Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.9% → 95.8%

Time: 5.9s

Alternatives: 7

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-298}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, -x, x\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-298)
   (fma (/ z y) (- x) x)
   (if (<= y 5e-55) (/ (* x (- y z)) y) (* (/ (- y z) y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-298) {
		tmp = fma((z / y), -x, x);
	} else if (y <= 5e-55) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = ((y - z) / y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-298)
		tmp = fma(Float64(z / y), Float64(-x), x);
	elseif (y <= 5e-55)
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	else
		tmp = Float64(Float64(Float64(y - z) / y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e-298], N[(N[(z / y), $MachinePrecision] * (-x) + x), $MachinePrecision], If[LessEqual[y, 5e-55], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999912e-299

   1. Initial program 80.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.1

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

   4. Applied rewrites 99.1%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. lift-neg.f64 N/A

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

      8. distribute-rgt-in N/A

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

      9. lift-/.f64 N/A

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

      10. clear-num N/A

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

      11. associate-/r/ N/A

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

      12. associate-*r* N/A

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

      13. div-inv N/A

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

      14. *-inverses N/A

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

      15. *-lft-identity N/A

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

      16. +-commutative N/A

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

      17. lift-neg.f64 N/A

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

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

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

      19. distribute-rgt-neg-out N/A

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

      20. lift-/.f64 N/A

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

      21. distribute-frac-neg N/A

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

      22. lift-neg.f64 N/A

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

      23. lift-/.f64 N/A

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

   6. Applied rewrites 99.2%

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

   if -9.99999999999999912e-299 < y < 5.0000000000000002e-55

   1. Initial program 98.3%

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

   if 5.0000000000000002e-55 < y

   1. Initial program 86.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

Alternative 2: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 2 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (or (<= t_0 0.0) (not (<= t_0 2e-102))) (* (/ x y) (- y z)) (/ x 1.0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e-102)) {
		tmp = (x / y) * (y - z);
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d-102))) then
        tmp = (x / y) * (y - z)
    else
        tmp = x / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e-102)) {
		tmp = (x / y) * (y - z);
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 2e-102):
		tmp = (x / y) * (y - z)
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 2e-102))
		tmp = Float64(Float64(x / y) * Float64(y - z));
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 2e-102)))
		tmp = (x / y) * (y - z);
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e-102]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0 or 1.99999999999999987e-102 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 92.9

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

   4. Applied rewrites 92.9%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 1.99999999999999987e-102

   1. Initial program 99.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 90.7%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0 \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 2 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (or (<= t_0 0.0) (not (<= t_0 2e+287))) (* (/ z y) (- x)) (/ x 1.0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+287)) {
		tmp = (z / y) * -x;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d+287))) then
        tmp = (z / y) * -x
    else
        tmp = x / 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+287)) {
		tmp = (z / y) * -x;
	} else {
		tmp = x / 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 2e+287):
		tmp = (z / y) * -x
	else:
		tmp = x / 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 2e+287))
		tmp = Float64(Float64(z / y) * Float64(-x));
	else
		tmp = Float64(x / 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 2e+287)))
		tmp = (z / y) * -x;
	else
		tmp = x / 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e+287]], $MachinePrecision]], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], N[(x / 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0 or 2.0000000000000002e287 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 79.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 61.3

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

   5. Applied rewrites 61.3%

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

   7. Applied rewrites 60.3%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2.0000000000000002e287

   1. Initial program 99.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 71.6%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 0 \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- y z)) y)))
   (if (<= t_0 0.0)
     (* (/ (- x) y) z)
     (if (<= t_0 2e+287) (/ x 1.0) (* (/ z y) (- x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (-x / y) * z;
	} else if (t_0 <= 2e+287) {
		tmp = x / 1.0;
	} else {
		tmp = (z / y) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y - z)) / y
    if (t_0 <= 0.0d0) then
        tmp = (-x / y) * z
    else if (t_0 <= 2d+287) then
        tmp = x / 1.0d0
    else
        tmp = (z / y) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * (y - z)) / y;
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (-x / y) * z;
	} else if (t_0 <= 2e+287) {
		tmp = x / 1.0;
	} else {
		tmp = (z / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * (y - z)) / y
	tmp = 0
	if t_0 <= 0.0:
		tmp = (-x / y) * z
	elif t_0 <= 2e+287:
		tmp = x / 1.0
	else:
		tmp = (z / y) * -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y - z)) / y)
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(-x) / y) * z);
	elseif (t_0 <= 2e+287)
		tmp = Float64(x / 1.0);
	else
		tmp = Float64(Float64(z / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * (y - z)) / y;
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = (-x / y) * z;
	elseif (t_0 <= 2e+287)
		tmp = x / 1.0;
	else
		tmp = (z / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[((-x) / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$0, 2e+287], N[(x / 1.0), $MachinePrecision], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -0.0

   1. Initial program 81.6%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 54.3

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

   5. Applied rewrites 54.3%

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < 2.0000000000000002e287

   1. Initial program 99.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 71.6%

      \[\leadsto \frac{x}{\color{blue}{1}} \]

   if 2.0000000000000002e287 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 78.4

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

   5. Applied rewrites 78.4%

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

   7. Applied rewrites 76.8%

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

Alternative 5: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1 \cdot 10^{+118}:\\ \;\;\;\;\frac{-x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) -1e+118) (* (/ (- x) y) z) (* (/ (- y z) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= -1e+118) {
		tmp = (-x / y) * z;
	} else {
		tmp = ((y - z) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((x * (y - z)) / y) <= (-1d+118)) then
        tmp = (-x / y) * z
    else
        tmp = ((y - z) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= -1e+118) {
		tmp = (-x / y) * z;
	} else {
		tmp = ((y - z) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y - z)) / y) <= -1e+118:
		tmp = (-x / y) * z
	else:
		tmp = ((y - z) / y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y - z)) / y) <= -1e+118)
		tmp = Float64(Float64(Float64(-x) / y) * z);
	else
		tmp = Float64(Float64(Float64(y - z) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * (y - z)) / y) <= -1e+118)
		tmp = (-x / y) * z;
	else
		tmp = ((y - z) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], -1e+118], N[(N[((-x) / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -9.99999999999999967e117

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 67.6

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

   5. Applied rewrites 67.6%

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

   if -9.99999999999999967e117 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 88.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 96.0

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

   4. Applied rewrites 96.0%

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

Alternative 6: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-298} \lor \neg \left(y \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-298) (not (<= y 5e-55)))
   (* (/ (- y z) y) x)
   (/ (* x (- y z)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-298) || !(y <= 5e-55)) {
		tmp = ((y - z) / y) * x;
	} else {
		tmp = (x * (y - z)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1d-298)) .or. (.not. (y <= 5d-55))) then
        tmp = ((y - z) / y) * x
    else
        tmp = (x * (y - z)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-298) || !(y <= 5e-55)) {
		tmp = ((y - z) / y) * x;
	} else {
		tmp = (x * (y - z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-298) or not (y <= 5e-55):
		tmp = ((y - z) / y) * x
	else:
		tmp = (x * (y - z)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-298) || !(y <= 5e-55))
		tmp = Float64(Float64(Float64(y - z) / y) * x);
	else
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e-298) || ~((y <= 5e-55)))
		tmp = ((y - z) / y) * x;
	else
		tmp = (x * (y - z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-298], N[Not[LessEqual[y, 5e-55]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999912e-299 or 5.0000000000000002e-55 < y

   1. Initial program 82.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

   if -9.99999999999999912e-299 < y < 5.0000000000000002e-55

   1. Initial program 98.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-298} \lor \neg \left(y \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{y - z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ x 1.0))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x / 1.0

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 95.8

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

4. Applied rewrites 95.8%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 50.1%

   \[\leadsto \frac{x}{\color{blue}{1}} \]
8. Add Preprocessing

Developer Target 1: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024307 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

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