150)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 6.2e+74)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -6.8e+173)
		tmp = x * ((y - a) / z);
	elseif (z <= -3.4e+91)
		tmp = (x * t) / x;
	elseif (z <= -4e+14)
		tmp = t_1;
	elseif (z <= -5e-91)
		tmp = x * (1.0 - (y / a));
	elseif (z <= -1.08e-150)
		tmp = y * ((t - x) / a);
	elseif (z <= 6.2e+74)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+173], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e+91], N[(N[(x * t), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[z, -4e+14], t$95$1, If[LessEqual[z, -5e-91], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-150], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+74], t$95$1, t]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6.80000000000000042e173

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. distribute-lft-out-- 69.5%

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

      3. div-sub 69.5%

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

      4. mul-1-neg 69.5%

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

      5. unsub-neg 69.5%

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

      6. div-sub 69.5%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 89.2%

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

      9. distribute-rgt-out-- 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in t around 0 41.2%

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

      1. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

   if -6.80000000000000042e173 < z < -3.4000000000000001e91

   1. Initial program 67.5%

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

      1. add-cube-cbrt 66.8%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}} \cdot \sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}} \]

      2. pow3 66.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \frac{t - x}{a - z}}\right)}^{3}} \]

      3. *-commutative 66.8%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)}}\right)}^{3} \]

      4. associate-*l/ 48.7%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\frac{\left(t - x\right) \cdot \left(y - z\right)}{a - z}}}\right)}^{3} \]

      5. associate-*r/ 67.0%

         \[\leadsto x + {\left(\sqrt[3]{\color{blue}{\left(t - x\right) \cdot \frac{y - z}{a - z}}}\right)}^{3} \]

   4. Applied egg-rr 67.0%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(t - x\right) \cdot \frac{y - z}{a - z}}\right)}^{3}} \]

   5. Taylor expanded in x around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

      4. associate-/l* 55.1%

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

      5. *-commutative 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in z around inf 39.6%

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

      1. associate-*r/ 52.0%

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

   10. Applied egg-rr 52.0%

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

   if -3.4000000000000001e91 < z < -4e14 or -1.08000000000000003e-150 < z < 6.20000000000000043e74

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 65.8%

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

   4. Taylor expanded in t around inf 57.8%

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

      1. associate-/l* 59.6%

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

   6. Simplified 59.6%

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

   if -4e14 < z < -4.99999999999999997e-91

   1. Initial program 80.5%

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

   3. Taylor expanded in z around 0 68.0%

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

   4. Taylor expanded in x around inf 61.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   5. 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%

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

   6. Simplified 61.7%

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

   if -4.99999999999999997e-91 < z < -1.08000000000000003e-150

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. div-sub 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in a around inf 65.0%

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

   if 6.20000000000000043e74 < z

   1. Initial program 51.7%

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

   3. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{t} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+74}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+98}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.78 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= x -1.65e+98)
     (- x (* x (/ y a)))
     (if (<= x -1.76e-50)
       t_1
       (if (<= x 4.1e-43)
         t_2
         (if (<= x 1.78e+56)
           t_1
           (if (<= x 6.2e+69)
             t_2
             (if (<= x 1e+200)
               (* x (- 1.0 (/ y a)))
               (* x (/ (- y a) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -1.65e+98) {
		tmp = x - (x * (y / a));
	} else if (x <= -1.76e-50) {
		tmp = t_1;
	} else if (x <= 4.1e-43) {
		tmp = t_2;
	} else if (x <= 1.78e+56) {
		tmp = t_1;
	} else if (x <= 6.2e+69) {
		tmp = t_2;
	} else if (x <= 1e+200) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * ((y - z) / (a - z))
    if (x <= (-1.65d+98)) then
        tmp = x - (x * (y / a))
    else if (x <= (-1.76d-50)) then
        tmp = t_1
    else if (x <= 4.1d-43) then
        tmp = t_2
    else if (x <= 1.78d+56) then
        tmp = t_1
    else if (x <= 6.2d+69) then
        tmp = t_2
    else if (x <= 1d+200) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -1.65e+98) {
		tmp = x - (x * (y / a));
	} else if (x <= -1.76e-50) {
		tmp = t_1;
	} else if (x <= 4.1e-43) {
		tmp = t_2;
	} else if (x <= 1.78e+56) {
		tmp = t_1;
	} else if (x <= 6.2e+69) {
		tmp = t_2;
	} else if (x <= 1e+200) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -1.65e+98:
		tmp = x - (x * (y / a))
	elif x <= -1.76e-50:
		tmp = t_1
	elif x <= 4.1e-43:
		tmp = t_2
	elif x <= 1.78e+56:
		tmp = t_1
	elif x <= 6.2e+69:
		tmp = t_2
	elif x <= 1e+200:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -1.65e+98)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (x <= -1.76e-50)
		tmp = t_1;
	elseif (x <= 4.1e-43)
		tmp = t_2;
	elseif (x <= 1.78e+56)
		tmp = t_1;
	elseif (x <= 6.2e+69)
		tmp = t_2;
	elseif (x <= 1e+200)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -1.65e+98)
		tmp = x - (x * (y / a));
	elseif (x <= -1.76e-50)
		tmp = t_1;
	elseif (x <= 4.1e-43)
		tmp = t_2;
	elseif (x <= 1.78e+56)
		tmp = t_1;
	elseif (x <= 6.2e+69)
		tmp = t_2;
	elseif (x <= 1e+200)
		tmp = x * (1.0 - (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+98], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.76e-50], t$95$1, If[LessEqual[x, 4.1e-43], t$95$2, If[LessEqual[x, 1.78e+56], t$95$1, If[LessEqual[x, 6.2e+69], t$95$2, If[LessEqual[x, 1e+200], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.65000000000000014e98

   1. Initial program 68.0%

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

   3. Taylor expanded in z around 0 55.2%

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

   4. Taylor expanded in t around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-/l* 65.0%

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

      3. distribute-rgt-neg-in 65.0%

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

      4. mul-1-neg 65.0%

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

      5. associate-*r/ 65.0%

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

      6. mul-1-neg 65.0%

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

   6. Simplified 65.0%

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

   if -1.65000000000000014e98 < x < -1.76e-50 or 4.0999999999999998e-43 < x < 1.78e56

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

   5. Simplified 59.3%

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

   if -1.76e-50 < x < 4.0999999999999998e-43 or 1.78e56 < x < 6.1999999999999997e69

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   if 6.1999999999999997e69 < x < 9.9999999999999997e199

   1. Initial program 76.8%

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

   3. Taylor expanded in z around 0 43.6%

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

   4. Taylor expanded in x around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   6. Simplified 60.7%

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

   if 9.9999999999999997e199 < x

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. distribute-lft-out-- 57.3%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. div-sub 57.3%

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

      7. associate-/l* 66.4%

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

      8. associate-/l* 81.1%

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

      9. distribute-rgt-out-- 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+98}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.78 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 10^{+200}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-52}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= x -2.25e+105)
     (- x (* x (/ y a)))
     (if (<= x -3.25e-52)
       (* (- t x) (/ y (- a z)))
       (if (<= x 8.2e-44)
         t_1
         (if (<= x 2.15e+56)
           (* y (/ (- t x) (- a z)))
           (if (<= x 9.2e+70)
             t_1
             (if (<= x 5.6e+199)
               (* x (- 1.0 (/ y a)))
               (* x (/ (- y a) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -2.25e+105) {
		tmp = x - (x * (y / a));
	} else if (x <= -3.25e-52) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 8.2e-44) {
		tmp = t_1;
	} else if (x <= 2.15e+56) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 9.2e+70) {
		tmp = t_1;
	} else if (x <= 5.6e+199) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (x <= (-2.25d+105)) then
        tmp = x - (x * (y / a))
    else if (x <= (-3.25d-52)) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 8.2d-44) then
        tmp = t_1
    else if (x <= 2.15d+56) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 9.2d+70) then
        tmp = t_1
    else if (x <= 5.6d+199) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -2.25e+105) {
		tmp = x - (x * (y / a));
	} else if (x <= -3.25e-52) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 8.2e-44) {
		tmp = t_1;
	} else if (x <= 2.15e+56) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 9.2e+70) {
		tmp = t_1;
	} else if (x <= 5.6e+199) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -2.25e+105:
		tmp = x - (x * (y / a))
	elif x <= -3.25e-52:
		tmp = (t - x) * (y / (a - z))
	elif x <= 8.2e-44:
		tmp = t_1
	elif x <= 2.15e+56:
		tmp = y * ((t - x) / (a - z))
	elif x <= 9.2e+70:
		tmp = t_1
	elif x <= 5.6e+199:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -2.25e+105)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (x <= -3.25e-52)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 8.2e-44)
		tmp = t_1;
	elseif (x <= 2.15e+56)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 9.2e+70)
		tmp = t_1;
	elseif (x <= 5.6e+199)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -2.25e+105)
		tmp = x - (x * (y / a));
	elseif (x <= -3.25e-52)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 8.2e-44)
		tmp = t_1;
	elseif (x <= 2.15e+56)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 9.2e+70)
		tmp = t_1;
	elseif (x <= 5.6e+199)
		tmp = x * (1.0 - (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e+105], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.25e-52], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-44], t$95$1, If[LessEqual[x, 2.15e+56], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+70], t$95$1, If[LessEqual[x, 5.6e+199], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.2500000000000001e105

   1. Initial program 68.0%

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

   3. Taylor expanded in z around 0 55.2%

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

   4. Taylor expanded in t around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-/l* 65.0%

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

      3. distribute-rgt-neg-in 65.0%

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

      4. mul-1-neg 65.0%

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

      5. associate-*r/ 65.0%

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

      6. mul-1-neg 65.0%

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

   6. Simplified 65.0%

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

   if -2.2500000000000001e105 < x < -3.25e-52

   1. Initial program 82.5%

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

   3. Taylor expanded in y around -inf 58.8%

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

      1. associate-*r/ 61.0%

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

      2. clear-num 61.0%

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

      3. div-inv 61.1%

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

      4. associate-/r/ 64.5%

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

   5. Applied egg-rr 64.5%

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

   if -3.25e-52 < x < 8.19999999999999984e-44 or 2.1500000000000002e56 < x < 9.19999999999999975e70

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

   if 8.19999999999999984e-44 < x < 2.1500000000000002e56

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. div-sub 54.9%

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

   5. Simplified 54.9%

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

   if 9.19999999999999975e70 < x < 5.6000000000000002e199

   1. Initial program 76.8%

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

   3. Taylor expanded in z around 0 43.6%

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

   4. Taylor expanded in x around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   6. Simplified 60.7%

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

   if 5.6000000000000002e199 < x

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. distribute-lft-out-- 57.3%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. div-sub 57.3%

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

      7. associate-/l* 66.4%

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

      8. associate-/l* 81.1%

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

      9. distribute-rgt-out-- 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. associate-/l* 61.7%

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

   8. Simplified 61.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - a}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{-52}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-182}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -8.4e+15)
     t_1
     (if (<= a -5.9e-182)
       t
       (if (<= a 2.1e-214)
         (* x (/ y z))
         (if (<= a 1.9e-136)
           t
           (if (<= a 6.4e+18) (* x (/ (- y a) z)) 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 <= -8.4e+15) {
		tmp = t_1;
	} else if (a <= -5.9e-182) {
		tmp = t;
	} else if (a <= 2.1e-214) {
		tmp = x * (y / z);
	} else if (a <= 1.9e-136) {
		tmp = t;
	} else if (a <= 6.4e+18) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-8.4d+15)) then
        tmp = t_1
    else if (a <= (-5.9d-182)) then
        tmp = t
    else if (a <= 2.1d-214) then
        tmp = x * (y / z)
    else if (a <= 1.9d-136) then
        tmp = t
    else if (a <= 6.4d+18) then
        tmp = x * ((y - a) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -8.4e+15) {
		tmp = t_1;
	} else if (a <= -5.9e-182) {
		tmp = t;
	} else if (a <= 2.1e-214) {
		tmp = x * (y / z);
	} else if (a <= 1.9e-136) {
		tmp = t;
	} else if (a <= 6.4e+18) {
		tmp = x * ((y - a) / z);
	} 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 <= -8.4e+15:
		tmp = t_1
	elif a <= -5.9e-182:
		tmp = t
	elif a <= 2.1e-214:
		tmp = x * (y / z)
	elif a <= 1.9e-136:
		tmp = t
	elif a <= 6.4e+18:
		tmp = x * ((y - a) / z)
	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 <= -8.4e+15)
		tmp = t_1;
	elseif (a <= -5.9e-182)
		tmp = t;
	elseif (a <= 2.1e-214)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.9e-136)
		tmp = t;
	elseif (a <= 6.4e+18)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	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 <= -8.4e+15)
		tmp = t_1;
	elseif (a <= -5.9e-182)
		tmp = t;
	elseif (a <= 2.1e-214)
		tmp = x * (y / z);
	elseif (a <= 1.9e-136)
		tmp = t;
	elseif (a <= 6.4e+18)
		tmp = x * ((y - a) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.4e+15], t$95$1, If[LessEqual[a, -5.9e-182], t, If[LessEqual[a, 2.1e-214], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-136], t, If[LessEqual[a, 6.4e+18], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.4e15 or 6.4e18 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 66.6%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   6. Simplified 57.5%

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

   if -8.4e15 < a < -5.89999999999999968e-182 or 2.09999999999999992e-214 < a < 1.9000000000000001e-136

   1. Initial program 57.9%

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

   3. Taylor expanded in z around inf 49.0%

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

   if -5.89999999999999968e-182 < a < 2.09999999999999992e-214

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. div-sub 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-neg-frac2 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in t around 0 50.7%

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

       1. associate-/l* 54.5%

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

   11. Simplified 54.5%

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

   if 1.9000000000000001e-136 < a < 6.4e18

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 59.3%

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

      1. associate--l+ 59.3%

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

      2. distribute-lft-out-- 59.3%

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

      3. div-sub 59.3%

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

      4. mul-1-neg 59.3%

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

      5. unsub-neg 59.3%

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

      6. div-sub 59.3%

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

      7. associate-/l* 61.9%

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

      8. associate-/l* 58.6%

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

      9. distribute-rgt-out-- 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in t around 0 29.2%

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

      1. associate-/l* 41.0%

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

   8. Simplified 41.0%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-182}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+67}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+199}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.65e+67)
     (- x (* x (/ y a)))
     (if (<= x -6e-34)
       t_1
       (if (<= x -1.32e-55)
         t_2
         (if (<= x 2.5e+19)
           t_1
           (if (<= x 9.5e+199) t_2 (* x (/ (- y a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.65e+67) {
		tmp = x - (x * (y / a));
	} else if (x <= -6e-34) {
		tmp = t_1;
	} else if (x <= -1.32e-55) {
		tmp = t_2;
	} else if (x <= 2.5e+19) {
		tmp = t_1;
	} else if (x <= 9.5e+199) {
		tmp = t_2;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-1.65d+67)) then
        tmp = x - (x * (y / a))
    else if (x <= (-6d-34)) then
        tmp = t_1
    else if (x <= (-1.32d-55)) then
        tmp = t_2
    else if (x <= 2.5d+19) then
        tmp = t_1
    else if (x <= 9.5d+199) then
        tmp = t_2
    else
        tmp = x * ((y - a) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.65e+67) {
		tmp = x - (x * (y / a));
	} else if (x <= -6e-34) {
		tmp = t_1;
	} else if (x <= -1.32e-55) {
		tmp = t_2;
	} else if (x <= 2.5e+19) {
		tmp = t_1;
	} else if (x <= 9.5e+199) {
		tmp = t_2;
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.65e+67:
		tmp = x - (x * (y / a))
	elif x <= -6e-34:
		tmp = t_1
	elif x <= -1.32e-55:
		tmp = t_2
	elif x <= 2.5e+19:
		tmp = t_1
	elif x <= 9.5e+199:
		tmp = t_2
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.65e+67)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (x <= -6e-34)
		tmp = t_1;
	elseif (x <= -1.32e-55)
		tmp = t_2;
	elseif (x <= 2.5e+19)
		tmp = t_1;
	elseif (x <= 9.5e+199)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.65e+67)
		tmp = x - (x * (y / a));
	elseif (x <= -6e-34)
		tmp = t_1;
	elseif (x <= -1.32e-55)
		tmp = t_2;
	elseif (x <= 2.5e+19)
		tmp = t_1;
	elseif (x <= 9.5e+199)
		tmp = t_2;
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+67], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-34], t$95$1, If[LessEqual[x, -1.32e-55], t$95$2, If[LessEqual[x, 2.5e+19], t$95$1, If[LessEqual[x, 9.5e+199], t$95$2, N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6500000000000001e67

   1. Initial program 67.5%

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

   3. Taylor expanded in z around 0 53.7%

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

   4. Taylor expanded in t around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-/l* 63.2%

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

      3. distribute-rgt-neg-in 63.2%

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

      4. mul-1-neg 63.2%

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

      5. associate-*r/ 63.2%

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

      6. mul-1-neg 63.2%

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

   6. Simplified 63.2%

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

   if -1.6500000000000001e67 < x < -6e-34 or -1.31999999999999993e-55 < x < 2.5e19

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. associate-/l* 71.1%

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

   5. Simplified 71.1%

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

   if -6e-34 < x < -1.31999999999999993e-55 or 2.5e19 < x < 9.49999999999999954e199

   1. Initial program 83.1%

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

   3. Taylor expanded in z around 0 48.3%

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

   4. Taylor expanded in x around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   6. Simplified 57.3%

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

   if 9.49999999999999954e199 < x

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. distribute-lft-out-- 57.3%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. div-sub 57.3%

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

      7. associate-/l* 66.4%

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

      8. associate-/l* 81.1%

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

      9. distribute-rgt-out-- 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in t around 0 42.5%

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

      1. associate-/l* 61.7%

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

   8. Simplified 61.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+67}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-42}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 24:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2.1e-22)
     t_2
     (if (<= a 4e-135)
       t_1
       (if (<= a 1.2e-42)
         (* (- t x) (/ y (- a z)))
         (if (<= a 24.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.1e-22) {
		tmp = t_2;
	} else if (a <= 4e-135) {
		tmp = t_1;
	} else if (a <= 1.2e-42) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 24.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-2.1d-22)) then
        tmp = t_2
    else if (a <= 4d-135) then
        tmp = t_1
    else if (a <= 1.2d-42) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 24.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.1e-22) {
		tmp = t_2;
	} else if (a <= 4e-135) {
		tmp = t_1;
	} else if (a <= 1.2e-42) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 24.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2.1e-22:
		tmp = t_2
	elif a <= 4e-135:
		tmp = t_1
	elif a <= 1.2e-42:
		tmp = (t - x) * (y / (a - z))
	elif a <= 24.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.1e-22)
		tmp = t_2;
	elseif (a <= 4e-135)
		tmp = t_1;
	elseif (a <= 1.2e-42)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 24.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.1e-22)
		tmp = t_2;
	elseif (a <= 4e-135)
		tmp = t_1;
	elseif (a <= 1.2e-42)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 24.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e-22], t$95$2, If[LessEqual[a, 4e-135], t$95$1, If[LessEqual[a, 1.2e-42], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 24.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.10000000000000008e-22 or 24 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -2.10000000000000008e-22 < a < 4.0000000000000002e-135 or 1.20000000000000001e-42 < a < 24

   1. Initial program 59.0%

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

   3. Taylor expanded in z around inf 77.0%

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

      1. associate--l+ 77.0%

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

      2. distribute-lft-out-- 77.0%

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

      3. div-sub 77.0%

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

      4. mul-1-neg 77.0%

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

      5. unsub-neg 77.0%

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

      6. div-sub 77.0%

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

      7. associate-/l* 81.6%

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

      8. associate-/l* 80.5%

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

      9. distribute-rgt-out-- 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 72.8%

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

      1. associate-*r/ 77.6%

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

   8. Simplified 77.6%

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

   if 4.0000000000000002e-135 < a < 1.20000000000000001e-42

   1. Initial program 62.1%

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

   3. Taylor expanded in y around -inf 66.5%

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

      1. associate-*r/ 64.7%

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

      2. clear-num 64.7%

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

      3. div-inv 64.5%

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

      4. associate-/r/ 70.8%

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

   5. Applied egg-rr 70.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-135}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-42}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 24:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.46 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -7.5e+90)
     t
     (if (<= z 3.05e-254)
       t_1
       (if (<= z 3e-215) (* t (/ y (- a z))) (if (<= z 2.46e+45) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7.5e+90) {
		tmp = t;
	} else if (z <= 3.05e-254) {
		tmp = t_1;
	} else if (z <= 3e-215) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.46e+45) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-7.5d+90)) then
        tmp = t
    else if (z <= 3.05d-254) then
        tmp = t_1
    else if (z <= 3d-215) then
        tmp = t * (y / (a - z))
    else if (z <= 2.46d+45) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -7.5e+90) {
		tmp = t;
	} else if (z <= 3.05e-254) {
		tmp = t_1;
	} else if (z <= 3e-215) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.46e+45) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -7.5e+90:
		tmp = t
	elif z <= 3.05e-254:
		tmp = t_1
	elif z <= 3e-215:
		tmp = t * (y / (a - z))
	elif z <= 2.46e+45:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -7.5e+90)
		tmp = t;
	elseif (z <= 3.05e-254)
		tmp = t_1;
	elseif (z <= 3e-215)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.46e+45)
		tmp = t_1;
	else
		tmp = t;
	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 (z <= -7.5e+90)
		tmp = t;
	elseif (z <= 3.05e-254)
		tmp = t_1;
	elseif (z <= 3e-215)
		tmp = t * (y / (a - z));
	elseif (z <= 2.46e+45)
		tmp = t_1;
	else
		tmp = t;
	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[z, -7.5e+90], t, If[LessEqual[z, 3.05e-254], t$95$1, If[LessEqual[z, 3e-215], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.46e+45], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000014e90 or 2.4599999999999999e45 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in z around inf 46.1%

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

   if -7.50000000000000014e90 < z < 3.05e-254 or 3.00000000000000025e-215 < z < 2.4599999999999999e45

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 68.9%

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

   4. Taylor expanded in x around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

   if 3.05e-254 < z < 3.00000000000000025e-215

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. div-sub 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in t around inf 74.9%

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

      1. associate-/l* 74.9%

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

   8. Simplified 74.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.46 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e+139)
   (+ t (* a (/ (- t x) z)))
   (if (<= z -2.6e+25)
     (* y (/ (- t x) (- a z)))
     (if (<= z 6.2e+21) (+ x (* y (/ (- t x) a))) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+139) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -2.6e+25) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.2e+21) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = 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 (z <= (-1.12d+139)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= (-2.6d+25)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 6.2d+21) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = 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 (z <= -1.12e+139) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -2.6e+25) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.2e+21) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e+139:
		tmp = t + (a * ((t - x) / z))
	elif z <= -2.6e+25:
		tmp = y * ((t - x) / (a - z))
	elif z <= 6.2e+21:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e+139)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= -2.6e+25)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 6.2e+21)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = 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 (z <= -1.12e+139)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= -2.6e+25)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 6.2e+21)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e+139], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e+25], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+21], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.12e139

   1. Initial program 48.3%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. associate--l+ 71.6%

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

      2. distribute-lft-out-- 71.6%

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

      3. div-sub 71.6%

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

      4. mul-1-neg 71.6%

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

      5. unsub-neg 71.6%

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

      6. div-sub 71.6%

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

      7. associate-/l* 76.6%

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

      8. associate-/l* 89.2%

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

      9. distribute-rgt-out-- 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around 0 53.3%

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

      1. sub-neg 53.3%

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

      2. mul-1-neg 53.3%

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

      3. remove-double-neg 53.3%

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

      4. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   if -1.12e139 < z < -2.5999999999999998e25

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. div-sub 56.7%

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

   5. Simplified 56.7%

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

   if -2.5999999999999998e25 < z < 6.2e21

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 78.0%

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

      1. associate-/l* 76.4%

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

   5. Simplified 76.4%

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

   if 6.2e21 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in x around 0 37.4%

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

      1. associate-/l* 59.2%

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

   5. Simplified 59.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+138}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+138)
   (+ t (* a (/ (- t x) z)))
   (if (<= z -2e+20)
     (* y (/ (- t x) (- a z)))
     (if (<= z 4.3e+21) (- x (/ (* y (- x t)) a)) (* t (/ (- y z) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+138) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -2e+20) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.3e+21) {
		tmp = x - ((y * (x - t)) / a);
	} else {
		tmp = 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 (z <= (-4.3d+138)) then
        tmp = t + (a * ((t - x) / z))
    else if (z <= (-2d+20)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 4.3d+21) then
        tmp = x - ((y * (x - t)) / a)
    else
        tmp = 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 (z <= -4.3e+138) {
		tmp = t + (a * ((t - x) / z));
	} else if (z <= -2e+20) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.3e+21) {
		tmp = x - ((y * (x - t)) / a);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+138:
		tmp = t + (a * ((t - x) / z))
	elif z <= -2e+20:
		tmp = y * ((t - x) / (a - z))
	elif z <= 4.3e+21:
		tmp = x - ((y * (x - t)) / a)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+138)
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	elseif (z <= -2e+20)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 4.3e+21)
		tmp = Float64(x - Float64(Float64(y * Float64(x - t)) / a));
	else
		tmp = 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 (z <= -4.3e+138)
		tmp = t + (a * ((t - x) / z));
	elseif (z <= -2e+20)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 4.3e+21)
		tmp = x - ((y * (x - t)) / a);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+138], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+20], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+21], N[(x - N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2999999999999998e138

   1. Initial program 48.3%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. associate--l+ 71.6%

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

      2. distribute-lft-out-- 71.6%

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

      3. div-sub 71.6%

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

      4. mul-1-neg 71.6%

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

      5. unsub-neg 71.6%

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

      6. div-sub 71.6%

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

      7. associate-/l* 76.6%

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

      8. associate-/l* 89.2%

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

      9. distribute-rgt-out-- 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around 0 53.3%

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

      1. sub-neg 53.3%

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

      2. mul-1-neg 53.3%

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

      3. remove-double-neg 53.3%

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

      4. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   if -4.2999999999999998e138 < z < -2e20

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. div-sub 56.7%

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

   5. Simplified 56.7%

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

   if -2e20 < z < 4.3e21

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 78.0%

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

   if 4.3e21 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in x around 0 37.4%

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

      1. associate-/l* 59.2%

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

   5. Simplified 59.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+138}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{y \cdot \left(x - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+89} \lor \neg \left(z \leq 9.5 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.3e+175)
   (* x (/ (- y a) z))
   (if (or (<= z -4.1e+89) (not (<= z 9.5e+43)))
     (* t (/ z (- z a)))
     (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.3e+175) {
		tmp = x * ((y - a) / z);
	} else if ((z <= -4.1e+89) || !(z <= 9.5e+43)) {
		tmp = t * (z / (z - a));
	} 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 (z <= (-5.3d+175)) then
        tmp = x * ((y - a) / z)
    else if ((z <= (-4.1d+89)) .or. (.not. (z <= 9.5d+43))) then
        tmp = t * (z / (z - a))
    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 (z <= -5.3e+175) {
		tmp = x * ((y - a) / z);
	} else if ((z <= -4.1e+89) || !(z <= 9.5e+43)) {
		tmp = t * (z / (z - a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.3e+175:
		tmp = x * ((y - a) / z)
	elif (z <= -4.1e+89) or not (z <= 9.5e+43):
		tmp = t * (z / (z - a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.3e+175)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif ((z <= -4.1e+89) || !(z <= 9.5e+43))
		tmp = Float64(t * Float64(z / Float64(z - a)));
	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 (z <= -5.3e+175)
		tmp = x * ((y - a) / z);
	elseif ((z <= -4.1e+89) || ~((z <= 9.5e+43)))
		tmp = t * (z / (z - a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.3e+175], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.1e+89], N[Not[LessEqual[z, 9.5e+43]], $MachinePrecision]], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.30000000000000012e175

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. distribute-lft-out-- 69.5%

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

      3. div-sub 69.5%

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

      4. mul-1-neg 69.5%

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

      5. unsub-neg 69.5%

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

      6. div-sub 69.5%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 89.2%

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

      9. distribute-rgt-out-- 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in t around 0 41.2%

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

      1. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

   if -5.30000000000000012e175 < z < -4.09999999999999985e89 or 9.5000000000000004e43 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in x around 0 38.7%

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

   4. Taylor expanded in y around 0 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/l* 54.8%

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

      3. distribute-lft-neg-in 54.8%

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

   6. Simplified 54.8%

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

   if -4.09999999999999985e89 < z < 9.5000000000000004e43

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 69.2%

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

   4. Taylor expanded in t around inf 57.4%

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

      1. associate-/l* 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+89} \lor \neg \left(z \leq 9.5 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-22} \lor \neg \left(a \leq 50\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.45e-22) (not (<= a 50.0)))
   (- x (* (- t x) (/ (- z y) a)))
   (+ t (* x (/ (- y a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e-22) || !(a <= 50.0)) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.45d-22)) .or. (.not. (a <= 50.0d0))) then
        tmp = x - ((t - x) * ((z - y) / a))
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.45e-22) || !(a <= 50.0)) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.45e-22) or not (a <= 50.0):
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.45e-22) || !(a <= 50.0))
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.45e-22) || ~((a <= 50.0)))
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.45e-22], N[Not[LessEqual[a, 50.0]], $MachinePrecision]], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4500000000000001e-22 or 50 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

   if -1.4500000000000001e-22 < a < 50

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. distribute-lft-out-- 73.5%

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

      3. div-sub 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. div-sub 73.5%

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

      7. associate-/l* 77.3%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. mul-1-neg 76.3%

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

      5. associate-*r/ 76.3%

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

      6. neg-mul-1 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-22} \lor \neg \left(a \leq 50\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-22} \lor \neg \left(a \leq 23000\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e-22) (not (<= a 23000.0)))
   (- x (* (- t x) (/ (- z y) a)))
   (+ t (* (/ (- t x) z) (- a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e-22) || !(a <= 23000.0)) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t + (((t - x) / z) * (a - 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 ((a <= (-1.4d-22)) .or. (.not. (a <= 23000.0d0))) then
        tmp = x - ((t - x) * ((z - y) / a))
    else
        tmp = t + (((t - x) / z) * (a - 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 ((a <= -1.4e-22) || !(a <= 23000.0)) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e-22) or not (a <= 23000.0):
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e-22) || !(a <= 23000.0))
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e-22) || ~((a <= 23000.0)))
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e-22], N[Not[LessEqual[a, 23000.0]], $MachinePrecision]], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.39999999999999997e-22 or 23000 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

   if -1.39999999999999997e-22 < a < 23000

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. distribute-lft-out-- 73.5%

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

      3. div-sub 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. div-sub 73.5%

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

      7. associate-/l* 77.3%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-22} \lor \neg \left(a \leq 23000\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-22} \lor \neg \left(a \leq 540000000000\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e-22) (not (<= a 540000000000.0)))
   (+ x (* y (/ (- t x) a)))
   (- t (* x (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-22) || !(a <= 540000000000.0)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = 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 <= (-1.9d-22)) .or. (.not. (a <= 540000000000.0d0))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = 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 <= -1.9e-22) || !(a <= 540000000000.0)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t - (x * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e-22) or not (a <= 540000000000.0):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t - (x * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e-22) || !(a <= 540000000000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e-22) || ~((a <= 540000000000.0)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t - (x * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e-22], N[Not[LessEqual[a, 540000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.90000000000000012e-22 or 5.4e11 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -1.90000000000000012e-22 < a < 5.4e11

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. distribute-lft-out-- 73.5%

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

      3. div-sub 73.5%

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

      4. mul-1-neg 73.5%

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

      5. unsub-neg 73.5%

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

      6. div-sub 73.5%

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

      7. associate-/l* 77.3%

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

      8. associate-/l* 75.5%

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

      9. distribute-rgt-out-- 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. mul-1-neg 76.3%

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

      5. associate-*r/ 76.3%

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

      6. neg-mul-1 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-22} \lor \neg \left(a \leq 540000000000\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 55000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+24) x (if (<= a 55000000.0) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+24) {
		tmp = x;
	} else if (a <= 55000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+24)) then
        tmp = x
    else if (a <= 55000000.0d0) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+24) {
		tmp = x;
	} else if (a <= 55000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+24:
		tmp = x
	elif a <= 55000000.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+24)
		tmp = x;
	elseif (a <= 55000000.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+24)
		tmp = x;
	elseif (a <= 55000000.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+24], x, If[LessEqual[a, 55000000.0], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000001e24 or 5.5e7 < a

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 45.1%

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

   if -1.10000000000000001e24 < a < 5.5e7

   1. Initial program 60.8%

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

   3. Taylor expanded in z around inf 38.5%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 55000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.7% 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 75.5%

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

3. Taylor expanded in z around inf 23.7%

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

4. Final simplification 23.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))