Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.8% → 99.2%

Time: 8.9s

Alternatives: 12

Speedup: 1.0×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z x) y) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+307)))
     (+ x (* y (/ (- z x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+307)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+307)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) * y) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+307):
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) * y) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+307))
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) * y) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+307)))
		tmp = x + (y * ((z - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+307]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 9.99999999999999986e306 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 78.6%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 9.99999999999999986e306

   1. Initial program 98.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \leq -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \leq 10^{+307}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{t}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-207}:\\ \;\;\;\;-x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z y) t)))
   (if (<= z -1.25e-24)
     t_1
     (if (<= z -6.5e-202)
       x
       (if (<= z 4.2e-207) (- (* x (/ y t))) (if (<= z 1e+15) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (z <= -1.25e-24) {
		tmp = t_1;
	} else if (z <= -6.5e-202) {
		tmp = x;
	} else if (z <= 4.2e-207) {
		tmp = -(x * (y / t));
	} else if (z <= 1e+15) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	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 = (z * y) / t
    if (z <= (-1.25d-24)) then
        tmp = t_1
    else if (z <= (-6.5d-202)) then
        tmp = x
    else if (z <= 4.2d-207) then
        tmp = -(x * (y / t))
    else if (z <= 1d+15) then
        tmp = 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 t_1 = (z * y) / t;
	double tmp;
	if (z <= -1.25e-24) {
		tmp = t_1;
	} else if (z <= -6.5e-202) {
		tmp = x;
	} else if (z <= 4.2e-207) {
		tmp = -(x * (y / t));
	} else if (z <= 1e+15) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) / t
	tmp = 0
	if z <= -1.25e-24:
		tmp = t_1
	elif z <= -6.5e-202:
		tmp = x
	elif z <= 4.2e-207:
		tmp = -(x * (y / t))
	elif z <= 1e+15:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) / t)
	tmp = 0.0
	if (z <= -1.25e-24)
		tmp = t_1;
	elseif (z <= -6.5e-202)
		tmp = x;
	elseif (z <= 4.2e-207)
		tmp = Float64(-Float64(x * Float64(y / t)));
	elseif (z <= 1e+15)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) / t;
	tmp = 0.0;
	if (z <= -1.25e-24)
		tmp = t_1;
	elseif (z <= -6.5e-202)
		tmp = x;
	elseif (z <= 4.2e-207)
		tmp = -(x * (y / t));
	elseif (z <= 1e+15)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.25e-24], t$95$1, If[LessEqual[z, -6.5e-202], x, If[LessEqual[z, 4.2e-207], (-N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 1e+15], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e-24 or 1e15 < z

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-/l* 86.5%

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

      3. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around -inf 70.8%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -1.24999999999999995e-24 < z < -6.49999999999999956e-202 or 4.20000000000000007e-207 < z < 1e15

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-/l* 93.6%

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

      3. fma-define 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around 0 62.1%

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

   if -6.49999999999999956e-202 < z < 4.20000000000000007e-207

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around -inf 63.0%

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

   6. Taylor expanded in z around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

      4. mul-1-neg 71.5%

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

      5. associate-*r/ 71.5%

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

      6. mul-1-neg 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-207}:\\ \;\;\;\;-x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-201} \lor \neg \left(y \leq 5.5 \cdot 10^{-21}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e-201) (not (<= y 5.5e-21)))
   (+ x (* y (/ (- z x) t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-201) || !(y <= 5.5e-21)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = x + (z * (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 ((y <= (-1d-201)) .or. (.not. (y <= 5.5d-21))) then
        tmp = x + (y * ((z - x) / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-201) || !(y <= 5.5e-21)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e-201) or not (y <= 5.5e-21):
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e-201) || !(y <= 5.5e-21))
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e-201) || ~((y <= 5.5e-21)))
		tmp = x + (y * ((z - x) / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e-201], N[Not[LessEqual[y, 5.5e-21]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999946e-202 or 5.49999999999999977e-21 < y

   1. Initial program 89.5%

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

      1. associate-/l* 97.0%

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

      2. *-commutative 97.0%

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

   4. Applied egg-rr 97.0%

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

   if -9.99999999999999946e-202 < y < 5.49999999999999977e-21

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-/l* 78.9%

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

      3. fma-define 78.9%

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

   3. Simplified 78.9%

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

      1. fma-undefine 78.9%

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

      2. associate-/l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 92.5%

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

      1. associate-*l/ 93.5%

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

      2. *-commutative 93.5%

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

   9. Simplified 93.5%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-201} \lor \neg \left(y \leq 5.5 \cdot 10^{-21}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-33} \lor \neg \left(z \leq 2.4 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-33) (not (<= z 2.4e-14)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-33) || !(z <= 2.4e-14)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (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 <= (-9.2d-33)) .or. (.not. (z <= 2.4d-14))) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (1.0d0 - (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 <= -9.2e-33) || !(z <= 2.4e-14)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-33) or not (z <= 2.4e-14):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-33) || !(z <= 2.4e-14))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e-33) || ~((z <= 2.4e-14)))
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-33], N[Not[LessEqual[z, 2.4e-14]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999942e-33 or 2.4e-14 < z

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-/l* 86.9%

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

      3. fma-define 86.9%

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

   3. Simplified 86.9%

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

      1. fma-undefine 86.9%

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

      2. associate-/l* 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-/l* 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in z around inf 84.8%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

   9. Simplified 87.9%

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

   if -9.19999999999999942e-33 < z < 2.4e-14

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-/l* 94.7%

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

      3. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 86.9%

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

      1. *-rgt-identity 86.9%

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

      2. mul-1-neg 86.9%

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

      3. associate-/l* 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

      5. mul-1-neg 91.8%

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

      6. distribute-lft-in 91.8%

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

      7. mul-1-neg 91.8%

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

      8. unsub-neg 91.8%

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

   7. Simplified 91.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-33} \lor \neg \left(z \leq 2.4 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-33} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e-33) (not (<= z 3.9e-14)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e-33) || !(z <= 3.9e-14)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (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 <= (-7.6d-33)) .or. (.not. (z <= 3.9d-14))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (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 <= -7.6e-33) || !(z <= 3.9e-14)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e-33) or not (z <= 3.9e-14):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e-33) || !(z <= 3.9e-14))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e-33) || ~((z <= 3.9e-14)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e-33], N[Not[LessEqual[z, 3.9e-14]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.59999999999999988e-33 or 3.8999999999999998e-14 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate-/l* 79.1%

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

   5. Simplified 79.1%

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

   if -7.59999999999999988e-33 < z < 3.8999999999999998e-14

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-/l* 94.7%

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

      3. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 86.9%

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

      1. *-rgt-identity 86.9%

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

      2. mul-1-neg 86.9%

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

      3. associate-/l* 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

      5. mul-1-neg 91.8%

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

      6. distribute-lft-in 91.8%

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

      7. mul-1-neg 91.8%

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

      8. unsub-neg 91.8%

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

   7. Simplified 91.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-33} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-24} \lor \neg \left(z \leq 2.3 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e-24) (not (<= z 2.3e+30)))
   (* y (/ (- z x) t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e-24) || !(z <= 2.3e+30)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (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 <= (-1.5d-24)) .or. (.not. (z <= 2.3d+30))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x * (1.0d0 - (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 <= -1.5e-24) || !(z <= 2.3e+30)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e-24) or not (z <= 2.3e+30):
		tmp = y * ((z - x) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e-24) || !(z <= 2.3e+30))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5e-24) || ~((z <= 2.3e+30)))
		tmp = y * ((z - x) / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e-24], N[Not[LessEqual[z, 2.3e+30]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999998e-24 or 2.3e30 < z

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-/l* 86.5%

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

      3. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around -inf 70.8%

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

      1. associate-/l* 86.5%

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

      2. *-commutative 86.5%

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

   7. Applied egg-rr 66.2%

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

   if -1.49999999999999998e-24 < z < 2.3e30

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around 0 84.9%

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

      1. *-rgt-identity 84.9%

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

      2. mul-1-neg 84.9%

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

      3. associate-/l* 89.1%

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

      4. distribute-rgt-neg-in 89.1%

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

      5. mul-1-neg 89.1%

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

      6. distribute-lft-in 89.1%

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

      7. mul-1-neg 89.1%

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

      8. unsub-neg 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-24} \lor \neg \left(z \leq 2.3 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+115} \lor \neg \left(z \leq 6 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e+115) (not (<= z 6e+26)))
   (/ (* z y) t)
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e+115) || !(z <= 6e+26)) {
		tmp = (z * y) / t;
	} else {
		tmp = x * (1.0 - (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 <= (-9d+115)) .or. (.not. (z <= 6d+26))) then
        tmp = (z * y) / t
    else
        tmp = x * (1.0d0 - (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 <= -9e+115) || !(z <= 6e+26)) {
		tmp = (z * y) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e+115) or not (z <= 6e+26):
		tmp = (z * y) / t
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e+115) || !(z <= 6e+26))
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e+115) || ~((z <= 6e+26)))
		tmp = (z * y) / t;
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e+115], N[Not[LessEqual[z, 6e+26]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999927e115 or 5.99999999999999994e26 < z

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-/l* 85.1%

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

      3. fma-define 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in y around -inf 72.9%

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

   6. Taylor expanded in z around inf 66.8%

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

   if -8.99999999999999927e115 < z < 5.99999999999999994e26

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 77.7%

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

      1. *-rgt-identity 77.7%

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

      2. mul-1-neg 77.7%

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

      3. associate-/l* 82.2%

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

      4. distribute-rgt-neg-in 82.2%

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

      5. mul-1-neg 82.2%

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

      6. distribute-lft-in 82.2%

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

      7. mul-1-neg 82.2%

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

      8. unsub-neg 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+115} \lor \neg \left(z \leq 6 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.7e-33)
   (+ x (* z (/ y t)))
   (if (<= z 4.5e-14) (* x (- 1.0 (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e-33) {
		tmp = x + (z * (y / t));
	} else if (z <= 4.5e-14) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	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 <= (-5.7d-33)) then
        tmp = x + (z * (y / t))
    else if (z <= 4.5d-14) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e-33) {
		tmp = x + (z * (y / t));
	} else if (z <= 4.5e-14) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.7e-33:
		tmp = x + (z * (y / t))
	elif z <= 4.5e-14:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.7e-33)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (z <= 4.5e-14)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.7e-33)
		tmp = x + (z * (y / t));
	elseif (z <= 4.5e-14)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.7e-33], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-14], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.70000000000000025e-33

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-/l* 90.3%

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

      3. fma-define 90.3%

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

   3. Simplified 90.3%

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

      1. fma-undefine 90.3%

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

      2. associate-/l* 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-/l* 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in z around inf 85.1%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

   9. Simplified 87.5%

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

   if -5.70000000000000025e-33 < z < 4.4999999999999998e-14

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-/l* 94.7%

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

      3. fma-define 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 86.9%

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

      1. *-rgt-identity 86.9%

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

      2. mul-1-neg 86.9%

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

      3. associate-/l* 91.8%

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

      4. distribute-rgt-neg-in 91.8%

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

      5. mul-1-neg 91.8%

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

      6. distribute-lft-in 91.8%

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

      7. mul-1-neg 91.8%

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

      8. unsub-neg 91.8%

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

   7. Simplified 91.8%

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

   if 4.4999999999999998e-14 < z

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/l* 83.9%

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

      3. fma-define 83.9%

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

   3. Simplified 83.9%

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

      1. fma-undefine 83.9%

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

      2. associate-/l* 92.6%

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

      3. *-commutative 92.6%

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

      4. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

   9. Simplified 88.2%

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

       1. clear-num 88.2%

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

       2. un-div-inv 88.2%

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

   11. Applied egg-rr 88.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-24) (not (<= z 3.2e+20))) (/ (* z y) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-24) || !(z <= 3.2e+20)) {
		tmp = (z * y) / t;
	} else {
		tmp = 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-24)) .or. (.not. (z <= 3.2d+20))) then
        tmp = (z * y) / t
    else
        tmp = 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-24) || !(z <= 3.2e+20)) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-24) or not (z <= 3.2e+20):
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-24) || !(z <= 3.2e+20))
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-24) || ~((z <= 3.2e+20)))
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-24], N[Not[LessEqual[z, 3.2e+20]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999992e-24 or 3.2e20 < z

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-/l* 86.5%

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

      3. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around -inf 70.8%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -1.64999999999999992e-24 < z < 3.2e20

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 51.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-25} \lor \neg \left(z \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e-25) (not (<= z 1.95e+17))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-25) || !(z <= 1.95e+17)) {
		tmp = y * (z / t);
	} else {
		tmp = 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 <= (-8.5d-25)) .or. (.not. (z <= 1.95d+17))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-25) || !(z <= 1.95e+17)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e-25) or not (z <= 1.95e+17):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e-25) || !(z <= 1.95e+17))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e-25) || ~((z <= 1.95e+17)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e-25], N[Not[LessEqual[z, 1.95e+17]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999981e-25 or 1.95e17 < z

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-/l* 86.5%

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

      3. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around -inf 70.8%

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

   6. Taylor expanded in z around inf 62.6%

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

      1. associate-/l* 77.6%

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

   8. Simplified 56.6%

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

   if -8.49999999999999981e-25 < z < 1.95e17

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 51.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-25} \lor \neg \left(z \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) * (y / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.6%

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

   1. +-commutative 92.6%

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

   2. associate-/l* 90.3%

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

   3. fma-define 90.3%

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

3. Simplified 90.3%

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

   1. fma-undefine 90.3%

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

   2. associate-/l* 92.6%

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

   3. *-commutative 92.6%

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

   4. associate-/l* 97.9%

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

6. Applied egg-rr 97.9%

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

7. Final simplification 97.9%

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

Alternative 12: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.6%

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

   1. +-commutative 92.6%

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

   2. associate-/l* 90.3%

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

   3. fma-define 90.3%

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

3. Simplified 90.3%

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

5. Taylor expanded in y around 0 38.1%

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

Developer target: 91.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 - ((x * (y / t)) + (-z * (y / t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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