Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3

Percentage Accurate: 97.9% → 100.0%

Time: 8.4s

Alternatives: 7

Speedup: 1.3×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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) + ((x - 1.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((x - 1.0d0) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y + z, -z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x (+ y z) (- z)))

C

double code(double x, double y, double z) {
	return fma(x, (y + z), -z);
}

Julia

function code(x, y, z)
	return fma(x, Float64(y + z), Float64(-z))
end

Wolfram

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

Derivation

1. Initial program 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.4%

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

   2. sub-neg 98.4%

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

   3. distribute-rgt-in 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. distribute-lft-out 100.0%

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

   8. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e+148)
   (* x z)
   (if (<= x -2.35e-27)
     (* x y)
     (if (<= x 6e-28) (- z) (if (<= x 9.2e+55) (* x y) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+148) {
		tmp = x * z;
	} else if (x <= -2.35e-27) {
		tmp = x * y;
	} else if (x <= 6e-28) {
		tmp = -z;
	} else if (x <= 9.2e+55) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	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 <= (-2.3d+148)) then
        tmp = x * z
    else if (x <= (-2.35d-27)) then
        tmp = x * y
    else if (x <= 6d-28) then
        tmp = -z
    else if (x <= 9.2d+55) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+148) {
		tmp = x * z;
	} else if (x <= -2.35e-27) {
		tmp = x * y;
	} else if (x <= 6e-28) {
		tmp = -z;
	} else if (x <= 9.2e+55) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e+148:
		tmp = x * z
	elif x <= -2.35e-27:
		tmp = x * y
	elif x <= 6e-28:
		tmp = -z
	elif x <= 9.2e+55:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e+148)
		tmp = Float64(x * z);
	elseif (x <= -2.35e-27)
		tmp = Float64(x * y);
	elseif (x <= 6e-28)
		tmp = Float64(-z);
	elseif (x <= 9.2e+55)
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.3e+148)
		tmp = x * z;
	elseif (x <= -2.35e-27)
		tmp = x * y;
	elseif (x <= 6e-28)
		tmp = -z;
	elseif (x <= 9.2e+55)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e+148], N[(x * z), $MachinePrecision], If[LessEqual[x, -2.35e-27], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-28], (-z), If[LessEqual[x, 9.2e+55], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3000000000000001e148 or 9.1999999999999995e55 < x

   1. Initial program 96.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. flip-+ 88.7%

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

      5. associate-*l/ 81.2%

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

   6. Applied egg-rr 81.2%

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

   7. Taylor expanded in z around inf 66.2%

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

      1. *-commutative 66.2%

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

   9. Simplified 66.2%

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

   if -2.3000000000000001e148 < x < -2.35000000000000016e-27 or 6.00000000000000005e-28 < x < 9.1999999999999995e55

   1. Initial program 98.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in y around inf 71.6%

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

   if -2.35000000000000016e-27 < x < 6.00000000000000005e-28

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around 0 74.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. mul-1-neg 74.5%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 74.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+148}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{-26} \lor \neg \left(x \leq 6 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.62e-26) (not (<= x 6e-28))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.62e-26) || !(x <= 6e-28)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	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 <= (-1.62d-26)) .or. (.not. (x <= 6d-28))) then
        tmp = x * (y + z)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.62e-26) || !(x <= 6e-28)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.62e-26) or not (x <= 6e-28):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.62e-26) || !(x <= 6e-28))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.62e-26) || ~((x <= 6e-28)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.62e-26], N[Not[LessEqual[x, 6e-28]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.62e-26 or 6.00000000000000005e-28 < x

   1. Initial program 97.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around inf 96.5%

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

      1. +-commutative 96.5%

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

   4. Simplified 96.5%

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

   if -1.62e-26 < x < 6.00000000000000005e-28

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around 0 74.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. mul-1-neg 74.5%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 74.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{-26} \lor \neg \left(x \leq 6 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \lor \neg \left(x \leq 7.5 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.3) (not (<= x 7.5e-20))) (* x (+ y z)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3) || !(x <= 7.5e-20)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) - z;
	}
	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 <= (-5.3d0)) .or. (.not. (x <= 7.5d-20))) then
        tmp = x * (y + z)
    else
        tmp = (x * y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3) || !(x <= 7.5e-20)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.3) or not (x <= 7.5e-20):
		tmp = x * (y + z)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.3) || !(x <= 7.5e-20))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(Float64(x * y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.3) || ~((x <= 7.5e-20)))
		tmp = x * (y + z);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.3], N[Not[LessEqual[x, 7.5e-20]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999982 or 7.49999999999999981e-20 < x

   1. Initial program 96.8%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around inf 99.1%

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

      1. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   if -5.29999999999999982 < x < 7.49999999999999981e-20

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

      6. associate-+r+ 100.0%

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

      7. unsub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

      1. +-commutative 100.0%

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

      2. flip-+ 58.3%

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

      3. associate-*r/ 58.1%

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

      4. difference-of-squares 58.3%

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

      5. sub-neg 58.3%

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

      6. add-sqr-sqrt 34.0%

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

      7. sqrt-unprod 57.9%

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

      8. sqr-neg 57.9%

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

      9. sqrt-unprod 23.9%

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

      10. add-sqr-sqrt 56.9%

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

      11. pow2 56.9%

          \[\leadsto \frac{x \cdot \color{blue}{{\left(y + z\right)}^{2}}}{y - z} - z \]

      12. sub-neg 56.9%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{\color{blue}{y + \left(-z\right)}} - z \]

      13. add-sqr-sqrt 33.0%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{y + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - z \]

      14. sqrt-unprod 56.7%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{y + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - z \]

      15. sqr-neg 56.7%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{y + \sqrt{\color{blue}{z \cdot z}}} - z \]

      16. sqrt-unprod 24.3%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{y + \color{blue}{\sqrt{z} \cdot \sqrt{z}}} - z \]

      17. add-sqr-sqrt 58.3%

          \[\leadsto \frac{x \cdot {\left(y + z\right)}^{2}}{y + \color{blue}{z}} - z \]

   5. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{\frac{x \cdot {\left(y + z\right)}^{2}}{y + z}} - z \]
   6. Step-by-step derivation

      1. associate-/l* 58.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y + z}{{\left(y + z\right)}^{2}}}} - z \]

      2. unpow2 58.5%

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

      3. associate-/r* 99.9%

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

      4. *-inverses 99.9%

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

      5. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \lor \neg \left(x \leq 7.5 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-28) (* x y) (if (<= x 5.8e-28) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-28) {
		tmp = x * y;
	} else if (x <= 5.8e-28) {
		tmp = -z;
	} else {
		tmp = 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 (x <= (-7.5d-28)) then
        tmp = x * y
    else if (x <= 5.8d-28) then
        tmp = -z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-28) {
		tmp = x * y;
	} else if (x <= 5.8e-28) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e-28:
		tmp = x * y
	elif x <= 5.8e-28:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-28)
		tmp = Float64(x * y);
	elseif (x <= 5.8e-28)
		tmp = Float64(-z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e-28)
		tmp = x * y;
	elseif (x <= 5.8e-28)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-28], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.8e-28], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000003e-28 or 5.80000000000000026e-28 < x

   1. Initial program 97.2%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in y around inf 52.5%

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

   if -7.5000000000000003e-28 < x < 5.80000000000000026e-28

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]

   2. Taylor expanded in x around 0 74.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. mul-1-neg 74.5%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 74.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-28}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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)) - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.4%

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

   2. sub-neg 98.4%

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

   3. distribute-rgt-in 98.4%

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

   4. metadata-eval 98.4%

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

   5. neg-mul-1 98.4%

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

   6. associate-+r+ 98.4%

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

   7. unsub-neg 98.4%

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

   8. +-commutative 98.4%

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

   9. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto x \cdot \left(y + z\right) - z \]

Alternative 7: 36.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 98.4%

   \[x \cdot y + \left(x - 1\right) \cdot z \]

2. Taylor expanded in x around 0 36.0%

   \[\leadsto \color{blue}{-1 \cdot z} \]
3. Step-by-step derivation

   1. mul-1-neg 36.0%

      \[\leadsto \color{blue}{-z} \]

4. Simplified 36.0%

   \[\leadsto \color{blue}{-z} \]

5. Final simplification 36.0%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))