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

Percentage Accurate: 67.8% → 90.7%

Time: 25.4s

Alternatives: 26

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-296}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -1e-296)
     (+ x (* (- x t) (/ (- z y) (- a z))))
     (if (<= t_1 0.0)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (/ (- y z) (- a z)) (- t x) x)))))

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 <= -1e-296) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-296)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-296

   1. Initial program 72.2%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   if -1e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. unsub-neg 99.8%

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

      10. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

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

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-*l/ 85.5%

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

      3. fma-def 85.6%

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

   3. Simplified 85.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-296}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-181}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{+225} \lor \neg \left(a \leq 4.6 \cdot 10^{+241}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z))))
        (t_2 (+ x (/ t (/ a y))))
        (t_3 (* t (/ (- y z) (- a z)))))
   (if (<= a -1.6e+35)
     t_2
     (if (<= a -7.4e-89)
       t_1
       (if (<= a -4.7e-181)
         t_3
         (if (<= a -2.4e-198)
           (* y (/ (- t x) (- a z)))
           (if (<= a 2.3e-24)
             t_3
             (if (<= a 3.2e+72)
               t_1
               (if (or (<= a 1.24e+225) (not (<= a 4.6e+241))) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = x + (t / (a / y));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.6e+35) {
		tmp = t_2;
	} else if (a <= -7.4e-89) {
		tmp = t_1;
	} else if (a <= -4.7e-181) {
		tmp = t_3;
	} else if (a <= -2.4e-198) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.3e-24) {
		tmp = t_3;
	} else if (a <= 3.2e+72) {
		tmp = t_1;
	} else if ((a <= 1.24e+225) || !(a <= 4.6e+241)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    t_2 = x + (t / (a / y))
    t_3 = t * ((y - z) / (a - z))
    if (a <= (-1.6d+35)) then
        tmp = t_2
    else if (a <= (-7.4d-89)) then
        tmp = t_1
    else if (a <= (-4.7d-181)) then
        tmp = t_3
    else if (a <= (-2.4d-198)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 2.3d-24) then
        tmp = t_3
    else if (a <= 3.2d+72) then
        tmp = t_1
    else if ((a <= 1.24d+225) .or. (.not. (a <= 4.6d+241))) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = x + (t / (a / y));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -1.6e+35) {
		tmp = t_2;
	} else if (a <= -7.4e-89) {
		tmp = t_1;
	} else if (a <= -4.7e-181) {
		tmp = t_3;
	} else if (a <= -2.4e-198) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 2.3e-24) {
		tmp = t_3;
	} else if (a <= 3.2e+72) {
		tmp = t_1;
	} else if ((a <= 1.24e+225) || !(a <= 4.6e+241)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = x + (t / (a / y))
	t_3 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -1.6e+35:
		tmp = t_2
	elif a <= -7.4e-89:
		tmp = t_1
	elif a <= -4.7e-181:
		tmp = t_3
	elif a <= -2.4e-198:
		tmp = y * ((t - x) / (a - z))
	elif a <= 2.3e-24:
		tmp = t_3
	elif a <= 3.2e+72:
		tmp = t_1
	elif (a <= 1.24e+225) or not (a <= 4.6e+241):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	t_3 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.6e+35)
		tmp = t_2;
	elseif (a <= -7.4e-89)
		tmp = t_1;
	elseif (a <= -4.7e-181)
		tmp = t_3;
	elseif (a <= -2.4e-198)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 2.3e-24)
		tmp = t_3;
	elseif (a <= 3.2e+72)
		tmp = t_1;
	elseif ((a <= 1.24e+225) || !(a <= 4.6e+241))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = x + (t / (a / y));
	t_3 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -1.6e+35)
		tmp = t_2;
	elseif (a <= -7.4e-89)
		tmp = t_1;
	elseif (a <= -4.7e-181)
		tmp = t_3;
	elseif (a <= -2.4e-198)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 2.3e-24)
		tmp = t_3;
	elseif (a <= 3.2e+72)
		tmp = t_1;
	elseif ((a <= 1.24e+225) || ~((a <= 4.6e+241)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+35], t$95$2, If[LessEqual[a, -7.4e-89], t$95$1, If[LessEqual[a, -4.7e-181], t$95$3, If[LessEqual[a, -2.4e-198], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-24], t$95$3, If[LessEqual[a, 3.2e+72], t$95$1, If[Or[LessEqual[a, 1.24e+225], N[Not[LessEqual[a, 4.6e+241]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.59999999999999991e35 or 3.2000000000000001e72 < a < 1.24e225 or 4.5999999999999999e241 < a

   1. Initial program 72.1%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in t around inf 84.6%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. associate-/l* 73.1%

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

   8. Simplified 73.1%

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

   if -1.59999999999999991e35 < a < -7.3999999999999995e-89 or 2.3000000000000001e-24 < a < 3.2000000000000001e72

   1. Initial program 75.1%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in y around -inf 63.5%

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

      1. associate-*l/ 68.7%

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

   7. Simplified 68.7%

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

   if -7.3999999999999995e-89 < a < -4.6999999999999998e-181 or -2.39999999999999986e-198 < a < 2.3000000000000001e-24 or 1.24e225 < a < 4.5999999999999999e241

   1. Initial program 63.1%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around 0 61.9%

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

      1. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

      1. clear-num 75.0%

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

      2. associate-/r/ 75.0%

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

      3. clear-num 75.1%

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

   9. Applied egg-rr 75.1%

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

   if -4.6999999999999998e-181 < a < -2.39999999999999986e-198

   1. Initial program 72.0%

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

      1. associate-*l/ 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. div-sub 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-89}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-181}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{+225} \lor \neg \left(a \leq 4.6 \cdot 10^{+241}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-175}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+228} \lor \neg \left(a \leq 4.6 \cdot 10^{+241}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -2.9e+35)
     t_2
     (if (<= a -2e-91)
       t_1
       (if (<= a -4.8e-170)
         (- t (/ y (/ z t)))
         (if (<= a -3.2e-197)
           (* y (/ (- t x) (- a z)))
           (if (<= a 6.6e-175)
             (/ (- t) (/ z (- y z)))
             (if (<= a 1.7e+73)
               t_1
               (if (or (<= a 1.12e+228) (not (<= a 4.6e+241)))
                 t_2
                 (/ (- t) (+ -1.0 (/ a z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -2.9e+35) {
		tmp = t_2;
	} else if (a <= -2e-91) {
		tmp = t_1;
	} else if (a <= -4.8e-170) {
		tmp = t - (y / (z / t));
	} else if (a <= -3.2e-197) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 6.6e-175) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.7e+73) {
		tmp = t_1;
	} else if ((a <= 1.12e+228) || !(a <= 4.6e+241)) {
		tmp = t_2;
	} else {
		tmp = -t / (-1.0 + (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 - x) * (y / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-2.9d+35)) then
        tmp = t_2
    else if (a <= (-2d-91)) then
        tmp = t_1
    else if (a <= (-4.8d-170)) then
        tmp = t - (y / (z / t))
    else if (a <= (-3.2d-197)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 6.6d-175) then
        tmp = -t / (z / (y - z))
    else if (a <= 1.7d+73) then
        tmp = t_1
    else if ((a <= 1.12d+228) .or. (.not. (a <= 4.6d+241))) then
        tmp = t_2
    else
        tmp = -t / ((-1.0d0) + (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 - x) * (y / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -2.9e+35) {
		tmp = t_2;
	} else if (a <= -2e-91) {
		tmp = t_1;
	} else if (a <= -4.8e-170) {
		tmp = t - (y / (z / t));
	} else if (a <= -3.2e-197) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 6.6e-175) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.7e+73) {
		tmp = t_1;
	} else if ((a <= 1.12e+228) || !(a <= 4.6e+241)) {
		tmp = t_2;
	} else {
		tmp = -t / (-1.0 + (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -2.9e+35:
		tmp = t_2
	elif a <= -2e-91:
		tmp = t_1
	elif a <= -4.8e-170:
		tmp = t - (y / (z / t))
	elif a <= -3.2e-197:
		tmp = y * ((t - x) / (a - z))
	elif a <= 6.6e-175:
		tmp = -t / (z / (y - z))
	elif a <= 1.7e+73:
		tmp = t_1
	elif (a <= 1.12e+228) or not (a <= 4.6e+241):
		tmp = t_2
	else:
		tmp = -t / (-1.0 + (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -2.9e+35)
		tmp = t_2;
	elseif (a <= -2e-91)
		tmp = t_1;
	elseif (a <= -4.8e-170)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (a <= -3.2e-197)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 6.6e-175)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 1.7e+73)
		tmp = t_1;
	elseif ((a <= 1.12e+228) || !(a <= 4.6e+241))
		tmp = t_2;
	else
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -2.9e+35)
		tmp = t_2;
	elseif (a <= -2e-91)
		tmp = t_1;
	elseif (a <= -4.8e-170)
		tmp = t - (y / (z / t));
	elseif (a <= -3.2e-197)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 6.6e-175)
		tmp = -t / (z / (y - z));
	elseif (a <= 1.7e+73)
		tmp = t_1;
	elseif ((a <= 1.12e+228) || ~((a <= 4.6e+241)))
		tmp = t_2;
	else
		tmp = -t / (-1.0 + (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+35], t$95$2, If[LessEqual[a, -2e-91], t$95$1, If[LessEqual[a, -4.8e-170], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.2e-197], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-175], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+73], t$95$1, If[Or[LessEqual[a, 1.12e+228], N[Not[LessEqual[a, 4.6e+241]], $MachinePrecision]], t$95$2, N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.89999999999999995e35 or 1.7000000000000001e73 < a < 1.11999999999999994e228 or 4.5999999999999999e241 < a

   1. Initial program 72.4%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 84.7%

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

   6. Taylor expanded in z around 0 69.5%

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

      1. associate-/l* 73.3%

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

   8. Simplified 73.3%

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

   if -2.89999999999999995e35 < a < -2.00000000000000004e-91 or 6.59999999999999997e-175 < a < 1.7000000000000001e73

   1. Initial program 72.0%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around -inf 59.2%

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

      1. associate-*l/ 63.4%

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

   7. Simplified 63.4%

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

   if -2.00000000000000004e-91 < a < -4.7999999999999999e-170

   1. Initial program 50.1%

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

      1. associate-*l/ 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in x around 0 66.9%

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

      1. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. associate-/l* 74.5%

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

      3. distribute-neg-frac 74.5%

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

   10. Simplified 74.5%

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

   11. Taylor expanded in z around 0 74.5%

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

       1. mul-1-neg 74.5%

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

       2. unsub-neg 74.5%

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

       3. *-commutative 74.5%

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

       4. associate-/l* 74.5%

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

   13. Simplified 74.5%

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

   if -4.7999999999999999e-170 < a < -3.1999999999999997e-197

   1. Initial program 73.7%

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

      1. associate-*l/ 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in y around inf 82.7%

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

      1. div-sub 82.7%

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

   7. Simplified 82.7%

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

   if -3.1999999999999997e-197 < a < 6.59999999999999997e-175

   1. Initial program 62.1%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around 0 69.6%

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

      1. associate-/l* 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in a around 0 62.3%

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

      1. mul-1-neg 62.3%

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

      2. associate-/l* 72.2%

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

      3. distribute-neg-frac 72.2%

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

   10. Simplified 72.2%

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

   if 1.11999999999999994e228 < a < 4.5999999999999999e241

   1. Initial program 81.1%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 81.1%

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

      1. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. associate-/l* 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. div-sub 99.7%

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

      5. sub-neg 99.7%

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

      6. *-inverses 99.7%

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

      7. metadata-eval 99.7%

         \[\leadsto \frac{-t}{\frac{a}{z} + \color{blue}{-1}} \]

   10. Simplified 99.7%

       \[\leadsto \color{blue}{\frac{-t}{\frac{a}{z} + -1}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-91}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-175}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+73}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+228} \lor \neg \left(a \leq 4.6 \cdot 10^{+241}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-296} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-296) (not (<= t_1 0.0)))
     (+ x (* (- x t) (/ (- z y) (- a z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

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 <= -1e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-1d-296)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) * ((z - y) / (a - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-296) or not (t_1 <= 0.0):
		tmp = x + ((x - t) * ((z - y) / (a - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-296) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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 <= -1e-296) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) * ((z - y) / (a - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-296], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1e-296 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 74.2%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   if -1e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. associate-*r/ 99.8%

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

      4. div-sub 99.8%

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

      5. distribute-lft-out-- 99.8%

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

      6. associate-*r/ 99.8%

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

      7. mul-1-neg 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. unsub-neg 99.8%

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

      10. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-296} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-31} \lor \neg \left(z \leq 3.9 \cdot 10^{+58}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -1.12e-38)
     t_1
     (if (<= z 4.8e-87)
       (+ x (/ (- t x) (/ a (- y z))))
       (if (or (<= z 2.3e-31) (not (<= z 3.9e+58)))
         t_1
         (+ x (/ (- y z) (/ (- a z) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.12e-38) {
		tmp = t_1;
	} else if (z <= 4.8e-87) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 2.3e-31) || !(z <= 3.9e+58)) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    if (z <= (-1.12d-38)) then
        tmp = t_1
    else if (z <= 4.8d-87) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if ((z <= 2.3d-31) .or. (.not. (z <= 3.9d+58))) then
        tmp = t_1
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.12e-38) {
		tmp = t_1;
	} else if (z <= 4.8e-87) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 2.3e-31) || !(z <= 3.9e+58)) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -1.12e-38:
		tmp = t_1
	elif z <= 4.8e-87:
		tmp = x + ((t - x) / (a / (y - z)))
	elif (z <= 2.3e-31) or not (z <= 3.9e+58):
		tmp = t_1
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -1.12e-38)
		tmp = t_1;
	elseif (z <= 4.8e-87)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif ((z <= 2.3e-31) || !(z <= 3.9e+58))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -1.12e-38)
		tmp = t_1;
	elseif (z <= 4.8e-87)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif ((z <= 2.3e-31) || ~((z <= 3.9e+58)))
		tmp = t_1;
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e-38], t$95$1, If[LessEqual[z, 4.8e-87], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.3e-31], N[Not[LessEqual[z, 3.9e+58]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1200000000000001e-38 or 4.7999999999999999e-87 < z < 2.2999999999999998e-31 or 3.9000000000000001e58 < z

   1. Initial program 48.4%

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

      1. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. associate-*r/ 68.7%

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

      3. associate-*r/ 68.7%

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

      4. div-sub 68.7%

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

      5. distribute-lft-out-- 68.7%

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

      6. associate-*r/ 68.7%

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

      7. mul-1-neg 68.7%

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

      8. distribute-rgt-out-- 68.8%

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

      9. unsub-neg 68.8%

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

      10. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   if -1.1200000000000001e-38 < z < 4.7999999999999999e-87

   1. Initial program 91.3%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in a around inf 82.5%

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

      1. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   if 2.2999999999999998e-31 < z < 3.9000000000000001e58

   1. Initial program 81.3%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 78.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-38}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-31} \lor \neg \left(z \leq 3.9 \cdot 10^{+58}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ t_2 := t - x \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- t x) (/ (- z y) a)))) (t_2 (- t (* x (/ (- a y) z)))))
   (if (<= z -1.2e-38)
     t_2
     (if (<= z 1.65e-55)
       t_1
       (if (<= z 7.5e-31)
         (/ (* y (- t x)) (- a z))
         (if (<= z 5.5e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * ((z - y) / a));
	double t_2 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -1.2e-38) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 7.5e-31) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 5.5e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t - x) * ((z - y) / a))
    t_2 = t - (x * ((a - y) / z))
    if (z <= (-1.2d-38)) then
        tmp = t_2
    else if (z <= 1.65d-55) then
        tmp = t_1
    else if (z <= 7.5d-31) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 5.5d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t - x) * ((z - y) / a));
	double t_2 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -1.2e-38) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 7.5e-31) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 5.5e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t - x) * ((z - y) / a))
	t_2 = t - (x * ((a - y) / z))
	tmp = 0
	if z <= -1.2e-38:
		tmp = t_2
	elif z <= 1.65e-55:
		tmp = t_1
	elif z <= 7.5e-31:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 5.5e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)))
	t_2 = Float64(t - Float64(x * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -1.2e-38)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 7.5e-31)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 5.5e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t - x) * ((z - y) / a));
	t_2 = t - (x * ((a - y) / z));
	tmp = 0.0;
	if (z <= -1.2e-38)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 7.5e-31)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 5.5e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-38], t$95$2, If[LessEqual[z, 1.65e-55], t$95$1, If[LessEqual[z, 7.5e-31], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000011e-38 or 5.50000000000000016e37 < z

   1. Initial program 44.3%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-*r/ 67.3%

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

      3. associate-*r/ 67.3%

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

      4. div-sub 67.3%

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

      5. distribute-lft-out-- 67.3%

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

      6. associate-*r/ 67.3%

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

      7. mul-1-neg 67.3%

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

      8. distribute-rgt-out-- 67.4%

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

      9. unsub-neg 67.4%

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

      10. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r/ 70.1%

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

      3. distribute-lft-neg-in 70.1%

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

   10. Simplified 70.1%

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

   if -1.20000000000000011e-38 < z < 1.65e-55 or 7.49999999999999975e-31 < z < 5.50000000000000016e37

   1. Initial program 90.3%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 84.7%

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

   if 1.65e-55 < z < 7.49999999999999975e-31

   1. Initial program 99.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around -inf 85.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-38}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+37}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - x \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+37}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* x (/ (- a y) z)))))
   (if (<= z -2e-38)
     t_1
     (if (<= z 1.7e-55)
       (+ x (/ (- t x) (/ a (- y z))))
       (if (<= z 1.05e-30)
         (/ (* y (- t x)) (- a z))
         (if (<= z 2.06e+37) (- x (* (- t x) (/ (- z y) a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -2e-38) {
		tmp = t_1;
	} else if (z <= 1.7e-55) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 1.05e-30) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.06e+37) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (x * ((a - y) / z))
    if (z <= (-2d-38)) then
        tmp = t_1
    else if (z <= 1.7d-55) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (z <= 1.05d-30) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 2.06d+37) then
        tmp = x - ((t - x) * ((z - y) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -2e-38) {
		tmp = t_1;
	} else if (z <= 1.7e-55) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 1.05e-30) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.06e+37) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (x * ((a - y) / z))
	tmp = 0
	if z <= -2e-38:
		tmp = t_1
	elif z <= 1.7e-55:
		tmp = x + ((t - x) / (a / (y - z)))
	elif z <= 1.05e-30:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 2.06e+37:
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(x * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -2e-38)
		tmp = t_1;
	elseif (z <= 1.7e-55)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (z <= 1.05e-30)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 2.06e+37)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (x * ((a - y) / z));
	tmp = 0.0;
	if (z <= -2e-38)
		tmp = t_1;
	elseif (z <= 1.7e-55)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (z <= 1.05e-30)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 2.06e+37)
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-38], t$95$1, If[LessEqual[z, 1.7e-55], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-30], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.06e+37], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9999999999999999e-38 or 2.05999999999999988e37 < z

   1. Initial program 44.3%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-*r/ 67.3%

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

      3. associate-*r/ 67.3%

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

      4. div-sub 67.3%

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

      5. distribute-lft-out-- 67.3%

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

      6. associate-*r/ 67.3%

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

      7. mul-1-neg 67.3%

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

      8. distribute-rgt-out-- 67.4%

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

      9. unsub-neg 67.4%

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

      10. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*r/ 70.1%

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

      3. distribute-lft-neg-in 70.1%

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

   10. Simplified 70.1%

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

   if -1.9999999999999999e-38 < z < 1.69999999999999986e-55

   1. Initial program 91.0%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around inf 80.3%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   if 1.69999999999999986e-55 < z < 1.0500000000000001e-30

   1. Initial program 99.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around -inf 85.9%

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

   if 1.0500000000000001e-30 < z < 2.05999999999999988e37

   1. Initial program 82.4%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in a around inf 82.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+37}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-29}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 10^{+57}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -3.7e-39)
     t_1
     (if (<= z 4.7e-87)
       (+ x (/ (- t x) (/ a (- y z))))
       (if (<= z 3.6e-29)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= z 1e+57) (+ x (/ (- y z) (/ (- a z) t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -3.7e-39) {
		tmp = t_1;
	} else if (z <= 4.7e-87) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 3.6e-29) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1e+57) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x - t) / (z / (y - a)))
    if (z <= (-3.7d-39)) then
        tmp = t_1
    else if (z <= 4.7d-87) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (z <= 3.6d-29) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 1d+57) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -3.7e-39) {
		tmp = t_1;
	} else if (z <= 4.7e-87) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 3.6e-29) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1e+57) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -3.7e-39:
		tmp = t_1
	elif z <= 4.7e-87:
		tmp = x + ((t - x) / (a / (y - z)))
	elif z <= 3.6e-29:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 1e+57:
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -3.7e-39)
		tmp = t_1;
	elseif (z <= 4.7e-87)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (z <= 3.6e-29)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 1e+57)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -3.7e-39)
		tmp = t_1;
	elseif (z <= 4.7e-87)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (z <= 3.6e-29)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 1e+57)
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-39], t$95$1, If[LessEqual[z, 4.7e-87], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-29], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+57], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.70000000000000015e-39 or 1.00000000000000005e57 < z

   1. Initial program 43.1%

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

      1. associate-*l/ 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-*r/ 67.6%

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

      7. mul-1-neg 67.6%

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

      8. distribute-rgt-out-- 67.7%

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

      9. unsub-neg 67.7%

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

      10. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   if -3.70000000000000015e-39 < z < 4.7000000000000001e-87

   1. Initial program 91.3%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in a around inf 82.5%

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

      1. associate-/l* 87.6%

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

   7. Simplified 87.6%

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

   if 4.7000000000000001e-87 < z < 3.59999999999999974e-29

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-*l/ 79.5%

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

      3. fma-def 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in z around -inf 78.0%

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

   if 3.59999999999999974e-29 < z < 1.00000000000000005e57

   1. Initial program 81.3%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 78.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-29}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 10^{+57}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x - t}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ (- x t) a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -6.4e-81)
     t_2
     (if (<= z 1.65e-55)
       t_1
       (if (<= z 1.25e-27)
         (* y (/ (- t x) (- a z)))
         (if (<= z 4.1e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.4e-81) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-27) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.1e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * ((x - t) / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-6.4d-81)) then
        tmp = t_2
    else if (z <= 1.65d-55) then
        tmp = t_1
    else if (z <= 1.25d-27) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 4.1d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((x - t) / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.4e-81) {
		tmp = t_2;
	} else if (z <= 1.65e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-27) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 4.1e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((x - t) / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -6.4e-81:
		tmp = t_2
	elif z <= 1.65e-55:
		tmp = t_1
	elif z <= 1.25e-27:
		tmp = y * ((t - x) / (a - z))
	elif z <= 4.1e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(x - t) / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.4e-81)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 1.25e-27)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 4.1e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((x - t) / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -6.4e-81)
		tmp = t_2;
	elseif (z <= 1.65e-55)
		tmp = t_1;
	elseif (z <= 1.25e-27)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 4.1e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e-81], t$95$2, If[LessEqual[z, 1.65e-55], t$95$1, If[LessEqual[z, 1.25e-27], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4e-81 or 4.0999999999999998e37 < z

   1. Initial program 47.3%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

      1. clear-num 61.5%

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

      2. associate-/r/ 61.6%

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

      3. clear-num 61.6%

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

   9. Applied egg-rr 61.6%

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

   if -6.4e-81 < z < 1.65e-55 or 1.25e-27 < z < 4.0999999999999998e37

   1. Initial program 89.7%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in a around inf 81.7%

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

      1. associate-/l* 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in y around inf 80.2%

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

      1. associate-*r/ 83.9%

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

   10. Simplified 83.9%

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

   if 1.65e-55 < z < 1.25e-27

   1. Initial program 99.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-55}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+37}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -9.6e-80)
     t_2
     (if (<= z 1.06e-55)
       t_1
       (if (<= z 1.95e-27)
         (* y (/ (- t x) (- a z)))
         (if (<= z 1.28e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.6e-80) {
		tmp = t_2;
	} else if (z <= 1.06e-55) {
		tmp = t_1;
	} else if (z <= 1.95e-27) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.28e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-9.6d-80)) then
        tmp = t_2
    else if (z <= 1.06d-55) then
        tmp = t_1
    else if (z <= 1.95d-27) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.28d+39) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.6e-80) {
		tmp = t_2;
	} else if (z <= 1.06e-55) {
		tmp = t_1;
	} else if (z <= 1.95e-27) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.28e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9.6e-80:
		tmp = t_2
	elif z <= 1.06e-55:
		tmp = t_1
	elif z <= 1.95e-27:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.28e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -9.6e-80)
		tmp = t_2;
	elseif (z <= 1.06e-55)
		tmp = t_1;
	elseif (z <= 1.95e-27)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.28e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9.6e-80)
		tmp = t_2;
	elseif (z <= 1.06e-55)
		tmp = t_1;
	elseif (z <= 1.95e-27)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.28e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e-80], t$95$2, If[LessEqual[z, 1.06e-55], t$95$1, If[LessEqual[z, 1.95e-27], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.28e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5999999999999996e-80 or 1.27999999999999994e39 < z

   1. Initial program 47.3%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

      1. clear-num 61.5%

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

      2. associate-/r/ 61.6%

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

      3. clear-num 61.6%

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

   9. Applied egg-rr 61.6%

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

   if -9.5999999999999996e-80 < z < 1.06e-55 or 1.94999999999999986e-27 < z < 1.27999999999999994e39

   1. Initial program 89.7%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 84.6%

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

   if 1.06e-55 < z < 1.94999999999999986e-27

   1. Initial program 99.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+39}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.2e-80)
     t_2
     (if (<= z 1.7e-55)
       t_1
       (if (<= z 1.35e-31)
         (/ (* y (- t x)) (- a z))
         (if (<= z 1.3e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.2e-80) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 1.35e-31) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.3e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-4.2d-80)) then
        tmp = t_2
    else if (z <= 1.7d-55) then
        tmp = t_1
    else if (z <= 1.35d-31) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 1.3d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.2e-80) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 1.35e-31) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.3e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.2e-80:
		tmp = t_2
	elif z <= 1.7e-55:
		tmp = t_1
	elif z <= 1.35e-31:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 1.3e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.2e-80)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 1.35e-31)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 1.3e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.2e-80)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 1.35e-31)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 1.3e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-80], t$95$2, If[LessEqual[z, 1.7e-55], t$95$1, If[LessEqual[z, 1.35e-31], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000003e-80 or 1.3e37 < z

   1. Initial program 47.3%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in x around 0 41.7%

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

      1. associate-/l* 61.6%

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

   7. Simplified 61.6%

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

      1. clear-num 61.5%

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

      2. associate-/r/ 61.6%

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

      3. clear-num 61.6%

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

   9. Applied egg-rr 61.6%

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

   if -4.20000000000000003e-80 < z < 1.69999999999999986e-55 or 1.35000000000000007e-31 < z < 1.3e37

   1. Initial program 89.7%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 84.6%

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

   if 1.69999999999999986e-55 < z < 1.35000000000000007e-31

   1. Initial program 99.6%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in y around -inf 85.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+175}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -9.6e-80)
     t_1
     (if (<= z 1.45e-55)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 2.4e+82)
         (/ (* y (- t x)) (- a z))
         (if (<= z 2e+175) (- t (* a (/ (- x t) z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.6e-80) {
		tmp = t_1;
	} else if (z <= 1.45e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.4e+82) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2e+175) {
		tmp = t - (a * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-9.6d-80)) then
        tmp = t_1
    else if (z <= 1.45d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 2.4d+82) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 2d+175) then
        tmp = t - (a * ((x - t) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.6e-80) {
		tmp = t_1;
	} else if (z <= 1.45e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 2.4e+82) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2e+175) {
		tmp = t - (a * ((x - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9.6e-80:
		tmp = t_1
	elif z <= 1.45e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 2.4e+82:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 2e+175:
		tmp = t - (a * ((x - t) / z))
	else:
		tmp = t_1
	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 (z <= -9.6e-80)
		tmp = t_1;
	elseif (z <= 1.45e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 2.4e+82)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 2e+175)
		tmp = Float64(t - Float64(a * Float64(Float64(x - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9.6e-80)
		tmp = t_1;
	elseif (z <= 1.45e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 2.4e+82)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 2e+175)
		tmp = t - (a * ((x - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e-80], t$95$1, If[LessEqual[z, 1.45e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+82], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+175], N[(t - N[(a * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5999999999999996e-80 or 1.9999999999999999e175 < z

   1. Initial program 46.6%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around 0 43.8%

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

      1. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

      1. clear-num 65.0%

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

      2. associate-/r/ 65.1%

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

      3. clear-num 65.1%

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

   9. Applied egg-rr 65.1%

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

   if -9.5999999999999996e-80 < z < 1.45e-55

   1. Initial program 90.4%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 85.7%

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

   if 1.45e-55 < z < 2.39999999999999998e82

   1. Initial program 79.5%

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

      1. associate-*l/ 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around -inf 58.7%

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

   if 2.39999999999999998e82 < z < 1.9999999999999999e175

   1. Initial program 40.4%

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

      1. associate-*l/ 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in z around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. associate-*r/ 73.7%

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

      3. associate-*r/ 73.7%

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

      4. div-sub 73.7%

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

      5. distribute-lft-out-- 73.7%

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

      6. associate-*r/ 73.7%

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

      7. mul-1-neg 73.7%

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

      8. distribute-rgt-out-- 73.7%

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

      9. unsub-neg 73.7%

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

      10. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

   8. Taylor expanded in y around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-*r/ 65.0%

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

      3. distribute-rgt-neg-in 65.0%

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

   10. Simplified 65.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+175}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - x \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* x (/ (- a y) z)))))
   (if (<= z -1.66e-38)
     t_1
     (if (<= z 1.42e-56)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 1.85e+35)
         (/ (* y (- t x)) (- a z))
         (if (<= z 2.3e+58) (- x (* t (/ z (- a z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -1.66e-38) {
		tmp = t_1;
	} else if (z <= 1.42e-56) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.85e+35) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.3e+58) {
		tmp = x - (t * (z / (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 = t - (x * ((a - y) / z))
    if (z <= (-1.66d-38)) then
        tmp = t_1
    else if (z <= 1.42d-56) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.85d+35) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 2.3d+58) then
        tmp = x - (t * (z / (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 = t - (x * ((a - y) / z));
	double tmp;
	if (z <= -1.66e-38) {
		tmp = t_1;
	} else if (z <= 1.42e-56) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.85e+35) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.3e+58) {
		tmp = x - (t * (z / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (x * ((a - y) / z))
	tmp = 0
	if z <= -1.66e-38:
		tmp = t_1
	elif z <= 1.42e-56:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.85e+35:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 2.3e+58:
		tmp = x - (t * (z / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(x * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -1.66e-38)
		tmp = t_1;
	elseif (z <= 1.42e-56)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.85e+35)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 2.3e+58)
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (x * ((a - y) / z));
	tmp = 0.0;
	if (z <= -1.66e-38)
		tmp = t_1;
	elseif (z <= 1.42e-56)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.85e+35)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 2.3e+58)
		tmp = x - (t * (z / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.66e-38], t$95$1, If[LessEqual[z, 1.42e-56], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+35], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+58], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.66000000000000006e-38 or 2.30000000000000002e58 < z

   1. Initial program 43.1%

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

      1. associate-*l/ 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. associate-*r/ 67.6%

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

      3. associate-*r/ 67.6%

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

      4. div-sub 67.6%

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

      5. distribute-lft-out-- 67.6%

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

      6. associate-*r/ 67.6%

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

      7. mul-1-neg 67.6%

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

      8. distribute-rgt-out-- 67.7%

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

      9. unsub-neg 67.7%

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

      10. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in t around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*r/ 71.4%

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

      3. distribute-lft-neg-in 71.4%

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

   10. Simplified 71.4%

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

   if -1.66000000000000006e-38 < z < 1.42e-56

   1. Initial program 91.0%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around 0 83.3%

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

   if 1.42e-56 < z < 1.85e35

   1. Initial program 87.7%

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

      1. associate-*l/ 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in y around -inf 70.4%

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

   if 1.85e35 < z < 2.30000000000000002e58

   1. Initial program 85.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

   6. Taylor expanded in y around 0 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-*l/ 83.3%

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

      3. neg-mul-1 83.3%

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

      4. distribute-rgt-neg-in 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{-38}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= a -1.5e+35)
     x
     (if (<= a -2.3e-47)
       t_1
       (if (<= a 1.06e-148) t (if (<= a 1.28e+73) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (a <= -1.5e+35) {
		tmp = x;
	} else if (a <= -2.3e-47) {
		tmp = t_1;
	} else if (a <= 1.06e-148) {
		tmp = t;
	} else if (a <= 1.28e+73) {
		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 - x) * (y / a)
    if (a <= (-1.5d+35)) then
        tmp = x
    else if (a <= (-2.3d-47)) then
        tmp = t_1
    else if (a <= 1.06d-148) then
        tmp = t
    else if (a <= 1.28d+73) 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 - x) * (y / a);
	double tmp;
	if (a <= -1.5e+35) {
		tmp = x;
	} else if (a <= -2.3e-47) {
		tmp = t_1;
	} else if (a <= 1.06e-148) {
		tmp = t;
	} else if (a <= 1.28e+73) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if a <= -1.5e+35:
		tmp = x
	elif a <= -2.3e-47:
		tmp = t_1
	elif a <= 1.06e-148:
		tmp = t
	elif a <= 1.28e+73:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (a <= -1.5e+35)
		tmp = x;
	elseif (a <= -2.3e-47)
		tmp = t_1;
	elseif (a <= 1.06e-148)
		tmp = t;
	elseif (a <= 1.28e+73)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (a <= -1.5e+35)
		tmp = x;
	elseif (a <= -2.3e-47)
		tmp = t_1;
	elseif (a <= 1.06e-148)
		tmp = t;
	elseif (a <= 1.28e+73)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+35], x, If[LessEqual[a, -2.3e-47], t$95$1, If[LessEqual[a, 1.06e-148], t, If[LessEqual[a, 1.28e+73], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999995e35 or 1.2800000000000001e73 < a

   1. Initial program 72.8%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 55.6%

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

   if -1.49999999999999995e35 < a < -2.29999999999999982e-47 or 1.06000000000000003e-148 < a < 1.2800000000000001e73

   1. Initial program 73.2%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around -inf 59.3%

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

      1. associate-*l/ 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in a around inf 42.9%

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

      1. associate-/l* 41.7%

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

      2. associate-/r/ 44.0%

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

   10. Simplified 44.0%

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

   if -2.29999999999999982e-47 < a < 1.06000000000000003e-148

   1. Initial program 61.0%

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

      1. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 45.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-47}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{+73}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -13000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -13000.0)
     t_2
     (if (<= z 4e-75)
       t_1
       (if (<= z 1.45e-29) (/ y (/ z (- x t))) (if (<= z 3.1e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -13000.0) {
		tmp = t_2;
	} else if (z <= 4e-75) {
		tmp = t_1;
	} else if (z <= 1.45e-29) {
		tmp = y / (z / (x - t));
	} else if (z <= 3.1e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    t_2 = t - (y / (z / t))
    if (z <= (-13000.0d0)) then
        tmp = t_2
    else if (z <= 4d-75) then
        tmp = t_1
    else if (z <= 1.45d-29) then
        tmp = y / (z / (x - t))
    else if (z <= 3.1d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -13000.0) {
		tmp = t_2;
	} else if (z <= 4e-75) {
		tmp = t_1;
	} else if (z <= 1.45e-29) {
		tmp = y / (z / (x - t));
	} else if (z <= 3.1e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -13000.0:
		tmp = t_2
	elif z <= 4e-75:
		tmp = t_1
	elif z <= 1.45e-29:
		tmp = y / (z / (x - t))
	elif z <= 3.1e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -13000.0)
		tmp = t_2;
	elseif (z <= 4e-75)
		tmp = t_1;
	elseif (z <= 1.45e-29)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	elseif (z <= 3.1e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -13000.0)
		tmp = t_2;
	elseif (z <= 4e-75)
		tmp = t_1;
	elseif (z <= 1.45e-29)
		tmp = y / (z / (x - t));
	elseif (z <= 3.1e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -13000.0], t$95$2, If[LessEqual[z, 4e-75], t$95$1, If[LessEqual[z, 1.45e-29], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13000 or 3.10000000000000018e38 < z

   1. Initial program 41.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in x around 0 40.3%

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

      1. associate-/l* 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in a around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. associate-/l* 56.1%

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

      3. distribute-neg-frac 56.1%

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

   10. Simplified 56.1%

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

   11. Taylor expanded in z around 0 52.5%

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

       1. mul-1-neg 52.5%

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

       2. unsub-neg 52.5%

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

       3. *-commutative 52.5%

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

       4. associate-/l* 56.0%

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

   13. Simplified 56.0%

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

   if -13000 < z < 3.9999999999999998e-75 or 1.45000000000000012e-29 < z < 3.10000000000000018e38

   1. Initial program 89.3%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 72.5%

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

   6. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   if 3.9999999999999998e-75 < z < 1.45000000000000012e-29

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around -inf 80.6%

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

      1. associate-*l/ 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in a around 0 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

   10. Simplified 78.9%

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

   11. Taylor expanded in y around 0 78.9%

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

       1. associate-/l* 78.9%

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

   13. Simplified 78.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -7000000:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= z -7000000.0)
     (/ (- t) (/ z (- y z)))
     (if (<= z 3.4e-76)
       t_1
       (if (<= z 1.5e-25)
         (/ y (/ z (- x t)))
         (if (<= z 2.2e+37) t_1 (- t (/ y (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -7000000.0) {
		tmp = -t / (z / (y - z));
	} else if (z <= 3.4e-76) {
		tmp = t_1;
	} else if (z <= 1.5e-25) {
		tmp = y / (z / (x - t));
	} else if (z <= 2.2e+37) {
		tmp = t_1;
	} else {
		tmp = t - (y / (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (z <= (-7000000.0d0)) then
        tmp = -t / (z / (y - z))
    else if (z <= 3.4d-76) then
        tmp = t_1
    else if (z <= 1.5d-25) then
        tmp = y / (z / (x - t))
    else if (z <= 2.2d+37) then
        tmp = t_1
    else
        tmp = t - (y / (z / 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 / (a / y));
	double tmp;
	if (z <= -7000000.0) {
		tmp = -t / (z / (y - z));
	} else if (z <= 3.4e-76) {
		tmp = t_1;
	} else if (z <= 1.5e-25) {
		tmp = y / (z / (x - t));
	} else if (z <= 2.2e+37) {
		tmp = t_1;
	} else {
		tmp = t - (y / (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if z <= -7000000.0:
		tmp = -t / (z / (y - z))
	elif z <= 3.4e-76:
		tmp = t_1
	elif z <= 1.5e-25:
		tmp = y / (z / (x - t))
	elif z <= 2.2e+37:
		tmp = t_1
	else:
		tmp = t - (y / (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (z <= -7000000.0)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (z <= 3.4e-76)
		tmp = t_1;
	elseif (z <= 1.5e-25)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	elseif (z <= 2.2e+37)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(y / Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (z <= -7000000.0)
		tmp = -t / (z / (y - z));
	elseif (z <= 3.4e-76)
		tmp = t_1;
	elseif (z <= 1.5e-25)
		tmp = y / (z / (x - t));
	elseif (z <= 2.2e+37)
		tmp = t_1;
	else
		tmp = t - (y / (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7000000.0], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-76], t$95$1, If[LessEqual[z, 1.5e-25], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+37], t$95$1, N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7e6

   1. Initial program 47.9%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in x around 0 39.4%

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

      1. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around 0 36.5%

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

      1. mul-1-neg 36.5%

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

      2. associate-/l* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   10. Simplified 52.7%

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

   if -7e6 < z < 3.3999999999999999e-76 or 1.4999999999999999e-25 < z < 2.2000000000000001e37

   1. Initial program 89.3%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 72.5%

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

   6. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   if 3.3999999999999999e-76 < z < 1.4999999999999999e-25

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around -inf 80.6%

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

      1. associate-*l/ 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in a around 0 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

   10. Simplified 78.9%

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

   11. Taylor expanded in y around 0 78.9%

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

       1. associate-/l* 78.9%

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

   13. Simplified 78.9%

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

   if 2.2000000000000001e37 < z

   1. Initial program 35.4%

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

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in x around 0 41.2%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 59.3%

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

      3. distribute-neg-frac 59.3%

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

   10. Simplified 59.3%

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

   11. Taylor expanded in z around 0 55.6%

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

       1. mul-1-neg 55.6%

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

       2. unsub-neg 55.6%

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

       3. *-commutative 55.6%

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

       4. associate-/l* 59.3%

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

   13. Simplified 59.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7000000:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2900000:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2900000.0)
   (/ (- t) (/ z (- y z)))
   (if (<= z 4.2e-125)
     (+ x (/ t (/ a y)))
     (if (<= z 1.5e+149)
       (* y (/ (- t x) (- a z)))
       (/ (- t) (+ -1.0 (/ a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2900000.0) {
		tmp = -t / (z / (y - z));
	} else if (z <= 4.2e-125) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.5e+149) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = -t / (-1.0 + (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 <= (-2900000.0d0)) then
        tmp = -t / (z / (y - z))
    else if (z <= 4.2d-125) then
        tmp = x + (t / (a / y))
    else if (z <= 1.5d+149) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = -t / ((-1.0d0) + (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 <= -2900000.0) {
		tmp = -t / (z / (y - z));
	} else if (z <= 4.2e-125) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.5e+149) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = -t / (-1.0 + (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2900000.0:
		tmp = -t / (z / (y - z))
	elif z <= 4.2e-125:
		tmp = x + (t / (a / y))
	elif z <= 1.5e+149:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = -t / (-1.0 + (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2900000.0)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (z <= 4.2e-125)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.5e+149)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2900000.0)
		tmp = -t / (z / (y - z));
	elseif (z <= 4.2e-125)
		tmp = x + (t / (a / y));
	elseif (z <= 1.5e+149)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = -t / (-1.0 + (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2900000.0], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-125], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+149], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e6

   1. Initial program 47.9%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in x around 0 39.4%

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

      1. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around 0 36.5%

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

      1. mul-1-neg 36.5%

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

      2. associate-/l* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   10. Simplified 52.7%

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

   if -2.9e6 < z < 4.2e-125

   1. Initial program 89.5%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in t around inf 74.2%

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

   6. Taylor expanded in z around 0 66.9%

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

      1. associate-/l* 70.2%

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

   8. Simplified 70.2%

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

   if 4.2e-125 < z < 1.50000000000000002e149

   1. Initial program 79.5%

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

      1. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around inf 56.0%

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

      1. div-sub 56.0%

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

   7. Simplified 56.0%

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

   if 1.50000000000000002e149 < z

   1. Initial program 28.4%

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

      1. associate-*l/ 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. associate-/l* 72.5%

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

      3. distribute-neg-frac 72.5%

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

      4. div-sub 72.5%

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

      5. sub-neg 72.5%

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

      6. *-inverses 72.5%

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

      7. metadata-eval 72.5%

         \[\leadsto \frac{-t}{\frac{a}{z} + \color{blue}{-1}} \]

   10. Simplified 72.5%

       \[\leadsto \color{blue}{\frac{-t}{\frac{a}{z} + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2900000:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.16e-27)
   (+ x (/ (- t x) (/ a (- y z))))
   (if (<= a 5.8e-99)
     (- t (* x (/ (- a y) z)))
     (+ x (/ (- y z) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-27) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (a <= 5.8e-99) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.16d-27)) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (a <= 5.8d-99) then
        tmp = t - (x * ((a - y) / z))
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-27) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (a <= 5.8e-99) {
		tmp = t - (x * ((a - y) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.16e-27:
		tmp = x + ((t - x) / (a / (y - z)))
	elif a <= 5.8e-99:
		tmp = t - (x * ((a - y) / z))
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.16e-27)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (a <= 5.8e-99)
		tmp = Float64(t - Float64(x * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.16e-27)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (a <= 5.8e-99)
		tmp = t - (x * ((a - y) / z));
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.16e-27], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-99], N[(t - N[(x * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16000000000000005e-27

   1. Initial program 72.7%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in a around inf 70.6%

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

      1. associate-/l* 82.3%

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

   7. Simplified 82.3%

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

   if -1.16000000000000005e-27 < a < 5.79999999999999971e-99

   1. Initial program 64.9%

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

      1. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate-*r/ 79.2%

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

      3. associate-*r/ 79.2%

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

      4. div-sub 79.2%

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

      5. distribute-lft-out-- 79.2%

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

      6. associate-*r/ 79.2%

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

      7. mul-1-neg 79.2%

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

      8. distribute-rgt-out-- 79.2%

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

      9. unsub-neg 79.2%

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

      10. associate-/l* 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in t around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*r/ 69.5%

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

      3. distribute-lft-neg-in 69.5%

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

   10. Simplified 69.5%

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

   if 5.79999999999999971e-99 < a

   1. Initial program 71.3%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 76.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;t - x \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e+21)
   x
   (if (<= a -4.7e-46) (* t (/ y a)) (if (<= a 3.2e-172) t (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+21) {
		tmp = x;
	} else if (a <= -4.7e-46) {
		tmp = t * (y / a);
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.2d+21)) then
        tmp = x
    else if (a <= (-4.7d-46)) then
        tmp = t * (y / a)
    else if (a <= 3.2d-172) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e+21) {
		tmp = x;
	} else if (a <= -4.7e-46) {
		tmp = t * (y / a);
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e+21:
		tmp = x
	elif a <= -4.7e-46:
		tmp = t * (y / a)
	elif a <= 3.2e-172:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e+21)
		tmp = x;
	elseif (a <= -4.7e-46)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.2e+21)
		tmp = x;
	elseif (a <= -4.7e-46)
		tmp = t * (y / a);
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e+21], x, If[LessEqual[a, -4.7e-46], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-172], t, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2e21

   1. Initial program 72.2%

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

      1. associate-*l/ 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in a around inf 49.4%

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

   if -4.2e21 < a < -4.69999999999999966e-46

   1. Initial program 84.4%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around -inf 74.9%

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

      1. associate-*l/ 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in a around inf 60.5%

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

      1. associate-/l* 65.5%

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

   10. Simplified 65.5%

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

   11. Taylor expanded in t around inf 39.2%

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

       1. associate-*r/ 44.8%

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

   13. Simplified 44.8%

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

   if -4.69999999999999966e-46 < a < 3.2000000000000001e-172

   1. Initial program 60.6%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 47.9%

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

   if 3.2000000000000001e-172 < a

   1. Initial program 71.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 69.7%

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

   6. Taylor expanded in z around inf 39.0%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+21)
   x
   (if (<= a -2e-90) (/ x (/ z y)) (if (<= a 2.9e-174) t (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x;
	} else if (a <= -2e-90) {
		tmp = x / (z / y);
	} else if (a <= 2.9e-174) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d+21)) then
        tmp = x
    else if (a <= (-2d-90)) then
        tmp = x / (z / y)
    else if (a <= 2.9d-174) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+21) {
		tmp = x;
	} else if (a <= -2e-90) {
		tmp = x / (z / y);
	} else if (a <= 2.9e-174) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+21:
		tmp = x
	elif a <= -2e-90:
		tmp = x / (z / y)
	elif a <= 2.9e-174:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+21)
		tmp = x;
	elseif (a <= -2e-90)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.9e-174)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+21)
		tmp = x;
	elseif (a <= -2e-90)
		tmp = x / (z / y);
	elseif (a <= 2.9e-174)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+21], x, If[LessEqual[a, -2e-90], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-174], t, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.05e21

   1. Initial program 72.7%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in a around inf 48.7%

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

   if -2.05e21 < a < -1.99999999999999999e-90

   1. Initial program 79.1%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around -inf 72.1%

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

      1. associate-*l/ 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in a around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

   10. Simplified 45.0%

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

   11. Taylor expanded in t around 0 38.2%

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

       1. associate-/l* 46.7%

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

   13. Simplified 46.7%

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

   if -1.99999999999999999e-90 < a < 2.9000000000000001e-174

   1. Initial program 60.1%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in z around inf 49.0%

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

   if 2.9000000000000001e-174 < a

   1. Initial program 71.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 69.7%

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

   6. Taylor expanded in z around inf 39.0%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-174}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+31)
   x
   (if (<= a -2.7e-45) (/ (- x) (/ a y)) (if (<= a 3.2e-172) t (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+31) {
		tmp = x;
	} else if (a <= -2.7e-45) {
		tmp = -x / (a / y);
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d+31)) then
        tmp = x
    else if (a <= (-2.7d-45)) then
        tmp = -x / (a / y)
    else if (a <= 3.2d-172) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+31) {
		tmp = x;
	} else if (a <= -2.7e-45) {
		tmp = -x / (a / y);
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+31:
		tmp = x
	elif a <= -2.7e-45:
		tmp = -x / (a / y)
	elif a <= 3.2e-172:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+31)
		tmp = x;
	elseif (a <= -2.7e-45)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+31)
		tmp = x;
	elseif (a <= -2.7e-45)
		tmp = -x / (a / y);
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+31], x, If[LessEqual[a, -2.7e-45], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-172], t, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9999999999999999e31

   1. Initial program 72.5%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in a around inf 52.0%

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

   if -1.9999999999999999e31 < a < -2.69999999999999985e-45

   1. Initial program 81.7%

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

      1. associate-*l/ 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in y around -inf 68.9%

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

      1. associate-*l/ 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in a around inf 56.6%

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

      1. associate-/l* 60.9%

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

   10. Simplified 60.9%

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

   11. Taylor expanded in t around 0 33.7%

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

       1. mul-1-neg 33.7%

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

       2. associate-/l* 42.6%

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

   13. Simplified 42.6%

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

   if -2.69999999999999985e-45 < a < 3.2000000000000001e-172

   1. Initial program 60.6%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 47.9%

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

   if 3.2000000000000001e-172 < a

   1. Initial program 71.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 69.7%

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

   6. Taylor expanded in z around inf 39.0%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 56.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4500000 \lor \neg \left(z \leq 10^{+39}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4500000.0) (not (<= z 1e+39)))
   (- t (/ y (/ z t)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4500000.0) || !(z <= 1e+39)) {
		tmp = t - (y / (z / t));
	} else {
		tmp = x + (t / (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 ((z <= (-4500000.0d0)) .or. (.not. (z <= 1d+39))) then
        tmp = t - (y / (z / t))
    else
        tmp = x + (t / (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 ((z <= -4500000.0) || !(z <= 1e+39)) {
		tmp = t - (y / (z / t));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4500000.0) or not (z <= 1e+39):
		tmp = t - (y / (z / t))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4500000.0) || !(z <= 1e+39))
		tmp = Float64(t - Float64(y / Float64(z / t)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4500000.0) || ~((z <= 1e+39)))
		tmp = t - (y / (z / t));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4500000.0], N[Not[LessEqual[z, 1e+39]], $MachinePrecision]], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e6 or 9.9999999999999994e38 < z

   1. Initial program 41.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in x around 0 40.3%

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

      1. associate-/l* 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in a around 0 37.2%

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

      1. mul-1-neg 37.2%

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

      2. associate-/l* 56.1%

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

      3. distribute-neg-frac 56.1%

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

   10. Simplified 56.1%

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

   11. Taylor expanded in z around 0 52.5%

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

       1. mul-1-neg 52.5%

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

       2. unsub-neg 52.5%

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

       3. *-commutative 52.5%

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

       4. associate-/l* 56.0%

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

   13. Simplified 56.0%

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

   if -4.5e6 < z < 9.9999999999999994e38

   1. Initial program 90.0%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in t around inf 71.8%

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

   6. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4500000 \lor \neg \left(z \leq 10^{+39}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+14) t (if (<= z 8.5e+86) (+ x (/ t (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = t;
	} else if (z <= 8.5e+86) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d+14)) then
        tmp = t
    else if (z <= 8.5d+86) then
        tmp = x + (t / (a / y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = t;
	} else if (z <= 8.5e+86) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+14:
		tmp = t
	elif z <= 8.5e+86:
		tmp = x + (t / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+14)
		tmp = t;
	elseif (z <= 8.5e+86)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e+14)
		tmp = t;
	elseif (z <= 8.5e+86)
		tmp = x + (t / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+14], t, If[LessEqual[z, 8.5e+86], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e14 or 8.5000000000000005e86 < z

   1. Initial program 37.9%

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

      1. associate-*l/ 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 53.6%

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

   if -2.8e14 < z < 8.5000000000000005e86

   1. Initial program 87.9%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in t around inf 71.3%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.7e+28) x (if (<= a 3.2e-172) t (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+28) {
		tmp = x;
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.7d+28)) then
        tmp = x
    else if (a <= 3.2d-172) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+28) {
		tmp = x;
	} else if (a <= 3.2e-172) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e+28:
		tmp = x
	elif a <= 3.2e-172:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e+28)
		tmp = x;
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e+28)
		tmp = x;
	elseif (a <= 3.2e-172)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e+28], x, If[LessEqual[a, 3.2e-172], t, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.69999999999999965e28

   1. Initial program 73.1%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in a around inf 51.1%

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

   if -4.69999999999999965e28 < a < 3.2000000000000001e-172

   1. Initial program 64.6%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in z around inf 42.1%

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

   if 3.2000000000000001e-172 < a

   1. Initial program 71.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 69.7%

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

   6. Taylor expanded in z around inf 39.0%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+28) x (if (<= a 1.52e-46) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+28) {
		tmp = x;
	} else if (a <= 1.52e-46) {
		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 <= (-9.5d+28)) then
        tmp = x
    else if (a <= 1.52d-46) 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 <= -9.5e+28) {
		tmp = x;
	} else if (a <= 1.52e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+28:
		tmp = x
	elif a <= 1.52e-46:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+28)
		tmp = x;
	elseif (a <= 1.52e-46)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+28)
		tmp = x;
	elseif (a <= 1.52e-46)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+28], x, If[LessEqual[a, 1.52e-46], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.49999999999999927e28 or 1.52000000000000006e-46 < a

   1. Initial program 73.3%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in a around inf 46.1%

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

   if -9.49999999999999927e28 < a < 1.52000000000000006e-46

   1. Initial program 64.5%

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

      1. associate-*l/ 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in z around inf 38.5%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 25.0% 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 69.0%

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

   1. associate-*l/ 82.9%

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

3. Simplified 82.9%

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

5. Taylor expanded in z around inf 25.5%

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

6. Final simplification 25.5%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))