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

Percentage Accurate: 68.1% → 88.9%

Time: 12.8s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+149}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= z -1.9e+162)
     t_1
     (if (<= z 3.8e+149) (+ x (/ (- t x) (/ (- a z) (- y z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -1.9e+162) {
		tmp = t_1;
	} else if (z <= 3.8e+149) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((y - a) / z) * (x - t))
    if (z <= (-1.9d+162)) then
        tmp = t_1
    else if (z <= 3.8d+149) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -1.9e+162) {
		tmp = t_1;
	} else if (z <= 3.8e+149) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if z <= -1.9e+162:
		tmp = t_1
	elif z <= 3.8e+149:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -1.9e+162)
		tmp = t_1;
	elseif (z <= 3.8e+149)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (z <= -1.9e+162)
		tmp = t_1;
	elseif (z <= 3.8e+149)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+162], t$95$1, If[LessEqual[z, 3.8e+149], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000012e162 or 3.8000000000000001e149 < z

   1. Initial program 22.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 68.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 68.3%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 87.4%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 87.4%

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

   if -1.90000000000000012e162 < z < 3.8000000000000001e149

   1. Initial program 81.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 93.1%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+162}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+149}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -4.5e+62)
     t_1
     (if (<= a -1.45e-37)
       (* t (/ (- y z) (- a z)))
       (if (<= a 3.45e+59) (+ t (* (/ (- y a) z) (- x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -4.5e+62) {
		tmp = t_1;
	} else if (a <= -1.45e-37) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.45e+59) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-4.5d+62)) then
        tmp = t_1
    else if (a <= (-1.45d-37)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 3.45d+59) then
        tmp = t + (((y - a) / z) * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -4.5e+62) {
		tmp = t_1;
	} else if (a <= -1.45e-37) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.45e+59) {
		tmp = t + (((y - a) / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -4.5e+62:
		tmp = t_1
	elif a <= -1.45e-37:
		tmp = t * ((y - z) / (a - z))
	elif a <= 3.45e+59:
		tmp = t + (((y - a) / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -4.5e+62)
		tmp = t_1;
	elseif (a <= -1.45e-37)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 3.45e+59)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -4.5e+62)
		tmp = t_1;
	elseif (a <= -1.45e-37)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 3.45e+59)
		tmp = t + (((y - a) / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+62], t$95$1, If[LessEqual[a, -1.45e-37], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.45e+59], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999999e62 or 3.4499999999999999e59 < a

   1. Initial program 65.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 91.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 91.7%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 91.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y - z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 81.0%

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

   if -4.49999999999999999e62 < a < -1.45000000000000002e-37

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 65.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 78.5%

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

   if -1.45000000000000002e-37 < a < 3.4499999999999999e59

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 76.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 76.3%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 83.7%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 83.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+190}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-58)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.05e-8)
     (+ x (* (- t x) (/ y a)))
     (if (<= z 9e+190) (+ t (* y (/ (- x t) z))) (+ t (* a (/ (- t x) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-58) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.05e-8) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9e+190) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d-58)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.05d-8) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 9d+190) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-58) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.05e-8) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9e+190) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-58:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.05e-8:
		tmp = x + ((t - x) * (y / a))
	elif z <= 9e+190:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-58)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.05e-8)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 9e+190)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e-58)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.05e-8)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 9e+190)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-58], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-8], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+190], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5000000000000004e-58

   1. Initial program 50.4%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 47.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 47.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 73.4%

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

   if -8.5000000000000004e-58 < z < 1.04999999999999997e-8

   1. Initial program 93.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 79.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 79.7%

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

   if 1.04999999999999997e-8 < z < 8.9999999999999999e190

   1. Initial program 59.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 64.1%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 64.1%

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

   6. Taylor expanded in a around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right)}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(y \cdot \color{blue}{\frac{t - x}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t - x}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{z}\right)\right)\right) \]

      5. --lowering--.f64 70.7%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), z\right)\right)\right) \]

   8. Simplified 70.7%

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

   if 8.9999999999999999e190 < z

   1. Initial program 13.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 69.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(a \cdot \color{blue}{\frac{t - x}{z}}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t - x}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), z\right)\right)\right) \]

   8. Simplified 84.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+190}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.026:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.4e-59)
     t_1
     (if (<= z 0.026)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 9.5e+221) t_1 (+ t (* a (/ (- t x) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.4e-59) {
		tmp = t_1;
	} else if (z <= 0.026) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9.5e+221) {
		tmp = t_1;
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.4d-59)) then
        tmp = t_1
    else if (z <= 0.026d0) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 9.5d+221) then
        tmp = t_1
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.4e-59) {
		tmp = t_1;
	} else if (z <= 0.026) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 9.5e+221) {
		tmp = t_1;
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.4e-59:
		tmp = t_1
	elif z <= 0.026:
		tmp = x + ((t - x) * (y / a))
	elif z <= 9.5e+221:
		tmp = t_1
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.4e-59)
		tmp = t_1;
	elseif (z <= 0.026)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 9.5e+221)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.4e-59)
		tmp = t_1;
	elseif (z <= 0.026)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 9.5e+221)
		tmp = t_1;
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-59], t$95$1, If[LessEqual[z, 0.026], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+221], t$95$1, N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999e-59 or 0.0259999999999999988 < z < 9.50000000000000044e221

   1. Initial program 51.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 47.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 47.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 69.0%

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

   if -1.3999999999999999e-59 < z < 0.0259999999999999988

   1. Initial program 93.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 79.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 79.9%

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

   if 9.50000000000000044e221 < z

   1. Initial program 8.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 74.0%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 74.0%

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

   6. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{a \cdot \left(t - x\right)}{z}\right)}\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(a \cdot \color{blue}{\frac{t - x}{z}}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{t - x}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 94.6%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), z\right)\right)\right) \]

   8. Simplified 94.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 0.026:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+221}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+150}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- y a) z) (- x t)))))
   (if (<= z -8e+161)
     t_1
     (if (<= z 1.7e+150) (+ x (* (- t x) (/ (- y z) (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -8e+161) {
		tmp = t_1;
	} else if (z <= 1.7e+150) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((y - a) / z) * (x - t))
    if (z <= (-8d+161)) then
        tmp = t_1
    else if (z <= 1.7d+150) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * (x - t));
	double tmp;
	if (z <= -8e+161) {
		tmp = t_1;
	} else if (z <= 1.7e+150) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * (x - t))
	tmp = 0
	if z <= -8e+161:
		tmp = t_1
	elif z <= 1.7e+150:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -8e+161)
		tmp = t_1;
	elseif (z <= 1.7e+150)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) / z) * (x - t));
	tmp = 0.0;
	if (z <= -8e+161)
		tmp = t_1;
	elseif (z <= 1.7e+150)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+161], t$95$1, If[LessEqual[z, 1.7e+150], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000003e161 or 1.69999999999999991e150 < z

   1. Initial program 22.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 68.3%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 68.3%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 87.4%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 87.4%

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

   if -8.0000000000000003e161 < z < 1.69999999999999991e150

   1. Initial program 81.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 93.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+161}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+150}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -1.85e+62)
     t_1
     (if (<= a 7.8e+58) (+ t (* (/ y z) (- x t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -1.85e+62) {
		tmp = t_1;
	} else if (a <= 7.8e+58) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-1.85d+62)) then
        tmp = t_1
    else if (a <= 7.8d+58) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -1.85e+62) {
		tmp = t_1;
	} else if (a <= 7.8e+58) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -1.85e+62:
		tmp = t_1
	elif a <= 7.8e+58:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -1.85e+62)
		tmp = t_1;
	elseif (a <= 7.8e+58)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -1.85e+62)
		tmp = t_1;
	elseif (a <= 7.8e+58)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e+62], t$95$1, If[LessEqual[a, 7.8e+58], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85000000000000007e62 or 7.8000000000000002e58 < a

   1. Initial program 65.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 91.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 91.7%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{a - z}}{y - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 91.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y - z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   9. Simplified 81.0%

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

   if -1.85000000000000007e62 < a < 7.8000000000000002e58

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 73.8%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 73.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 80.2%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 80.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{z}\right)}, \mathsf{\_.f64}\left(t, x\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{\_.f64}\left(\color{blue}{t}, x\right)\right)\right) \]

   10. Simplified 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+58}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) a)))))
   (if (<= a -1.05e+64)
     t_1
     (if (<= a 1.15e+59) (+ t (* (/ y z) (- x t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / a));
	double tmp;
	if (a <= -1.05e+64) {
		tmp = t_1;
	} else if (a <= 1.15e+59) {
		tmp = t + ((y / z) * (x - 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) * ((t - x) / a))
    if (a <= (-1.05d+64)) then
        tmp = t_1
    else if (a <= 1.15d+59) then
        tmp = t + ((y / z) * (x - 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) * ((t - x) / a));
	double tmp;
	if (a <= -1.05e+64) {
		tmp = t_1;
	} else if (a <= 1.15e+59) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / a))
	tmp = 0
	if a <= -1.05e+64:
		tmp = t_1
	elif a <= 1.15e+59:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -1.05e+64)
		tmp = t_1;
	elseif (a <= 1.15e+59)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / a));
	tmp = 0.0;
	if (a <= -1.05e+64)
		tmp = t_1;
	elseif (a <= 1.15e+59)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+64], t$95$1, If[LessEqual[a, 1.15e+59], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05e64 or 1.15000000000000004e59 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{t - x}{a}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{t - x}}{a}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{a}\right)\right)\right) \]

      7. --lowering--.f64 77.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), a\right)\right)\right) \]

   5. Simplified 77.0%

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

   if -1.05e64 < a < 1.15000000000000004e59

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 73.8%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 73.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 80.2%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 80.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{z}\right)}, \mathsf{\_.f64}\left(t, x\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{\_.f64}\left(\color{blue}{t}, x\right)\right)\right) \]

   10. Simplified 78.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+64}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+67)
   (+ x (/ (- t x) (/ a y)))
   (if (<= a 3.7e+59) (+ t (* (/ y z) (- x t))) (+ x (* (- t x) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+67) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.7e+59) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.4d+67)) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 3.7d+59) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+67) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.7e+59) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+67:
		tmp = x + ((t - x) / (a / y))
	elif a <= 3.7e+59:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+67)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 3.7e+59)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.4e+67)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 3.7e+59)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+67], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+59], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4000000000000002e67

   1. Initial program 58.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 78.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{y}{a}\right), \color{blue}{x}\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{1}{\frac{a}{y}}\right), x\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t - x}{\frac{a}{y}}\right), x\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(\frac{a}{y}\right)\right), x\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{a}{y}\right)\right), x\right) \]

      7. /-lowering-/.f64 78.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(a, y\right)\right), x\right) \]

   9. Applied egg-rr 78.2%

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

   if -3.4000000000000002e67 < a < 3.69999999999999997e59

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 73.8%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 73.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - a}{z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{y - a}{z} \cdot \color{blue}{\left(t - x\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{y - a}{z}\right), \color{blue}{\left(t - x\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - a\right), z\right), \left(\color{blue}{t} - x\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \left(t - x\right)\right)\right) \]

      6. --lowering--.f64 80.2%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 80.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{z}\right)}, \mathsf{\_.f64}\left(t, x\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{\_.f64}\left(\color{blue}{t}, x\right)\right)\right) \]

   10. Simplified 78.3%

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

   if 3.69999999999999997e59 < a

   1. Initial program 71.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 68.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 68.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.7e-171) t_1 (if (<= t 1.9e-34) (* x (- 1.0 (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.7e-171) {
		tmp = t_1;
	} else if (t <= 1.9e-34) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-1.7d-171)) then
        tmp = t_1
    else if (t <= 1.9d-34) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.7e-171) {
		tmp = t_1;
	} else if (t <= 1.9e-34) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.7e-171:
		tmp = t_1
	elif t <= 1.9e-34:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.7e-171)
		tmp = t_1;
	elseif (t <= 1.9e-34)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.7e-171)
		tmp = t_1;
	elseif (t <= 1.9e-34)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-171], t$95$1, If[LessEqual[t, 1.9e-34], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.69999999999999993e-171 or 1.9000000000000001e-34 < t

   1. Initial program 62.6%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 50.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 50.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right) \]

      6. --lowering--.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right) \]

   7. Applied egg-rr 70.5%

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

   if -1.69999999999999993e-171 < t < 1.9000000000000001e-34

   1. Initial program 73.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 79.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 79.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 67.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 67.3%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - \frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 65.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 65.0%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+45) t (if (<= z 3.8e+100) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+45) {
		tmp = t;
	} else if (z <= 3.8e+100) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.3d+45)) then
        tmp = t
    else if (z <= 3.8d+100) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+45) {
		tmp = t;
	} else if (z <= 3.8e+100) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+45:
		tmp = t
	elif z <= 3.8e+100:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+45)
		tmp = t;
	elseif (z <= 3.8e+100)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+45)
		tmp = t;
	elseif (z <= 3.8e+100)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+45], t, If[LessEqual[z, 3.8e+100], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3000000000000001e45 or 3.79999999999999963e100 < z

   1. Initial program 37.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 55.0%

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

   if -3.3000000000000001e45 < z < 3.79999999999999963e100

   1. Initial program 86.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 94.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 71.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 71.8%

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

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(\frac{y}{a}\right)\right)\right) \]

      2. sub-neg N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - \frac{y}{a}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   10. Simplified 58.2%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.00043:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.4e+85) t (if (<= z 0.00043) (* t (/ y (- a z))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.4e+85) {
		tmp = t;
	} else if (z <= 0.00043) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.4d+85)) then
        tmp = t
    else if (z <= 0.00043d0) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.4e+85) {
		tmp = t;
	} else if (z <= 0.00043) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.4e+85:
		tmp = t
	elif z <= 0.00043:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.4e+85)
		tmp = t;
	elseif (z <= 0.00043)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.4e+85)
		tmp = t;
	elseif (z <= 0.00043)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.4e+85], t, If[LessEqual[z, 0.00043], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000004e85 or 4.29999999999999989e-4 < z

   1. Initial program 39.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 53.1%

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

   if -7.4000000000000004e85 < z < 4.29999999999999989e-4

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(y - z\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \left(a - z\right)\right) \]

      4. --lowering--.f64 39.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 39.5%

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

   6. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      4. --lowering--.f64 38.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 38.0%

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

Alternative 12: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.00106:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+60) t (if (<= z 0.00106) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+60) {
		tmp = t;
	} else if (z <= 0.00106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+60)) then
        tmp = t
    else if (z <= 0.00106d0) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+60) {
		tmp = t;
	} else if (z <= 0.00106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+60:
		tmp = t
	elif z <= 0.00106:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+60)
		tmp = t;
	elseif (z <= 0.00106)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+60)
		tmp = t;
	elseif (z <= 0.00106)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+60], t, If[LessEqual[z, 0.00106], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000013e60 or 0.00105999999999999996 < z

   1. Initial program 40.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 51.9%

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

   if -4.50000000000000013e60 < z < 0.00105999999999999996

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 33.5%

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

Alternative 13: 25.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.9%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 28.0%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 14: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 65.9%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

   7. --lowering--.f64 84.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

4. Applied egg-rr 84.0%

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

5. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)}\right) \]

   2. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

   3. unsub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

   7. --lowering--.f64 45.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

7. Simplified 45.0%

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

8. Taylor expanded in z around inf

   \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{1}\right)\right) \]
9. Step-by-step derivation

10. Simplified 2.8%

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

    1. metadata-eval N/A

       \[\leadsto x \cdot 0 \]

    2. mul0-rgt 2.8%

       \[\leadsto 0 \]

12. Applied egg-rr 2.8%

    \[\leadsto \color{blue}{0} \]
13. Add Preprocessing

Developer Target 1: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

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