Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 83.9% → 98.3%

Time: 8.8s

Alternatives: 12

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 83.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+281)))
     (* (/ x (- t z)) (- y z))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+281)) {
		tmp = (x / (t - z)) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+281)) {
		tmp = (x / (t - z)) * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+281):
		tmp = (x / (t - z)) * (y - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+281))
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+281)))
		tmp = (x / (t - z)) * (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+281]], $MachinePrecision]], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -inf.0 or 2.0000000000000001e281 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 41.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2.0000000000000001e281

   1. Initial program 97.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -\infty \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \left({\left(t - z\right)}^{-1} \cdot \left(y - z\right)\right) \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (* (pow (- t z) -1.0) (- y z)) x))

C

double code(double x, double y, double z, double t) {
	return (pow((t - z), -1.0) * (y - z)) * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((t - z) ** (-1.0d0)) * (y - z)) * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return (Math.pow((t - z), -1.0) * (y - z)) * x;
}

Python

def code(x, y, z, t):
	return (math.pow((t - z), -1.0) * (y - z)) * x

Julia

function code(x, y, z, t)
	return Float64(Float64((Float64(t - z) ^ -1.0) * Float64(y - z)) * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((t - z) ^ -1.0) * (y - z)) * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Power[N[(t - z), $MachinePrecision], -1.0], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lower-/.f64 81.3

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

4. Applied rewrites 81.3%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*l/ N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. flip-- N/A

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

   8. difference-of-squares-rev N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-+.f64 N/A

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

   13. associate-/r/ N/A

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

   14. associate-*l/ N/A

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

   15. *-commutative N/A

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

   16. associate-*l/ N/A

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

   17. lift-*.f64 N/A

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

   18. associate-*r* N/A

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

   19. lower-*.f64 N/A

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

6. Applied rewrites 97.6%

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

7. Final simplification 97.6%

   \[\leadsto \left({\left(t - z\right)}^{-1} \cdot \left(y - z\right)\right) \cdot x \]
8. Add Preprocessing

Alternative 3: 56.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{-321}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (<= t_1 -1e+185)
     (* (/ x (- t z)) y)
     (if (<= t_1 1e-321) (/ (* (- y z) x) t) (- x (/ (* y x) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -1e+185) {
		tmp = (x / (t - z)) * y;
	} else if (t_1 <= 1e-321) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y - z)) / (t - z)
    if (t_1 <= (-1d+185)) then
        tmp = (x / (t - z)) * y
    else if (t_1 <= 1d-321) then
        tmp = ((y - z) * x) / t
    else
        tmp = x - ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -1e+185) {
		tmp = (x / (t - z)) * y;
	} else if (t_1 <= 1e-321) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -1e+185:
		tmp = (x / (t - z)) * y
	elif t_1 <= 1e-321:
		tmp = ((y - z) * x) / t
	else:
		tmp = x - ((y * x) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -1e+185)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (t_1 <= 1e-321)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	else
		tmp = Float64(x - Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -1e+185)
		tmp = (x / (t - z)) * y;
	elseif (t_1 <= 1e-321)
		tmp = ((y - z) * x) / t;
	else
		tmp = x - ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+185], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e-321], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -9.9999999999999998e184

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -9.9999999999999998e184 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 9.98013e-322

   1. Initial program 96.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.5

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

   4. Applied rewrites 80.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 58.9

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

   7. Applied rewrites 58.9%

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

   if 9.98013e-322 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 81.9%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 65.2

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

   5. Applied rewrites 65.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 60.3%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -1 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 10^{-321}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+171} \lor \neg \left(z \leq 1.25 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t - y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e+171) (not (<= z 1.25e+172)))
   (fma x (/ (- t y) z) x)
   (* (/ x (- t z)) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+171) || !(z <= 1.25e+172)) {
		tmp = fma(x, ((t - y) / z), x);
	} else {
		tmp = (x / (t - z)) * (y - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e+171) || !(z <= 1.25e+172))
		tmp = fma(x, Float64(Float64(t - y) / z), x);
	else
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(y - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e+171], N[Not[LessEqual[z, 1.25e+172]], $MachinePrecision]], N[(x * N[(N[(t - y), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000004e171 or 1.25e172 < z

   1. Initial program 71.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 50.8

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

   4. Applied rewrites 50.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. difference-of-squares-rev N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. associate-/r/ N/A

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

      14. associate-*l/ N/A

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

      15. lift-*.f64 N/A

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

      16. times-frac N/A

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

      17. *-commutative N/A

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

      18. associate-*r/ N/A

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

      19. lower-/.f64 N/A

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

   6. Applied rewrites 71.8%

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

   7. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-commutative N/A

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

      6. mul-1-neg N/A

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

      7. distribute-rgt-in N/A

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

      8. +-commutative N/A

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

   9. Applied rewrites 90.9%

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

   if -7.6000000000000004e171 < z < 1.25e172

   1. Initial program 89.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.5

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

   4. Applied rewrites 91.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+171} \lor \neg \left(z \leq 1.25 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t - y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+27} \lor \neg \left(y \leq 1.6 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{y}{t - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e+27) (not (<= y 1.6e+21)))
   (* (/ y (- t z)) x)
   (* (/ z (- t z)) (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e+27) || !(y <= 1.6e+21)) {
		tmp = (y / (t - z)) * x;
	} else {
		tmp = (z / (t - z)) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d+27)) .or. (.not. (y <= 1.6d+21))) then
        tmp = (y / (t - z)) * x
    else
        tmp = (z / (t - z)) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e+27) || !(y <= 1.6e+21)) {
		tmp = (y / (t - z)) * x;
	} else {
		tmp = (z / (t - z)) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e+27) or not (y <= 1.6e+21):
		tmp = (y / (t - z)) * x
	else:
		tmp = (z / (t - z)) * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e+27) || !(y <= 1.6e+21))
		tmp = Float64(Float64(y / Float64(t - z)) * x);
	else
		tmp = Float64(Float64(z / Float64(t - z)) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e+27) || ~((y <= 1.6e+21)))
		tmp = (y / (t - z)) * x;
	else
		tmp = (z / (t - z)) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e+27], N[Not[LessEqual[y, 1.6e+21]], $MachinePrecision]], N[(N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(z / N[(t - z), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e27 or 1.6e21 < y

   1. Initial program 82.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 82.2

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

   4. Applied rewrites 82.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. difference-of-squares-rev N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. associate-/r/ N/A

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

      14. associate-*l/ N/A

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

      15. *-commutative N/A

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

      16. associate-*l/ N/A

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

      17. lift-*.f64 N/A

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

      18. associate-*r* N/A

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

      19. lower-*.f64 N/A

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

   6. Applied rewrites 96.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 74.7

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

   9. Applied rewrites 74.7%

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

   if -4.4999999999999999e27 < y < 1.6e21

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 86.0

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

   5. Applied rewrites 86.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+27} \lor \neg \left(y \leq 1.6 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{y}{t - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t - y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e-28)
   (* (/ (- z y) z) x)
   (if (<= z 2.85e+24) (* (/ (- y z) t) x) (fma x (/ (- t y) z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e-28) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 2.85e+24) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = fma(x, ((t - y) / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e-28)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 2.85e+24)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = fma(x, Float64(Float64(t - y) / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e-28], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 2.85e+24], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(N[(t - y), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e-28

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.4

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

   5. Applied rewrites 79.4%

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

   if -1.6500000000000001e-28 < z < 2.8500000000000002e24

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if 2.8500000000000002e24 < z

   1. Initial program 75.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 74.4

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

   4. Applied rewrites 74.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. difference-of-squares-rev N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-+.f64 N/A

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

      13. associate-/r/ N/A

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

      14. associate-*l/ N/A

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

      15. lift-*.f64 N/A

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

      16. times-frac N/A

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

      17. *-commutative N/A

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

      18. associate-*r/ N/A

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

      19. lower-/.f64 N/A

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

   6. Applied rewrites 75.9%

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

   7. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-commutative N/A

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

      6. mul-1-neg N/A

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

      7. distribute-rgt-in N/A

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

      8. +-commutative N/A

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

   9. Applied rewrites 76.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+24}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t - y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-28} \lor \neg \left(z \leq 2.85 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-28) (not (<= z 2.85e+24)))
   (* (/ (- z y) z) x)
   (* (/ (- y z) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-28) || !(z <= 2.85e+24)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = ((y - z) / t) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d-28)) .or. (.not. (z <= 2.85d+24))) then
        tmp = ((z - y) / z) * x
    else
        tmp = ((y - z) / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-28) || !(z <= 2.85e+24)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = ((y - z) / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-28) or not (z <= 2.85e+24):
		tmp = ((z - y) / z) * x
	else:
		tmp = ((y - z) / t) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-28) || !(z <= 2.85e+24))
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	else
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-28) || ~((z <= 2.85e+24)))
		tmp = ((z - y) / z) * x;
	else
		tmp = ((y - z) / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-28], N[Not[LessEqual[z, 2.85e+24]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6500000000000001e-28 or 2.8500000000000002e24 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1.6500000000000001e-28 < z < 2.8500000000000002e24

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-28} \lor \neg \left(z \leq 2.85 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+23} \lor \neg \left(t \leq 1.52\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e+23) (not (<= t 1.52)))
   (* (/ (- y z) t) x)
   (- x (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e+23) || !(t <= 1.52)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.1d+23)) .or. (.not. (t <= 1.52d0))) then
        tmp = ((y - z) / t) * x
    else
        tmp = x - ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e+23) || !(t <= 1.52)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e+23) or not (t <= 1.52):
		tmp = ((y - z) / t) * x
	else:
		tmp = x - ((y * x) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e+23) || !(t <= 1.52))
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = Float64(x - Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e+23) || ~((t <= 1.52)))
		tmp = ((y - z) / t) * x;
	else
		tmp = x - ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e+23], N[Not[LessEqual[t, 1.52]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.09999999999999996e23 or 1.52 < t

   1. Initial program 83.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if -4.09999999999999996e23 < t < 1.52

   1. Initial program 85.7%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+23} \lor \neg \left(t \leq 1.52\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-28} \lor \neg \left(z \leq 2.85 \cdot 10^{+24}\right):\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-28) (not (<= z 2.85e+24)))
   (- x (/ (* y x) z))
   (/ (* (- y z) x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-28) || !(z <= 2.85e+24)) {
		tmp = x - ((y * x) / z);
	} else {
		tmp = ((y - z) * x) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.45d-28)) .or. (.not. (z <= 2.85d+24))) then
        tmp = x - ((y * x) / z)
    else
        tmp = ((y - z) * x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-28) || !(z <= 2.85e+24)) {
		tmp = x - ((y * x) / z);
	} else {
		tmp = ((y - z) * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-28) or not (z <= 2.85e+24):
		tmp = x - ((y * x) / z)
	else:
		tmp = ((y - z) * x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-28) || !(z <= 2.85e+24))
		tmp = Float64(x - Float64(Float64(y * x) / z));
	else
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-28) || ~((z <= 2.85e+24)))
		tmp = x - ((y * x) / z);
	else
		tmp = ((y - z) * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-28], N[Not[LessEqual[z, 2.85e+24]], $MachinePrecision]], N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000006e-28 or 2.8500000000000002e24 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.4%

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

   if -1.45000000000000006e-28 < z < 2.8500000000000002e24

   1. Initial program 91.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.7

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

   4. Applied rewrites 91.7%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 74.2

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

   7. Applied rewrites 74.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-28} \lor \neg \left(z \leq 2.85 \cdot 10^{+24}\right):\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-28} \lor \neg \left(z \leq 3.5 \cdot 10^{+24}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-28) (not (<= z 3.5e+24))) (* 1.0 x) (/ (* (- y z) x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-28) || !(z <= 3.5e+24)) {
		tmp = 1.0 * x;
	} else {
		tmp = ((y - z) * x) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d-28)) .or. (.not. (z <= 3.5d+24))) then
        tmp = 1.0d0 * x
    else
        tmp = ((y - z) * x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-28) || !(z <= 3.5e+24)) {
		tmp = 1.0 * x;
	} else {
		tmp = ((y - z) * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-28) or not (z <= 3.5e+24):
		tmp = 1.0 * x
	else:
		tmp = ((y - z) * x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-28) || !(z <= 3.5e+24))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-28) || ~((z <= 3.5e+24)))
		tmp = 1.0 * x;
	else
		tmp = ((y - z) * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-28], N[Not[LessEqual[z, 3.5e+24]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-28 or 3.5000000000000002e24 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 63.9%

      \[\leadsto 1 \cdot x \]

   if -1.7e-28 < z < 3.5000000000000002e24

   1. Initial program 91.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.7

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

   4. Applied rewrites 91.7%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 74.2

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

   7. Applied rewrites 74.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-28} \lor \neg \left(z \leq 3.5 \cdot 10^{+24}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-35} \lor \neg \left(z \leq 4.4 \cdot 10^{+80}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-35) (not (<= z 4.4e+80))) (* 1.0 x) (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-35) || !(z <= 4.4e+80)) {
		tmp = 1.0 * x;
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.45d-35)) .or. (.not. (z <= 4.4d+80))) then
        tmp = 1.0d0 * x
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-35) || !(z <= 4.4e+80)) {
		tmp = 1.0 * x;
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-35) or not (z <= 4.4e+80):
		tmp = 1.0 * x
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-35) || !(z <= 4.4e+80))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-35) || ~((z <= 4.4e+80)))
		tmp = 1.0 * x;
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-35], N[Not[LessEqual[z, 4.4e+80]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e-35 or 4.40000000000000005e80 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. *-lft-identity N/A

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

      9. metadata-eval N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

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

      16. metadata-eval N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 65.8%

      \[\leadsto 1 \cdot x \]

   if -1.4500000000000001e-35 < z < 4.40000000000000005e80

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.5

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

   5. Applied rewrites 61.5%

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

   7. Applied rewrites 66.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-35} \lor \neg \left(z \leq 4.4 \cdot 10^{+80}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 84.7%

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

3. Taylor expanded in t around 0

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

   1. mul-1-neg N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. distribute-lft-neg-in N/A

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

   5. lower-*.f64 N/A

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

   6. distribute-neg-frac N/A

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

   7. lower-/.f64 N/A

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

   8. *-lft-identity N/A

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

   9. metadata-eval N/A

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

   10. fp-cancel-sign-sub-inv N/A

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

   11. +-commutative N/A

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

   12. distribute-neg-in N/A

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

   13. mul-1-neg N/A

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

   14. remove-double-neg N/A

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

   15. mul-1-neg N/A

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

   16. metadata-eval N/A

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

   17. fp-cancel-sub-sign-inv N/A

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

   18. *-lft-identity N/A

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

   19. lower--.f64 52.0

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

5. Applied rewrites 52.0%

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

6. Taylor expanded in y around 0

   \[\leadsto 1 \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 37.5%

   \[\leadsto 1 \cdot x \]
9. Add Preprocessing

Developer Target 1: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

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