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

Percentage Accurate: 67.5% → 90.9%

Time: 19.3s

Alternatives: 20

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double tmp;
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	tmp = 0.0
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 89.2%

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

      3. fma-define 89.2%

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

   3. Simplified 89.2%

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

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

   1. Initial program 4.7%

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

      1. clear-num 4.3%

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

      2. inv-pow 4.3%

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

      3. *-commutative 4.3%

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

      4. associate-/r* 4.5%

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

   4. Applied egg-rr 4.5%

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

      1. unpow-1 4.5%

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

      2. associate-/l/ 4.3%

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

      3. *-commutative 4.3%

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

   6. Simplified 4.3%

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

   7. Taylor expanded in t around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-*r/ 99.5%

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

      3. associate-*r/ 99.5%

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

      4. mul-1-neg 99.5%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 90.3%

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

Alternative 2: 55.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{t - z}{t}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a))))
        (t_2 (* y (/ (- t z) t)))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= t -4.8e+217)
     t_2
     (if (<= t -5e+171)
       (* x (/ (- z a) t))
       (if (<= t -1.75e+92)
         t_2
         (if (<= t -3.4e-91)
           t_3
           (if (<= t 6.8e-106)
             t_1
             (if (<= t 1.9e-29) t_3 (if (<= t 5.2e+72) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = y * ((t - z) / t);
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_2;
	} else if (t <= -5e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.75e+92) {
		tmp = t_2;
	} else if (t <= -3.4e-91) {
		tmp = t_3;
	} else if (t <= 6.8e-106) {
		tmp = t_1;
	} else if (t <= 1.9e-29) {
		tmp = t_3;
	} else if (t <= 5.2e+72) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = y * ((t - z) / t)
    t_3 = z * ((y - x) / (a - t))
    if (t <= (-4.8d+217)) then
        tmp = t_2
    else if (t <= (-5d+171)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.75d+92)) then
        tmp = t_2
    else if (t <= (-3.4d-91)) then
        tmp = t_3
    else if (t <= 6.8d-106) then
        tmp = t_1
    else if (t <= 1.9d-29) then
        tmp = t_3
    else if (t <= 5.2d+72) 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 * (z / a));
	double t_2 = y * ((t - z) / t);
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_2;
	} else if (t <= -5e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.75e+92) {
		tmp = t_2;
	} else if (t <= -3.4e-91) {
		tmp = t_3;
	} else if (t <= 6.8e-106) {
		tmp = t_1;
	} else if (t <= 1.9e-29) {
		tmp = t_3;
	} else if (t <= 5.2e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = y * ((t - z) / t)
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if t <= -4.8e+217:
		tmp = t_2
	elif t <= -5e+171:
		tmp = x * ((z - a) / t)
	elif t <= -1.75e+92:
		tmp = t_2
	elif t <= -3.4e-91:
		tmp = t_3
	elif t <= 6.8e-106:
		tmp = t_1
	elif t <= 1.9e-29:
		tmp = t_3
	elif t <= 5.2e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(t - z) / t))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.8e+217)
		tmp = t_2;
	elseif (t <= -5e+171)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.75e+92)
		tmp = t_2;
	elseif (t <= -3.4e-91)
		tmp = t_3;
	elseif (t <= 6.8e-106)
		tmp = t_1;
	elseif (t <= 1.9e-29)
		tmp = t_3;
	elseif (t <= 5.2e+72)
		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 * (z / a));
	t_2 = y * ((t - z) / t);
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (t <= -4.8e+217)
		tmp = t_2;
	elseif (t <= -5e+171)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.75e+92)
		tmp = t_2;
	elseif (t <= -3.4e-91)
		tmp = t_3;
	elseif (t <= 6.8e-106)
		tmp = t_1;
	elseif (t <= 1.9e-29)
		tmp = t_3;
	elseif (t <= 5.2e+72)
		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[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+217], t$95$2, If[LessEqual[t, -5e+171], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e+92], t$95$2, If[LessEqual[t, -3.4e-91], t$95$3, If[LessEqual[t, 6.8e-106], t$95$1, If[LessEqual[t, 1.9e-29], t$95$3, If[LessEqual[t, 5.2e+72], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.7999999999999996e217 or -5.0000000000000004e171 < t < -1.74999999999999993e92 or 5.19999999999999963e72 < t

   1. Initial program 42.3%

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

      1. clear-num 42.2%

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

      2. inv-pow 42.2%

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

      3. *-commutative 42.2%

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

      4. associate-/r* 63.5%

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

   4. Applied egg-rr 63.5%

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

   5. Taylor expanded in x around 0 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*r/ 45.8%

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

   7. Simplified 45.8%

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

   8. Taylor expanded in a around 0 44.7%

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

      1. mul-1-neg 44.7%

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

   10. Simplified 44.7%

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

   11. Taylor expanded in y around 0 50.1%

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

       1. mul-1-neg 50.1%

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

       2. distribute-frac-neg2 50.1%

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

       3. associate-/l* 67.1%

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

   13. Simplified 67.1%

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

   if -4.7999999999999996e217 < t < -5.0000000000000004e171

   1. Initial program 3.0%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 68.5%

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

      1. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   if -1.74999999999999993e92 < t < -3.40000000000000027e-91 or 6.79999999999999965e-106 < t < 1.89999999999999988e-29

   1. Initial program 75.2%

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

      1. clear-num 75.0%

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

      2. inv-pow 75.0%

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

      3. *-commutative 75.0%

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

      4. associate-/r* 88.4%

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

   4. Applied egg-rr 88.4%

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

   5. Taylor expanded in z around inf 56.2%

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

      1. div-sub 57.9%

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

   7. Simplified 57.9%

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

   if -3.40000000000000027e-91 < t < 6.79999999999999965e-106 or 1.89999999999999988e-29 < t < 5.19999999999999963e72

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0 70.4%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. associate-/l* 72.6%

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

   6. Simplified 72.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-28}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+193}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= t -4.8e+217)
     t_1
     (if (<= t -3.15e+171)
       (* x (/ (- z a) t))
       (if (<= t -3e+101)
         t_1
         (if (<= t -2e-91)
           (* z (/ (- y x) (- a t)))
           (if (<= t 4.8e-28)
             (- x (* z (/ (- x y) a)))
             (if (<= t 1.55e+193) (* (- z t) (/ y (- a t))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -3.15e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -3e+101) {
		tmp = t_1;
	} else if (t <= -2e-91) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.8e-28) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 1.55e+193) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (t <= (-4.8d+217)) then
        tmp = t_1
    else if (t <= (-3.15d+171)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-3d+101)) then
        tmp = t_1
    else if (t <= (-2d-91)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 4.8d-28) then
        tmp = x - (z * ((x - y) / a))
    else if (t <= 1.55d+193) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -3.15e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -3e+101) {
		tmp = t_1;
	} else if (t <= -2e-91) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.8e-28) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 1.55e+193) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if t <= -4.8e+217:
		tmp = t_1
	elif t <= -3.15e+171:
		tmp = x * ((z - a) / t)
	elif t <= -3e+101:
		tmp = t_1
	elif t <= -2e-91:
		tmp = z * ((y - x) / (a - t))
	elif t <= 4.8e-28:
		tmp = x - (z * ((x - y) / a))
	elif t <= 1.55e+193:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -3.15e+171)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -3e+101)
		tmp = t_1;
	elseif (t <= -2e-91)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 4.8e-28)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	elseif (t <= 1.55e+193)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -3.15e+171)
		tmp = x * ((z - a) / t);
	elseif (t <= -3e+101)
		tmp = t_1;
	elseif (t <= -2e-91)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 4.8e-28)
		tmp = x - (z * ((x - y) / a));
	elseif (t <= 1.55e+193)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+217], t$95$1, If[LessEqual[t, -3.15e+171], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e+101], t$95$1, If[LessEqual[t, -2e-91], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-28], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+193], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.7999999999999996e217 or -3.1500000000000002e171 < t < -2.99999999999999993e101 or 1.54999999999999993e193 < t

   1. Initial program 36.2%

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

      1. clear-num 36.0%

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

      2. inv-pow 36.0%

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

      3. *-commutative 36.0%

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

      4. associate-/r* 59.7%

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

   4. Applied egg-rr 59.7%

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

   5. Taylor expanded in x around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r/ 43.5%

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

   7. Simplified 43.5%

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

   8. Taylor expanded in a around 0 43.5%

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

      1. mul-1-neg 43.5%

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

   10. Simplified 43.5%

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

   11. Taylor expanded in y around 0 53.1%

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

       1. mul-1-neg 53.1%

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

       2. distribute-frac-neg2 53.1%

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

       3. associate-/l* 77.0%

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

   13. Simplified 77.0%

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

   if -4.7999999999999996e217 < t < -3.1500000000000002e171

   1. Initial program 3.0%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 68.5%

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

      1. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   if -2.99999999999999993e101 < t < -2.00000000000000004e-91

   1. Initial program 76.3%

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

      1. clear-num 76.2%

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

      2. inv-pow 76.2%

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

      3. *-commutative 76.2%

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

      4. associate-/r* 85.7%

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

   4. Applied egg-rr 85.7%

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

   5. Taylor expanded in z around inf 56.4%

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

      1. div-sub 56.4%

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

   7. Simplified 56.4%

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

   if -2.00000000000000004e-91 < t < 4.8000000000000004e-28

   1. Initial program 85.8%

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

   3. Taylor expanded in t around 0 70.7%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if 4.8000000000000004e-28 < t < 1.54999999999999993e193

   1. Initial program 63.4%

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

      1. clear-num 63.2%

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

      2. inv-pow 63.2%

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

      3. *-commutative 63.2%

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

      4. associate-/r* 78.0%

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

   4. Applied egg-rr 78.0%

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

   5. Taylor expanded in x around 0 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*r/ 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-28}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+193}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= a -5.8e+39)
     x
     (if (<= a 3.45e-269)
       t_1
       (if (<= a 1.8e-84)
         y
         (if (<= a 1.45e-21)
           t_1
           (if (<= a 8.5e+18)
             y
             (if (<= a 1.55e+64)
               (* y (/ (- z t) a))
               (if (<= a 4.2e+79) y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -5.8e+39) {
		tmp = x;
	} else if (a <= 3.45e-269) {
		tmp = t_1;
	} else if (a <= 1.8e-84) {
		tmp = y;
	} else if (a <= 1.45e-21) {
		tmp = t_1;
	} else if (a <= 8.5e+18) {
		tmp = y;
	} else if (a <= 1.55e+64) {
		tmp = y * ((z - t) / a);
	} else if (a <= 4.2e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (a <= (-5.8d+39)) then
        tmp = x
    else if (a <= 3.45d-269) then
        tmp = t_1
    else if (a <= 1.8d-84) then
        tmp = y
    else if (a <= 1.45d-21) then
        tmp = t_1
    else if (a <= 8.5d+18) then
        tmp = y
    else if (a <= 1.55d+64) then
        tmp = y * ((z - t) / a)
    else if (a <= 4.2d+79) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -5.8e+39) {
		tmp = x;
	} else if (a <= 3.45e-269) {
		tmp = t_1;
	} else if (a <= 1.8e-84) {
		tmp = y;
	} else if (a <= 1.45e-21) {
		tmp = t_1;
	} else if (a <= 8.5e+18) {
		tmp = y;
	} else if (a <= 1.55e+64) {
		tmp = y * ((z - t) / a);
	} else if (a <= 4.2e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if a <= -5.8e+39:
		tmp = x
	elif a <= 3.45e-269:
		tmp = t_1
	elif a <= 1.8e-84:
		tmp = y
	elif a <= 1.45e-21:
		tmp = t_1
	elif a <= 8.5e+18:
		tmp = y
	elif a <= 1.55e+64:
		tmp = y * ((z - t) / a)
	elif a <= 4.2e+79:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (a <= -5.8e+39)
		tmp = x;
	elseif (a <= 3.45e-269)
		tmp = t_1;
	elseif (a <= 1.8e-84)
		tmp = y;
	elseif (a <= 1.45e-21)
		tmp = t_1;
	elseif (a <= 8.5e+18)
		tmp = y;
	elseif (a <= 1.55e+64)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= 4.2e+79)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (a <= -5.8e+39)
		tmp = x;
	elseif (a <= 3.45e-269)
		tmp = t_1;
	elseif (a <= 1.8e-84)
		tmp = y;
	elseif (a <= 1.45e-21)
		tmp = t_1;
	elseif (a <= 8.5e+18)
		tmp = y;
	elseif (a <= 1.55e+64)
		tmp = y * ((z - t) / a);
	elseif (a <= 4.2e+79)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+39], x, If[LessEqual[a, 3.45e-269], t$95$1, If[LessEqual[a, 1.8e-84], y, If[LessEqual[a, 1.45e-21], t$95$1, If[LessEqual[a, 8.5e+18], y, If[LessEqual[a, 1.55e+64], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+79], y, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.80000000000000059e39 or 4.20000000000000016e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 50.4%

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

   if -5.80000000000000059e39 < a < 3.45e-269 or 1.80000000000000002e-84 < a < 1.45e-21

   1. Initial program 65.7%

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

   3. Taylor expanded in x around -inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

      3. +-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in t around -inf 47.8%

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

      1. associate-/l* 53.1%

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

   8. Simplified 53.1%

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

   if 3.45e-269 < a < 1.80000000000000002e-84 or 1.45e-21 < a < 8.5e18 or 1.55e64 < a < 4.20000000000000016e79

   1. Initial program 64.4%

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

   3. Taylor expanded in t around inf 57.5%

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

   if 8.5e18 < a < 1.55e64

   1. Initial program 72.7%

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

      1. clear-num 72.2%

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

      2. inv-pow 72.2%

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

      3. *-commutative 72.2%

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

      4. associate-/r* 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in x around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r/ 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in a around inf 55.3%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= a -8.5e+39)
     x
     (if (<= a 6.1e-271)
       t_1
       (if (<= a 4.5e-85)
         y
         (if (<= a 1.55e-23)
           t_1
           (if (<= a 5.5e+19)
             y
             (if (<= a 1.25e+66)
               (* (- z t) (/ y a))
               (if (<= a 3.2e+79) y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -8.5e+39) {
		tmp = x;
	} else if (a <= 6.1e-271) {
		tmp = t_1;
	} else if (a <= 4.5e-85) {
		tmp = y;
	} else if (a <= 1.55e-23) {
		tmp = t_1;
	} else if (a <= 5.5e+19) {
		tmp = y;
	} else if (a <= 1.25e+66) {
		tmp = (z - t) * (y / a);
	} else if (a <= 3.2e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (a <= (-8.5d+39)) then
        tmp = x
    else if (a <= 6.1d-271) then
        tmp = t_1
    else if (a <= 4.5d-85) then
        tmp = y
    else if (a <= 1.55d-23) then
        tmp = t_1
    else if (a <= 5.5d+19) then
        tmp = y
    else if (a <= 1.25d+66) then
        tmp = (z - t) * (y / a)
    else if (a <= 3.2d+79) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -8.5e+39) {
		tmp = x;
	} else if (a <= 6.1e-271) {
		tmp = t_1;
	} else if (a <= 4.5e-85) {
		tmp = y;
	} else if (a <= 1.55e-23) {
		tmp = t_1;
	} else if (a <= 5.5e+19) {
		tmp = y;
	} else if (a <= 1.25e+66) {
		tmp = (z - t) * (y / a);
	} else if (a <= 3.2e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if a <= -8.5e+39:
		tmp = x
	elif a <= 6.1e-271:
		tmp = t_1
	elif a <= 4.5e-85:
		tmp = y
	elif a <= 1.55e-23:
		tmp = t_1
	elif a <= 5.5e+19:
		tmp = y
	elif a <= 1.25e+66:
		tmp = (z - t) * (y / a)
	elif a <= 3.2e+79:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (a <= -8.5e+39)
		tmp = x;
	elseif (a <= 6.1e-271)
		tmp = t_1;
	elseif (a <= 4.5e-85)
		tmp = y;
	elseif (a <= 1.55e-23)
		tmp = t_1;
	elseif (a <= 5.5e+19)
		tmp = y;
	elseif (a <= 1.25e+66)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (a <= 3.2e+79)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (a <= -8.5e+39)
		tmp = x;
	elseif (a <= 6.1e-271)
		tmp = t_1;
	elseif (a <= 4.5e-85)
		tmp = y;
	elseif (a <= 1.55e-23)
		tmp = t_1;
	elseif (a <= 5.5e+19)
		tmp = y;
	elseif (a <= 1.25e+66)
		tmp = (z - t) * (y / a);
	elseif (a <= 3.2e+79)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+39], x, If[LessEqual[a, 6.1e-271], t$95$1, If[LessEqual[a, 4.5e-85], y, If[LessEqual[a, 1.55e-23], t$95$1, If[LessEqual[a, 5.5e+19], y, If[LessEqual[a, 1.25e+66], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+79], y, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.49999999999999971e39 or 3.20000000000000003e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 50.4%

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

   if -8.49999999999999971e39 < a < 6.09999999999999992e-271 or 4.50000000000000004e-85 < a < 1.5499999999999999e-23

   1. Initial program 65.7%

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

   3. Taylor expanded in x around -inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

      3. +-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in t around -inf 47.8%

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

      1. associate-/l* 53.1%

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

   8. Simplified 53.1%

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

   if 6.09999999999999992e-271 < a < 4.50000000000000004e-85 or 1.5499999999999999e-23 < a < 5.5e19 or 1.24999999999999998e66 < a < 3.20000000000000003e79

   1. Initial program 64.4%

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

   3. Taylor expanded in t around inf 57.5%

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

   if 5.5e19 < a < 1.24999999999999998e66

   1. Initial program 72.7%

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

      1. clear-num 72.2%

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

      2. inv-pow 72.2%

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

      3. *-commutative 72.2%

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

      4. associate-/r* 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in x around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r/ 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in a around inf 55.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+66}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ t_2 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- t z)) (- t a))))
        (t_2 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -5e+46)
     t_2
     (if (<= t -1.45e-230)
       t_1
       (if (<= t 1.9e-210)
         (- x (* z (/ (- x y) a)))
         (if (<= t 2.5e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (t - z)) / (t - a));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -5e+46) {
		tmp = t_2;
	} else if (t <= -1.45e-230) {
		tmp = t_1;
	} else if (t <= 1.9e-210) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 2.5e+44) {
		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 - z)) / (t - a))
    t_2 = y + ((z - a) * ((x - y) / t))
    if (t <= (-5d+46)) then
        tmp = t_2
    else if (t <= (-1.45d-230)) then
        tmp = t_1
    else if (t <= 1.9d-210) then
        tmp = x - (z * ((x - y) / a))
    else if (t <= 2.5d+44) 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 - z)) / (t - a));
	double t_2 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -5e+46) {
		tmp = t_2;
	} else if (t <= -1.45e-230) {
		tmp = t_1;
	} else if (t <= 1.9e-210) {
		tmp = x - (z * ((x - y) / a));
	} else if (t <= 2.5e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (t - z)) / (t - a))
	t_2 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -5e+46:
		tmp = t_2
	elif t <= -1.45e-230:
		tmp = t_1
	elif t <= 1.9e-210:
		tmp = x - (z * ((x - y) / a))
	elif t <= 2.5e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(t - a)))
	t_2 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -5e+46)
		tmp = t_2;
	elseif (t <= -1.45e-230)
		tmp = t_1;
	elseif (t <= 1.9e-210)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	elseif (t <= 2.5e+44)
		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 - z)) / (t - a));
	t_2 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -5e+46)
		tmp = t_2;
	elseif (t <= -1.45e-230)
		tmp = t_1;
	elseif (t <= 1.9e-210)
		tmp = x - (z * ((x - y) / a));
	elseif (t <= 2.5e+44)
		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[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+46], t$95$2, If[LessEqual[t, -1.45e-230], t$95$1, If[LessEqual[t, 1.9e-210], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e46 or 2.4999999999999998e44 < t

   1. Initial program 40.1%

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

   3. Taylor expanded in t around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. distribute-lft-out-- 70.6%

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

      3. div-sub 70.6%

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

      4. mul-1-neg 70.6%

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

      5. unsub-neg 70.6%

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

      6. div-sub 70.6%

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

      7. associate-/l* 76.2%

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

      8. associate-/l* 82.8%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -5.0000000000000002e46 < t < -1.45000000000000003e-230 or 1.90000000000000002e-210 < t < 2.4999999999999998e44

   1. Initial program 87.5%

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

   if -1.45000000000000003e-230 < t < 1.90000000000000002e-210

   1. Initial program 83.7%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+46}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-230}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(t - z\right)}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a - t}{z - t}}\\ t_2 := x - z \cdot \frac{x - y}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ (- a t) (- z t)))) (t_2 (- x (* z (/ (- x y) a)))))
   (if (<= a -3e+140)
     t_2
     (if (<= a -3.5e-60)
       t_1
       (if (<= a 5.7e-270)
         (* z (/ (- y x) (- a t)))
         (if (<= a 2.9e+79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / ((a - t) / (z - t));
	double t_2 = x - (z * ((x - y) / a));
	double tmp;
	if (a <= -3e+140) {
		tmp = t_2;
	} else if (a <= -3.5e-60) {
		tmp = t_1;
	} else if (a <= 5.7e-270) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.9e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y / ((a - t) / (z - t))
    t_2 = x - (z * ((x - y) / a))
    if (a <= (-3d+140)) then
        tmp = t_2
    else if (a <= (-3.5d-60)) then
        tmp = t_1
    else if (a <= 5.7d-270) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 2.9d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / ((a - t) / (z - t));
	double t_2 = x - (z * ((x - y) / a));
	double tmp;
	if (a <= -3e+140) {
		tmp = t_2;
	} else if (a <= -3.5e-60) {
		tmp = t_1;
	} else if (a <= 5.7e-270) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.9e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / ((a - t) / (z - t))
	t_2 = x - (z * ((x - y) / a))
	tmp = 0
	if a <= -3e+140:
		tmp = t_2
	elif a <= -3.5e-60:
		tmp = t_1
	elif a <= 5.7e-270:
		tmp = z * ((y - x) / (a - t))
	elif a <= 2.9e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(Float64(a - t) / Float64(z - t)))
	t_2 = Float64(x - Float64(z * Float64(Float64(x - y) / a)))
	tmp = 0.0
	if (a <= -3e+140)
		tmp = t_2;
	elseif (a <= -3.5e-60)
		tmp = t_1;
	elseif (a <= 5.7e-270)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 2.9e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / ((a - t) / (z - t));
	t_2 = x - (z * ((x - y) / a));
	tmp = 0.0;
	if (a <= -3e+140)
		tmp = t_2;
	elseif (a <= -3.5e-60)
		tmp = t_1;
	elseif (a <= 5.7e-270)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 2.9e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+140], t$95$2, If[LessEqual[a, -3.5e-60], t$95$1, If[LessEqual[a, 5.7e-270], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.99999999999999997e140 or 2.89999999999999992e79 < a

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 65.5%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -2.99999999999999997e140 < a < -3.49999999999999976e-60 or 5.7000000000000002e-270 < a < 2.89999999999999992e79

   1. Initial program 67.4%

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

      1. clear-num 67.3%

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

      2. inv-pow 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-/r* 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in x around 0 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-*r/ 57.6%

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

      3. *-commutative 57.6%

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

      4. associate-/r/ 66.9%

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

   7. Simplified 66.9%

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

   if -3.49999999999999976e-60 < a < 5.7000000000000002e-270

   1. Initial program 61.8%

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

      1. clear-num 61.6%

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

      2. inv-pow 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-/r* 68.1%

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

   4. Applied egg-rr 68.1%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. div-sub 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+140}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+48} \lor \neg \left(t \leq 1.15 \cdot 10^{+72}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -4.8e+217)
     t_1
     (if (<= t -5.5e+171)
       (* x (/ (- z a) t))
       (if (or (<= t -2e+48) (not (<= t 1.15e+72)))
         t_1
         (+ x (* y (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -5.5e+171) {
		tmp = x * ((z - a) / t);
	} else if ((t <= -2e+48) || !(t <= 1.15e+72)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y / t))
    if (t <= (-4.8d+217)) then
        tmp = t_1
    else if (t <= (-5.5d+171)) then
        tmp = x * ((z - a) / t)
    else if ((t <= (-2d+48)) .or. (.not. (t <= 1.15d+72))) then
        tmp = t_1
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -5.5e+171) {
		tmp = x * ((z - a) / t);
	} else if ((t <= -2e+48) || !(t <= 1.15e+72)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -4.8e+217:
		tmp = t_1
	elif t <= -5.5e+171:
		tmp = x * ((z - a) / t)
	elif (t <= -2e+48) or not (t <= 1.15e+72):
		tmp = t_1
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -5.5e+171)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif ((t <= -2e+48) || !(t <= 1.15e+72))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -5.5e+171)
		tmp = x * ((z - a) / t);
	elseif ((t <= -2e+48) || ~((t <= 1.15e+72)))
		tmp = t_1;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+217], t$95$1, If[LessEqual[t, -5.5e+171], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2e+48], N[Not[LessEqual[t, 1.15e+72]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7999999999999996e217 or -5.5000000000000003e171 < t < -2.00000000000000009e48 or 1.15e72 < t

   1. Initial program 42.6%

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

      1. clear-num 42.4%

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

      2. inv-pow 42.4%

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

      3. *-commutative 42.4%

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

      4. associate-/r* 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in x around 0 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-*r/ 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in a around 0 43.9%

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

      1. mul-1-neg 43.9%

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

   10. Simplified 43.9%

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

   11. Taylor expanded in z around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*l/ 63.4%

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

       3. unsub-neg 63.4%

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

       4. *-commutative 63.4%

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

   13. Simplified 63.4%

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

   if -4.7999999999999996e217 < t < -5.5000000000000003e171

   1. Initial program 3.0%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 68.5%

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

      1. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   if -2.00000000000000009e48 < t < 1.15e72

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 60.7%

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

   4. Taylor expanded in y around inf 56.0%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+48} \lor \neg \left(t \leq 1.15 \cdot 10^{+72}\right):\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+48} \lor \neg \left(t \leq 1.9 \cdot 10^{+74}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= t -4.8e+217)
     t_1
     (if (<= t -1.05e+171)
       (* x (/ (- z a) t))
       (if (or (<= t -4.6e+48) (not (<= t 1.9e+74)))
         t_1
         (+ x (* y (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -1.05e+171) {
		tmp = x * ((z - a) / t);
	} else if ((t <= -4.6e+48) || !(t <= 1.9e+74)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (t <= (-4.8d+217)) then
        tmp = t_1
    else if (t <= (-1.05d+171)) then
        tmp = x * ((z - a) / t)
    else if ((t <= (-4.6d+48)) .or. (.not. (t <= 1.9d+74))) then
        tmp = t_1
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (t <= -4.8e+217) {
		tmp = t_1;
	} else if (t <= -1.05e+171) {
		tmp = x * ((z - a) / t);
	} else if ((t <= -4.6e+48) || !(t <= 1.9e+74)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if t <= -4.8e+217:
		tmp = t_1
	elif t <= -1.05e+171:
		tmp = x * ((z - a) / t)
	elif (t <= -4.6e+48) or not (t <= 1.9e+74):
		tmp = t_1
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -1.05e+171)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif ((t <= -4.6e+48) || !(t <= 1.9e+74))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (t <= -4.8e+217)
		tmp = t_1;
	elseif (t <= -1.05e+171)
		tmp = x * ((z - a) / t);
	elseif ((t <= -4.6e+48) || ~((t <= 1.9e+74)))
		tmp = t_1;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+217], t$95$1, If[LessEqual[t, -1.05e+171], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.6e+48], N[Not[LessEqual[t, 1.9e+74]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7999999999999996e217 or -1.0500000000000001e171 < t < -4.6e48 or 1.8999999999999999e74 < t

   1. Initial program 42.6%

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

      1. clear-num 42.4%

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

      2. inv-pow 42.4%

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

      3. *-commutative 42.4%

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

      4. associate-/r* 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in x around 0 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-*r/ 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in a around 0 43.9%

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

      1. mul-1-neg 43.9%

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

   10. Simplified 43.9%

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

   11. Taylor expanded in y around 0 49.7%

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

       1. mul-1-neg 49.7%

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

       2. distribute-frac-neg2 49.7%

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

       3. associate-/l* 65.1%

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

   13. Simplified 65.1%

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

   if -4.7999999999999996e217 < t < -1.0500000000000001e171

   1. Initial program 3.0%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 68.5%

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

      1. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   if -4.6e48 < t < 1.8999999999999999e74

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 60.7%

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

   4. Taylor expanded in y around inf 56.0%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+48} \lor \neg \left(t \leq 1.9 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - a}{t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- z a) t))))
   (if (<= a -1.15e+40)
     x
     (if (<= a 6.5e-271)
       t_1
       (if (<= a 1.15e-84)
         y
         (if (<= a 1.22e-26) t_1 (if (<= a 2.4e+79) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -1.15e+40) {
		tmp = x;
	} else if (a <= 6.5e-271) {
		tmp = t_1;
	} else if (a <= 1.15e-84) {
		tmp = y;
	} else if (a <= 1.22e-26) {
		tmp = t_1;
	} else if (a <= 2.4e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - a) / t)
    if (a <= (-1.15d+40)) then
        tmp = x
    else if (a <= 6.5d-271) then
        tmp = t_1
    else if (a <= 1.15d-84) then
        tmp = y
    else if (a <= 1.22d-26) then
        tmp = t_1
    else if (a <= 2.4d+79) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((z - a) / t);
	double tmp;
	if (a <= -1.15e+40) {
		tmp = x;
	} else if (a <= 6.5e-271) {
		tmp = t_1;
	} else if (a <= 1.15e-84) {
		tmp = y;
	} else if (a <= 1.22e-26) {
		tmp = t_1;
	} else if (a <= 2.4e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((z - a) / t)
	tmp = 0
	if a <= -1.15e+40:
		tmp = x
	elif a <= 6.5e-271:
		tmp = t_1
	elif a <= 1.15e-84:
		tmp = y
	elif a <= 1.22e-26:
		tmp = t_1
	elif a <= 2.4e+79:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(z - a) / t))
	tmp = 0.0
	if (a <= -1.15e+40)
		tmp = x;
	elseif (a <= 6.5e-271)
		tmp = t_1;
	elseif (a <= 1.15e-84)
		tmp = y;
	elseif (a <= 1.22e-26)
		tmp = t_1;
	elseif (a <= 2.4e+79)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((z - a) / t);
	tmp = 0.0;
	if (a <= -1.15e+40)
		tmp = x;
	elseif (a <= 6.5e-271)
		tmp = t_1;
	elseif (a <= 1.15e-84)
		tmp = y;
	elseif (a <= 1.22e-26)
		tmp = t_1;
	elseif (a <= 2.4e+79)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+40], x, If[LessEqual[a, 6.5e-271], t$95$1, If[LessEqual[a, 1.15e-84], y, If[LessEqual[a, 1.22e-26], t$95$1, If[LessEqual[a, 2.4e+79], y, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.14999999999999997e40 or 2.39999999999999986e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 50.4%

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

   if -1.14999999999999997e40 < a < 6.5000000000000005e-271 or 1.1499999999999999e-84 < a < 1.22e-26

   1. Initial program 65.7%

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

   3. Taylor expanded in x around -inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

      3. +-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in t around -inf 47.8%

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

      1. associate-/l* 53.1%

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

   8. Simplified 53.1%

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

   if 6.5000000000000005e-271 < a < 1.1499999999999999e-84 or 1.22e-26 < a < 2.39999999999999986e79

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 50.1%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.55e+218)
   y
   (if (<= t -5e+171)
     (* x (/ (- z a) t))
     (if (<= t -4.4e+83) y (if (<= t 2.9e+79) (+ x (* y (/ z a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+218) {
		tmp = y;
	} else if (t <= -5e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -4.4e+83) {
		tmp = y;
	} else if (t <= 2.9e+79) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.55d+218)) then
        tmp = y
    else if (t <= (-5d+171)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-4.4d+83)) then
        tmp = y
    else if (t <= 2.9d+79) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.55e+218) {
		tmp = y;
	} else if (t <= -5e+171) {
		tmp = x * ((z - a) / t);
	} else if (t <= -4.4e+83) {
		tmp = y;
	} else if (t <= 2.9e+79) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.55e+218:
		tmp = y
	elif t <= -5e+171:
		tmp = x * ((z - a) / t)
	elif t <= -4.4e+83:
		tmp = y
	elif t <= 2.9e+79:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.55e+218)
		tmp = y;
	elseif (t <= -5e+171)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -4.4e+83)
		tmp = y;
	elseif (t <= 2.9e+79)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.55e+218)
		tmp = y;
	elseif (t <= -5e+171)
		tmp = x * ((z - a) / t);
	elseif (t <= -4.4e+83)
		tmp = y;
	elseif (t <= 2.9e+79)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.55e+218], y, If[LessEqual[t, -5e+171], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e+83], y, If[LessEqual[t, 2.9e+79], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5500000000000001e218 or -5.0000000000000004e171 < t < -4.39999999999999997e83 or 2.89999999999999992e79 < t

   1. Initial program 42.6%

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

   3. Taylor expanded in t around inf 59.1%

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

   if -1.5500000000000001e218 < t < -5.0000000000000004e171

   1. Initial program 3.0%

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

   3. Taylor expanded in x around -inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. +-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in t around -inf 68.5%

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

      1. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   if -4.39999999999999997e83 < t < 2.89999999999999992e79

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 60.1%

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

   4. Taylor expanded in y around inf 55.6%

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

      1. associate-/l* 61.2%

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

   6. Simplified 61.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - t}{z}}{x - y}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ (- x y) t)))))
   (if (<= t -6.5e+50)
     t_1
     (if (<= t 3.4e-30)
       (+ x (/ -1.0 (/ (/ (- a t) z) (- x y))))
       (if (<= t 1.22e+42) (- x (/ (* y (- t z)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -6.5e+50) {
		tmp = t_1;
	} else if (t <= 3.4e-30) {
		tmp = x + (-1.0 / (((a - t) / z) / (x - y)));
	} else if (t <= 1.22e+42) {
		tmp = x - ((y * (t - z)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z - a) * ((x - y) / t))
    if (t <= (-6.5d+50)) then
        tmp = t_1
    else if (t <= 3.4d-30) then
        tmp = x + ((-1.0d0) / (((a - t) / z) / (x - y)))
    else if (t <= 1.22d+42) then
        tmp = x - ((y * (t - z)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * ((x - y) / t));
	double tmp;
	if (t <= -6.5e+50) {
		tmp = t_1;
	} else if (t <= 3.4e-30) {
		tmp = x + (-1.0 / (((a - t) / z) / (x - y)));
	} else if (t <= 1.22e+42) {
		tmp = x - ((y * (t - z)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * ((x - y) / t))
	tmp = 0
	if t <= -6.5e+50:
		tmp = t_1
	elif t <= 3.4e-30:
		tmp = x + (-1.0 / (((a - t) / z) / (x - y)))
	elif t <= 1.22e+42:
		tmp = x - ((y * (t - z)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -6.5e+50)
		tmp = t_1;
	elseif (t <= 3.4e-30)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - t) / z) / Float64(x - y))));
	elseif (t <= 1.22e+42)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * ((x - y) / t));
	tmp = 0.0;
	if (t <= -6.5e+50)
		tmp = t_1;
	elseif (t <= 3.4e-30)
		tmp = x + (-1.0 / (((a - t) / z) / (x - y)));
	elseif (t <= 1.22e+42)
		tmp = x - ((y * (t - z)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+50], t$95$1, If[LessEqual[t, 3.4e-30], N[(x + N[(-1.0 / N[(N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+42], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000003e50 or 1.22e42 < t

   1. Initial program 40.4%

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

   3. Taylor expanded in t around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. distribute-lft-out-- 71.2%

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

      3. div-sub 71.2%

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

      4. mul-1-neg 71.2%

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

      5. unsub-neg 71.2%

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

      6. div-sub 71.2%

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

      7. associate-/l* 76.9%

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

      8. associate-/l* 83.6%

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

      9. distribute-rgt-out-- 83.8%

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

   5. Simplified 83.8%

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

   if -6.5000000000000003e50 < t < 3.4000000000000003e-30

   1. Initial program 85.6%

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

      1. clear-num 85.1%

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

      2. inv-pow 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-/r* 92.2%

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

   4. Applied egg-rr 92.2%

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

      1. unpow-1 92.2%

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

      2. associate-/l/ 85.1%

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

      3. *-commutative 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in z around inf 77.3%

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

      1. associate-/r* 83.1%

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

   9. Simplified 83.1%

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

   if 3.4000000000000003e-30 < t < 1.22e42

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   5. Simplified 85.3%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - t}{z}}{x - y}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= a -3.8e+39)
     t_1
     (if (<= a 6.2e-267)
       (* z (/ (- y x) (- a t)))
       (if (<= a 2.3e+79) (* (- z t) (/ y (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (a <= -3.8e+39) {
		tmp = t_1;
	} else if (a <= 6.2e-267) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.3e+79) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (a <= (-3.8d+39)) then
        tmp = t_1
    else if (a <= 6.2d-267) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 2.3d+79) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (a <= -3.8e+39) {
		tmp = t_1;
	} else if (a <= 6.2e-267) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.3e+79) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if a <= -3.8e+39:
		tmp = t_1
	elif a <= 6.2e-267:
		tmp = z * ((y - x) / (a - t))
	elif a <= 2.3e+79:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -3.8e+39)
		tmp = t_1;
	elseif (a <= 6.2e-267)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 2.3e+79)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (a <= -3.8e+39)
		tmp = t_1;
	elseif (a <= 6.2e-267)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 2.3e+79)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+39], t$95$1, If[LessEqual[a, 6.2e-267], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+79], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7999999999999998e39 or 2.3e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in t around 0 59.1%

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

   4. Taylor expanded in y around inf 60.8%

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

      1. associate-/l* 67.9%

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

   6. Simplified 67.9%

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

   if -3.7999999999999998e39 < a < 6.2000000000000002e-267

   1. Initial program 63.1%

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

      1. clear-num 62.9%

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

      2. inv-pow 62.9%

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

      3. *-commutative 62.9%

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

      4. associate-/r* 68.1%

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

   4. Applied egg-rr 68.1%

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

   5. Taylor expanded in z around inf 59.5%

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

      1. div-sub 60.8%

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

   7. Simplified 60.8%

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

   if 6.2000000000000002e-267 < a < 2.3e79

   1. Initial program 68.6%

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

      1. clear-num 68.4%

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

      2. inv-pow 68.4%

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

      3. *-commutative 68.4%

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

      4. associate-/r* 77.7%

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

   4. Applied egg-rr 77.7%

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

   5. Taylor expanded in x around 0 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-*r/ 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+199}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.3e+96)
   (* x (+ (/ (- z t) (- t a)) 1.0))
   (if (<= x 2.8e-36)
     (/ y (/ (- a t) (- z t)))
     (if (<= x 4.2e+199) (- x (* z (/ (- x y) a))) (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.3e+96) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (x <= 2.8e-36) {
		tmp = y / ((a - t) / (z - t));
	} else if (x <= 4.2e+199) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-8.3d+96)) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else if (x <= 2.8d-36) then
        tmp = y / ((a - t) / (z - t))
    else if (x <= 4.2d+199) then
        tmp = x - (z * ((x - y) / a))
    else
        tmp = x * ((z - a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.3e+96) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else if (x <= 2.8e-36) {
		tmp = y / ((a - t) / (z - t));
	} else if (x <= 4.2e+199) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = x * ((z - a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.3e+96:
		tmp = x * (((z - t) / (t - a)) + 1.0)
	elif x <= 2.8e-36:
		tmp = y / ((a - t) / (z - t))
	elif x <= 4.2e+199:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = x * ((z - a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.3e+96)
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	elseif (x <= 2.8e-36)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (x <= 4.2e+199)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = Float64(x * Float64(Float64(z - a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.3e+96)
		tmp = x * (((z - t) / (t - a)) + 1.0);
	elseif (x <= 2.8e-36)
		tmp = y / ((a - t) / (z - t));
	elseif (x <= 4.2e+199)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = x * ((z - a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.3e+96], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-36], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+199], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.2999999999999997e96

   1. Initial program 56.8%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   if -8.2999999999999997e96 < x < 2.8000000000000001e-36

   1. Initial program 75.7%

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

      1. clear-num 75.1%

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

      2. inv-pow 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-/r* 83.7%

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

   4. Applied egg-rr 83.7%

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

   5. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*r/ 61.1%

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

      3. *-commutative 61.1%

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

      4. associate-/r/ 73.1%

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

   7. Simplified 73.1%

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

   if 2.8000000000000001e-36 < x < 4.1999999999999999e199

   1. Initial program 65.2%

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

   3. Taylor expanded in t around 0 56.0%

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

      1. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   if 4.1999999999999999e199 < x

   1. Initial program 42.1%

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

   3. Taylor expanded in x around -inf 85.9%

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

      1. associate-*r* 85.9%

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

      2. neg-mul-1 85.9%

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

      3. +-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in t around -inf 54.5%

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

      1. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.3 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+199}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+120} \lor \neg \left(x \leq 1.7 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.2e+120) (not (<= x 1.7e+127)))
   (* x (+ (/ (- z t) (- t a)) 1.0))
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.2e+120) || !(x <= 1.7e+127)) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-4.2d+120)) .or. (.not. (x <= 1.7d+127))) then
        tmp = x * (((z - t) / (t - a)) + 1.0d0)
    else
        tmp = x + (y * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.2e+120) || !(x <= 1.7e+127)) {
		tmp = x * (((z - t) / (t - a)) + 1.0);
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.2e+120) or not (x <= 1.7e+127):
		tmp = x * (((z - t) / (t - a)) + 1.0)
	else:
		tmp = x + (y * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.2e+120) || !(x <= 1.7e+127))
		tmp = Float64(x * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -4.2e+120) || ~((x <= 1.7e+127)))
		tmp = x * (((z - t) / (t - a)) + 1.0);
	else
		tmp = x + (y * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.2e+120], N[Not[LessEqual[x, 1.7e+127]], $MachinePrecision]], N[(x * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000001e120 or 1.69999999999999989e127 < x

   1. Initial program 51.1%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. mul-1-neg 63.9%

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

      2. unsub-neg 63.9%

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

   5. Simplified 63.9%

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

   if -4.2000000000000001e120 < x < 1.69999999999999989e127

   1. Initial program 74.7%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. associate-/l* 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+120} \lor \neg \left(x \leq 1.7 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -35000000000 \lor \neg \left(a \leq 2.15 \cdot 10^{-32}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -35000000000.0) (not (<= a 2.15e-32)))
   (+ x (* y (/ (- z t) (- a t))))
   (+ y (* (- z a) (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -35000000000.0) || !(a <= 2.15e-32)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((x - y) / 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 <= (-35000000000.0d0)) .or. (.not. (a <= 2.15d-32))) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((z - a) * ((x - y) / 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 <= -35000000000.0) || !(a <= 2.15e-32)) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((z - a) * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -35000000000.0) or not (a <= 2.15e-32):
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((z - a) * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -35000000000.0) || !(a <= 2.15e-32))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -35000000000.0) || ~((a <= 2.15e-32)))
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((z - a) * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -35000000000.0], N[Not[LessEqual[a, 2.15e-32]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5e10 or 2.14999999999999995e-32 < a

   1. Initial program 71.7%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   if -3.5e10 < a < 2.14999999999999995e-32

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 77.7%

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

      1. associate--l+ 77.7%

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

      2. distribute-lft-out-- 77.7%

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

      3. div-sub 79.5%

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

      4. mul-1-neg 79.5%

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

      5. unsub-neg 79.5%

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

      6. div-sub 77.7%

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

      7. associate-/l* 78.9%

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

      8. associate-/l* 76.2%

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

      9. distribute-rgt-out-- 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -35000000000 \lor \neg \left(a \leq 2.15 \cdot 10^{-32}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.25e+39)
   x
   (if (<= a 8.2e-271) (* x (/ z t)) (if (<= a 4.8e+79) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.25e+39) {
		tmp = x;
	} else if (a <= 8.2e-271) {
		tmp = x * (z / t);
	} else if (a <= 4.8e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.25d+39)) then
        tmp = x
    else if (a <= 8.2d-271) then
        tmp = x * (z / t)
    else if (a <= 4.8d+79) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.25e+39) {
		tmp = x;
	} else if (a <= 8.2e-271) {
		tmp = x * (z / t);
	} else if (a <= 4.8e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.25e+39:
		tmp = x
	elif a <= 8.2e-271:
		tmp = x * (z / t)
	elif a <= 4.8e+79:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.25e+39)
		tmp = x;
	elseif (a <= 8.2e-271)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 4.8e+79)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.25e+39)
		tmp = x;
	elseif (a <= 8.2e-271)
		tmp = x * (z / t);
	elseif (a <= 4.8e+79)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.25e+39], x, If[LessEqual[a, 8.2e-271], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+79], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2500000000000001e39 or 4.79999999999999971e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 50.4%

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

   if -3.2500000000000001e39 < a < 8.2000000000000005e-271

   1. Initial program 63.1%

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

   3. Taylor expanded in x around -inf 47.8%

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

      1. associate-*r* 47.8%

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

      2. neg-mul-1 47.8%

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

      3. +-commutative 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in a around 0 40.9%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

   if 8.2000000000000005e-271 < a < 4.79999999999999971e79

   1. Initial program 68.6%

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

   3. Taylor expanded in t around inf 44.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+39)
   x
   (if (<= a 8.2e-270) (/ x (/ t z)) (if (<= a 4.4e+79) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+39) {
		tmp = x;
	} else if (a <= 8.2e-270) {
		tmp = x / (t / z);
	} else if (a <= 4.4e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.2d+39)) then
        tmp = x
    else if (a <= 8.2d-270) then
        tmp = x / (t / z)
    else if (a <= 4.4d+79) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+39) {
		tmp = x;
	} else if (a <= 8.2e-270) {
		tmp = x / (t / z);
	} else if (a <= 4.4e+79) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+39:
		tmp = x
	elif a <= 8.2e-270:
		tmp = x / (t / z)
	elif a <= 4.4e+79:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+39)
		tmp = x;
	elseif (a <= 8.2e-270)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 4.4e+79)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+39)
		tmp = x;
	elseif (a <= 8.2e-270)
		tmp = x / (t / z);
	elseif (a <= 4.4e+79)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+39], x, If[LessEqual[a, 8.2e-270], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+79], y, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.19999999999999969e39 or 4.3999999999999998e79 < a

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 50.4%

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

   if -7.19999999999999969e39 < a < 8.1999999999999993e-270

   1. Initial program 63.1%

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

   3. Taylor expanded in x around -inf 47.8%

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

      1. associate-*r* 47.8%

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

      2. neg-mul-1 47.8%

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

      3. +-commutative 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in a around 0 40.9%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

      1. clear-num 45.9%

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

      2. un-div-inv 46.0%

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

   10. Applied egg-rr 46.0%

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

   if 8.1999999999999993e-270 < a < 4.3999999999999998e79

   1. Initial program 68.6%

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

   3. Taylor expanded in t around inf 44.8%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+79}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-24) y (if (<= t 9.8e-23) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-24) {
		tmp = y;
	} else if (t <= 9.8e-23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.6d-24)) then
        tmp = y
    else if (t <= 9.8d-23) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-24) {
		tmp = y;
	} else if (t <= 9.8e-23) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e-24:
		tmp = y
	elif t <= 9.8e-23:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-24)
		tmp = y;
	elseif (t <= 9.8e-23)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e-24)
		tmp = y;
	elseif (t <= 9.8e-23)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-24], y, If[LessEqual[t, 9.8e-23], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000006e-24 or 9.7999999999999996e-23 < t

   1. Initial program 49.5%

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

   3. Taylor expanded in t around inf 46.2%

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

   if -1.60000000000000006e-24 < t < 9.7999999999999996e-23

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 39.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-24}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.4%

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

3. Taylor expanded in a around inf 26.0%

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

4. Final simplification 26.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))