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

Percentage Accurate: 98.0% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.3×

• 21.0% 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: 98.0% 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 97.6%

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

   1. *-commutative 97.6%

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

   2. sub-neg 97.6%

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

   3. distribute-rgt-in 97.7%

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

   4. associate-+r+ 97.7%

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

   5. distribute-lft-out 100.0%

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

   6. fma-def 100.0%

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

   7. metadata-eval 100.0%

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

   8. mul-1-neg 100.0%

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

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: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+39} \lor \neg \left(x \leq 5.1 \cdot 10^{+210}\right) \land x \leq 1.25 \cdot 10^{+271}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+26)
   (* x z)
   (if (<= x -6.8e-25)
     (* x y)
     (if (<= x 4.5e-31)
       (- z)
       (if (or (<= x 5.8e+39) (and (not (<= x 5.1e+210)) (<= x 1.25e+271)))
         (* x y)
         (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+26) {
		tmp = x * z;
	} else if (x <= -6.8e-25) {
		tmp = x * y;
	} else if (x <= 4.5e-31) {
		tmp = -z;
	} else if ((x <= 5.8e+39) || (!(x <= 5.1e+210) && (x <= 1.25e+271))) {
		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 <= (-1.3d+26)) then
        tmp = x * z
    else if (x <= (-6.8d-25)) then
        tmp = x * y
    else if (x <= 4.5d-31) then
        tmp = -z
    else if ((x <= 5.8d+39) .or. (.not. (x <= 5.1d+210)) .and. (x <= 1.25d+271)) 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 <= -1.3e+26) {
		tmp = x * z;
	} else if (x <= -6.8e-25) {
		tmp = x * y;
	} else if (x <= 4.5e-31) {
		tmp = -z;
	} else if ((x <= 5.8e+39) || (!(x <= 5.1e+210) && (x <= 1.25e+271))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+26:
		tmp = x * z
	elif x <= -6.8e-25:
		tmp = x * y
	elif x <= 4.5e-31:
		tmp = -z
	elif (x <= 5.8e+39) or (not (x <= 5.1e+210) and (x <= 1.25e+271)):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+26)
		tmp = Float64(x * z);
	elseif (x <= -6.8e-25)
		tmp = Float64(x * y);
	elseif (x <= 4.5e-31)
		tmp = Float64(-z);
	elseif ((x <= 5.8e+39) || (!(x <= 5.1e+210) && (x <= 1.25e+271)))
		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 <= -1.3e+26)
		tmp = x * z;
	elseif (x <= -6.8e-25)
		tmp = x * y;
	elseif (x <= 4.5e-31)
		tmp = -z;
	elseif ((x <= 5.8e+39) || (~((x <= 5.1e+210)) && (x <= 1.25e+271)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+26], N[(x * z), $MachinePrecision], If[LessEqual[x, -6.8e-25], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.5e-31], (-z), If[Or[LessEqual[x, 5.8e+39], And[N[Not[LessEqual[x, 5.1e+210]], $MachinePrecision], LessEqual[x, 1.25e+271]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.30000000000000001e26 or 5.80000000000000059e39 < x < 5.1000000000000001e210 or 1.2500000000000001e271 < x

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. /-rgt-identity 100.0%

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

      3. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 66.0%

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

   if -1.30000000000000001e26 < x < -6.80000000000000003e-25 or 4.5000000000000004e-31 < x < 5.80000000000000059e39 or 5.1000000000000001e210 < x < 1.2500000000000001e271

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 68.4%

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

   if -6.80000000000000003e-25 < x < 4.5000000000000004e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+39} \lor \neg \left(x \leq 5.1 \cdot 10^{+210}\right) \land x \leq 1.25 \cdot 10^{+271}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-27} \lor \neg \left(x \leq 4.5 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e-27) (not (<= x 4.5e-30))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e-27) || !(x <= 4.5e-30)) {
		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 <= (-7.5d-27)) .or. (.not. (x <= 4.5d-30))) 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 <= -7.5e-27) || !(x <= 4.5e-30)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.5e-27) or not (x <= 4.5e-30):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.5e-27) || !(x <= 4.5e-30))
		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 <= -7.5e-27) || ~((x <= 4.5e-30)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.5e-27], N[Not[LessEqual[x, 4.5e-30]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000029e-27 or 4.49999999999999967e-30 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 95.4%

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

      1. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if -7.50000000000000029e-27 < x < 4.49999999999999967e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-27} \lor \neg \left(x \leq 4.5 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 2.95 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 2.95e-5))) (* x (+ y z)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 2.95e-5)) {
		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 <= (-1.0d0)) .or. (.not. (x <= 2.95d-5))) 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 <= -1.0) || !(x <= 2.95e-5)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.0) or not (x <= 2.95e-5):
		tmp = x * (y + z)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 2.95e-5))
		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 <= -1.0) || ~((x <= 2.95e-5)))
		tmp = x * (y + z);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 2.95e-5]], $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 < -1 or 2.9499999999999999e-5 < x

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 98.9%

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

      1. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   if -1 < x < 2.9499999999999999e-5

   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. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

      8. distribute-lft-out 100.0%

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

   3. Simplified 100.0%

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

      1. flip-+ 57.5%

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

      2. associate-*r/ 56.8%

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

      3. difference-of-squares 56.9%

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

      4. sub-neg 56.9%

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

      5. add-sqr-sqrt 19.9%

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

      6. sqrt-unprod 57.1%

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

      7. sqr-neg 57.1%

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

      8. sqrt-unprod 37.1%

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

      9. add-sqr-sqrt 57.2%

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

      10. pow2 57.2%

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

      11. sub-neg 57.2%

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

      12. add-sqr-sqrt 20.1%

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

      13. sqrt-unprod 56.1%

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

      14. sqr-neg 56.1%

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

      15. sqrt-unprod 36.9%

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

      16. add-sqr-sqrt 56.9%

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

   5. Applied egg-rr 56.9%

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

      1. associate-/l* 57.6%

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

      2. unpow2 57.6%

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

      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 98.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 2.95 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-35) (* x y) (if (<= x 3.3e-30) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-35) {
		tmp = x * y;
	} else if (x <= 3.3e-30) {
		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 <= (-4.2d-35)) then
        tmp = x * y
    else if (x <= 3.3d-30) 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 <= -4.2e-35) {
		tmp = x * y;
	} else if (x <= 3.3e-30) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-35:
		tmp = x * y
	elif x <= 3.3e-30:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-35)
		tmp = Float64(x * y);
	elseif (x <= 3.3e-30)
		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 <= -4.2e-35)
		tmp = x * y;
	elseif (x <= 3.3e-30)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-35], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.3e-30], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-35 or 3.3000000000000003e-30 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 49.6%

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

   if -4.2e-35 < x < 3.3000000000000003e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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 97.6%

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

   1. *-commutative 97.6%

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

   2. sub-neg 97.6%

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

   3. distribute-rgt-in 97.7%

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

   4. associate-+r+ 97.7%

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

   5. metadata-eval 97.7%

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

   6. mul-1-neg 97.7%

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

   7. unsub-neg 97.7%

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

   8. distribute-lft-out 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 7: 36.6% 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 97.6%

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

2. Taylor expanded in x around 0 37.9%

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

   1. mul-1-neg 37.9%

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

4. Simplified 37.9%

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

5. Final simplification 37.9%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))