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

Percentage Accurate: 98.0% → 100.0%

Time: 4.8s

Alternatives: 8

Speedup: 1.3×

• 20.8% 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 97.2%

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

   1. *-commutative 97.2%

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

   2. sub-neg 97.2%

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

   3. distribute-rgt-in 97.2%

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

   4. metadata-eval 97.2%

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

   5. neg-mul-1 97.2%

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

   6. associate-+r+ 97.2%

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

   7. distribute-lft-out 99.9%

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

   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: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+97} \lor \neg \left(x \leq 1.16 \cdot 10^{+113}\right) \land \left(x \leq 1.7 \cdot 10^{+170} \lor \neg \left(x \leq 4.2 \cdot 10^{+235}\right) \land x \leq 2.5 \cdot 10^{+258}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+73)
   (* x z)
   (if (<= x -0.0066)
     (* x y)
     (if (<= x 1.14e-138)
       (- z)
       (if (<= x 2.1e+63)
         (* x y)
         (if (or (<= x 8.6e+97)
                 (and (not (<= x 1.16e+113))
                      (or (<= x 1.7e+170)
                          (and (not (<= x 4.2e+235)) (<= x 2.5e+258)))))
           (* x z)
           (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+73) {
		tmp = x * z;
	} else if (x <= -0.0066) {
		tmp = x * y;
	} else if (x <= 1.14e-138) {
		tmp = -z;
	} else if (x <= 2.1e+63) {
		tmp = x * y;
	} else if ((x <= 8.6e+97) || (!(x <= 1.16e+113) && ((x <= 1.7e+170) || (!(x <= 4.2e+235) && (x <= 2.5e+258))))) {
		tmp = x * 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 <= (-1d+73)) then
        tmp = x * z
    else if (x <= (-0.0066d0)) then
        tmp = x * y
    else if (x <= 1.14d-138) then
        tmp = -z
    else if (x <= 2.1d+63) then
        tmp = x * y
    else if ((x <= 8.6d+97) .or. (.not. (x <= 1.16d+113)) .and. (x <= 1.7d+170) .or. (.not. (x <= 4.2d+235)) .and. (x <= 2.5d+258)) then
        tmp = x * 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 <= -1e+73) {
		tmp = x * z;
	} else if (x <= -0.0066) {
		tmp = x * y;
	} else if (x <= 1.14e-138) {
		tmp = -z;
	} else if (x <= 2.1e+63) {
		tmp = x * y;
	} else if ((x <= 8.6e+97) || (!(x <= 1.16e+113) && ((x <= 1.7e+170) || (!(x <= 4.2e+235) && (x <= 2.5e+258))))) {
		tmp = x * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+73:
		tmp = x * z
	elif x <= -0.0066:
		tmp = x * y
	elif x <= 1.14e-138:
		tmp = -z
	elif x <= 2.1e+63:
		tmp = x * y
	elif (x <= 8.6e+97) or (not (x <= 1.16e+113) and ((x <= 1.7e+170) or (not (x <= 4.2e+235) and (x <= 2.5e+258)))):
		tmp = x * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+73)
		tmp = Float64(x * z);
	elseif (x <= -0.0066)
		tmp = Float64(x * y);
	elseif (x <= 1.14e-138)
		tmp = Float64(-z);
	elseif (x <= 2.1e+63)
		tmp = Float64(x * y);
	elseif ((x <= 8.6e+97) || (!(x <= 1.16e+113) && ((x <= 1.7e+170) || (!(x <= 4.2e+235) && (x <= 2.5e+258)))))
		tmp = Float64(x * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+73)
		tmp = x * z;
	elseif (x <= -0.0066)
		tmp = x * y;
	elseif (x <= 1.14e-138)
		tmp = -z;
	elseif (x <= 2.1e+63)
		tmp = x * y;
	elseif ((x <= 8.6e+97) || (~((x <= 1.16e+113)) && ((x <= 1.7e+170) || (~((x <= 4.2e+235)) && (x <= 2.5e+258)))))
		tmp = x * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+73], N[(x * z), $MachinePrecision], If[LessEqual[x, -0.0066], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.14e-138], (-z), If[LessEqual[x, 2.1e+63], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 8.6e+97], And[N[Not[LessEqual[x, 1.16e+113]], $MachinePrecision], Or[LessEqual[x, 1.7e+170], And[N[Not[LessEqual[x, 4.2e+235]], $MachinePrecision], LessEqual[x, 2.5e+258]]]]], N[(x * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999983e72 or 2.1000000000000002e63 < x < 8.5999999999999996e97 or 1.1600000000000001e113 < x < 1.7000000000000001e170 or 4.2000000000000001e235 < x < 2.5e258

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 71.8%

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

      1. sub-neg 71.8%

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

      2. metadata-eval 71.8%

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

      3. distribute-rgt-in 71.8%

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

      4. mul-1-neg 71.8%

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

      5. sub-neg 71.8%

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

      6. *-commutative 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in x around inf 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   if -9.99999999999999983e72 < x < -0.0066 or 1.1399999999999999e-138 < x < 2.1000000000000002e63 or 8.5999999999999996e97 < x < 1.1600000000000001e113 or 1.7000000000000001e170 < x < 4.2000000000000001e235 or 2.5e258 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 69.0%

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

   if -0.0066 < x < 1.1399999999999999e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+97} \lor \neg \left(x \leq 1.16 \cdot 10^{+113}\right) \land \left(x \leq 1.7 \cdot 10^{+170} \lor \neg \left(x \leq 4.2 \cdot 10^{+235}\right) \land x \leq 2.5 \cdot 10^{+258}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0066) (not (<= x 5.1e-138))) (* x (+ y z)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0066) || !(x <= 5.1e-138)) {
		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 <= (-0.0066d0)) .or. (.not. (x <= 5.1d-138))) 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 <= -0.0066) || !(x <= 5.1e-138)) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0066) or not (x <= 5.1e-138):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0066) || !(x <= 5.1e-138))
		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 <= -0.0066) || ~((x <= 5.1e-138)))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0066], N[Not[LessEqual[x, 5.1e-138]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 5.1000000000000002e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -0.0066 < x < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0074 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0074) (not (<= x 5.1e-138))) (* x (+ y z)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0074) || !(x <= 5.1e-138)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (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) :: tmp
    if ((x <= (-0.0074d0)) .or. (.not. (x <= 5.1d-138))) then
        tmp = x * (y + z)
    else
        tmp = z * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0074) || !(x <= 5.1e-138)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0074) or not (x <= 5.1e-138):
		tmp = x * (y + z)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0074) || !(x <= 5.1e-138))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(z * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0074) || ~((x <= 5.1e-138)))
		tmp = x * (y + z);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0074], N[Not[LessEqual[x, 5.1e-138]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0074000000000000003 or 5.1000000000000002e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. +-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -0.0074000000000000003 < x < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0074 \lor \neg \left(x \leq 5.1 \cdot 10^{-138}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -14.0) (not (<= x 1.0))) (* x (+ y z)) (- (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -14.0) || !(x <= 1.0)) {
		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 <= (-14.0d0)) .or. (.not. (x <= 1.0d0))) 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 <= -14.0) || !(x <= 1.0)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -14.0) or not (x <= 1.0):
		tmp = x * (y + z)
	else:
		tmp = (x * y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -14.0) || !(x <= 1.0))
		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 <= -14.0) || ~((x <= 1.0)))
		tmp = x * (y + z);
	else
		tmp = (x * y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -14.0], N[Not[LessEqual[x, 1.0]], $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 < -14 or 1 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 99.2%

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

      1. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   if -14 < x < 1

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-rgt-in 99.9%

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

      4. metadata-eval 99.9%

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

      5. neg-mul-1 99.9%

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

      6. associate-+r+ 99.9%

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

      7. unsub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-lft-out 99.9%

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

   3. Simplified 99.9%

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

      1. +-commutative 99.9%

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

      2. flip-+ 56.5%

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

      3. associate-*r/ 55.6%

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

      4. difference-of-squares 55.8%

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

      5. sub-neg 55.8%

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

      6. add-sqr-sqrt 23.3%

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

      7. sqrt-unprod 55.6%

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

      8. sqr-neg 55.6%

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

      9. sqrt-unprod 32.2%

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

      10. add-sqr-sqrt 55.1%

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

      11. pow2 55.1%

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

      12. sub-neg 55.1%

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

      13. add-sqr-sqrt 22.9%

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

      14. sqrt-unprod 54.5%

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

      15. sqr-neg 54.5%

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

      16. sqrt-unprod 32.5%

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

      17. add-sqr-sqrt 55.8%

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

   5. Applied egg-rr 55.8%

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

      1. associate-/l* 56.6%

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

      2. unpow2 56.6%

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

      3. associate-/r* 99.8%

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

      4. *-inverses 99.8%

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

      5. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - z\\ \end{array} \]

Alternative 6: 60.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0066) (* x y) (if (<= x 5.1e-138) (- z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0066) {
		tmp = x * y;
	} else if (x <= 5.1e-138) {
		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 <= (-0.0066d0)) then
        tmp = x * y
    else if (x <= 5.1d-138) 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 <= -0.0066) {
		tmp = x * y;
	} else if (x <= 5.1e-138) {
		tmp = -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0066:
		tmp = x * y
	elif x <= 5.1e-138:
		tmp = -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0066)
		tmp = Float64(x * y);
	elseif (x <= 5.1e-138)
		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 <= -0.0066)
		tmp = x * y;
	elseif (x <= 5.1e-138)
		tmp = -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0066], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.1e-138], (-z), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 5.1000000000000002e-138 < x

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 54.4%

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

   if -0.0066 < x < 5.1000000000000002e-138

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-138}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 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 97.2%

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

   1. *-commutative 97.2%

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

   2. sub-neg 97.2%

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

   3. distribute-rgt-in 97.2%

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

   4. metadata-eval 97.2%

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

   5. neg-mul-1 97.2%

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

   6. associate-+r+ 97.2%

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

   7. unsub-neg 97.2%

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

   8. +-commutative 97.2%

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

   9. distribute-lft-out 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 8: 37.6% 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 97.2%

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

2. Taylor expanded in x around 0 32.4%

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

   1. mul-1-neg 32.4%

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

4. Simplified 32.4%

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

5. Final simplification 32.4%

   \[\leadsto -z \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))