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

Percentage Accurate: 98.0% → 100.0%

Time: 4.8s

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 97.2%

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

   1. *-commutative 97.2%

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

   2. distribute-rgt-out-- 97.2%

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

   3. cancel-sign-sub-inv 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 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 60.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-104}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+41} \lor \neg \left(x \leq 3.5 \cdot 10^{+97}\right) \land x \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e-26)
   (* x y)
   (if (<= x -6e-104)
     (- z)
     (if (<= x -6.9e-125)
       (* x y)
       (if (<= x 3.7e-84)
         (- z)
         (if (or (<= x 1.55e+41) (and (not (<= x 3.5e+97)) (<= x 7.2e+157)))
           (* x y)
           (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e-26) {
		tmp = x * y;
	} else if (x <= -6e-104) {
		tmp = -z;
	} else if (x <= -6.9e-125) {
		tmp = x * y;
	} else if (x <= 3.7e-84) {
		tmp = -z;
	} else if ((x <= 1.55e+41) || (!(x <= 3.5e+97) && (x <= 7.2e+157))) {
		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 <= (-2.1d-26)) then
        tmp = x * y
    else if (x <= (-6d-104)) then
        tmp = -z
    else if (x <= (-6.9d-125)) then
        tmp = x * y
    else if (x <= 3.7d-84) then
        tmp = -z
    else if ((x <= 1.55d+41) .or. (.not. (x <= 3.5d+97)) .and. (x <= 7.2d+157)) 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 <= -2.1e-26) {
		tmp = x * y;
	} else if (x <= -6e-104) {
		tmp = -z;
	} else if (x <= -6.9e-125) {
		tmp = x * y;
	} else if (x <= 3.7e-84) {
		tmp = -z;
	} else if ((x <= 1.55e+41) || (!(x <= 3.5e+97) && (x <= 7.2e+157))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e-26:
		tmp = x * y
	elif x <= -6e-104:
		tmp = -z
	elif x <= -6.9e-125:
		tmp = x * y
	elif x <= 3.7e-84:
		tmp = -z
	elif (x <= 1.55e+41) or (not (x <= 3.5e+97) and (x <= 7.2e+157)):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e-26)
		tmp = Float64(x * y);
	elseif (x <= -6e-104)
		tmp = Float64(-z);
	elseif (x <= -6.9e-125)
		tmp = Float64(x * y);
	elseif (x <= 3.7e-84)
		tmp = Float64(-z);
	elseif ((x <= 1.55e+41) || (!(x <= 3.5e+97) && (x <= 7.2e+157)))
		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 <= -2.1e-26)
		tmp = x * y;
	elseif (x <= -6e-104)
		tmp = -z;
	elseif (x <= -6.9e-125)
		tmp = x * y;
	elseif (x <= 3.7e-84)
		tmp = -z;
	elseif ((x <= 1.55e+41) || (~((x <= 3.5e+97)) && (x <= 7.2e+157)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e-26], N[(x * y), $MachinePrecision], If[LessEqual[x, -6e-104], (-z), If[LessEqual[x, -6.9e-125], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.7e-84], (-z), If[Or[LessEqual[x, 1.55e+41], And[N[Not[LessEqual[x, 3.5e+97]], $MachinePrecision], LessEqual[x, 7.2e+157]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000008e-26 or -6.0000000000000005e-104 < x < -6.89999999999999973e-125 or 3.6999999999999999e-84 < x < 1.55e41 or 3.5000000000000001e97 < x < 7.20000000000000049e157

   1. Initial program 99.1%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.0%

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

   if -2.10000000000000008e-26 < x < -6.0000000000000005e-104 or -6.89999999999999973e-125 < x < 3.6999999999999999e-84

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

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

      1. mul-1-neg 81.4%

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

   5. Simplified 81.4%

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

   if 1.55e41 < x < 3.5000000000000001e97 or 7.20000000000000049e157 < x

   1. Initial program 85.3%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.3%

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

   4. Taylor expanded in x around inf 69.3%

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

      1. *-commutative 69.3%

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

   6. Simplified 69.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-104}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+41} \lor \neg \left(x \leq 3.5 \cdot 10^{+97}\right) \land x \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-26} \lor \neg \left(x \leq -7.5 \cdot 10^{-104} \lor \neg \left(x \leq -7.2 \cdot 10^{-125}\right) \land x \leq 8.5 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e-26)
         (not
          (or (<= x -7.5e-104) (and (not (<= x -7.2e-125)) (<= x 8.5e-84)))))
   (* x (+ y z))
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-26) || !((x <= -7.5e-104) || (!(x <= -7.2e-125) && (x <= 8.5e-84)))) {
		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 <= (-4.3d-26)) .or. (.not. (x <= (-7.5d-104)) .or. (.not. (x <= (-7.2d-125))) .and. (x <= 8.5d-84))) 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 <= -4.3e-26) || !((x <= -7.5e-104) || (!(x <= -7.2e-125) && (x <= 8.5e-84)))) {
		tmp = x * (y + z);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e-26) or not ((x <= -7.5e-104) or (not (x <= -7.2e-125) and (x <= 8.5e-84))):
		tmp = x * (y + z)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e-26) || !((x <= -7.5e-104) || (!(x <= -7.2e-125) && (x <= 8.5e-84))))
		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 <= -4.3e-26) || ~(((x <= -7.5e-104) || (~((x <= -7.2e-125)) && (x <= 8.5e-84)))))
		tmp = x * (y + z);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-26], N[Not[Or[LessEqual[x, -7.5e-104], And[N[Not[LessEqual[x, -7.2e-125]], $MachinePrecision], LessEqual[x, 8.5e-84]]]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -4.29999999999999988e-26 or -7.5e-104 < x < -7.2000000000000004e-125 or 8.4999999999999994e-84 < x

   1. Initial program 95.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.2%

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

      1. +-commutative 94.2%

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

   5. Simplified 94.2%

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

   if -4.29999999999999988e-26 < x < -7.5e-104 or -7.2000000000000004e-125 < x < 8.4999999999999994e-84

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

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

      1. mul-1-neg 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-26} \lor \neg \left(x \leq -7.5 \cdot 10^{-104} \lor \neg \left(x \leq -7.2 \cdot 10^{-125}\right) \land x \leq 8.5 \cdot 10^{-84}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-26} \lor \neg \left(x \leq -2.3 \cdot 10^{-101}\right) \land \left(x \leq -7.2 \cdot 10^{-125} \lor \neg \left(x \leq 2.8 \cdot 10^{-83}\right)\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-26)
         (and (not (<= x -2.3e-101))
              (or (<= x -7.2e-125) (not (<= x 2.8e-83)))))
   (* x (+ y z))
   (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-26) || (!(x <= -2.3e-101) && ((x <= -7.2e-125) || !(x <= 2.8e-83)))) {
		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 <= (-6d-26)) .or. (.not. (x <= (-2.3d-101))) .and. (x <= (-7.2d-125)) .or. (.not. (x <= 2.8d-83))) 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 <= -6e-26) || (!(x <= -2.3e-101) && ((x <= -7.2e-125) || !(x <= 2.8e-83)))) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-26) or (not (x <= -2.3e-101) and ((x <= -7.2e-125) or not (x <= 2.8e-83))):
		tmp = x * (y + z)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-26) || (!(x <= -2.3e-101) && ((x <= -7.2e-125) || !(x <= 2.8e-83))))
		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 <= -6e-26) || (~((x <= -2.3e-101)) && ((x <= -7.2e-125) || ~((x <= 2.8e-83)))))
		tmp = x * (y + z);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-26], And[N[Not[LessEqual[x, -2.3e-101]], $MachinePrecision], Or[LessEqual[x, -7.2e-125], N[Not[LessEqual[x, 2.8e-83]], $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 < -6.00000000000000023e-26 or -2.2999999999999999e-101 < x < -7.2000000000000004e-125 or 2.8000000000000001e-83 < x

   1. Initial program 95.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.2%

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

      1. +-commutative 94.2%

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

   5. Simplified 94.2%

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

   if -6.00000000000000023e-26 < x < -2.2999999999999999e-101 or -7.2000000000000004e-125 < x < 2.8000000000000001e-83

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-26} \lor \neg \left(x \leq -2.3 \cdot 10^{-101}\right) \land \left(x \leq -7.2 \cdot 10^{-125} \lor \neg \left(x \leq 2.8 \cdot 10^{-83}\right)\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-25} \lor \neg \left(x \leq -6.2 \cdot 10^{-104}\right) \land \left(x \leq -7.2 \cdot 10^{-125} \lor \neg \left(x \leq 2.8 \cdot 10^{-83}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-25)
         (and (not (<= x -6.2e-104))
              (or (<= x -7.2e-125) (not (<= x 2.8e-83)))))
   (* x y)
   (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-25) || (!(x <= -6.2e-104) && ((x <= -7.2e-125) || !(x <= 2.8e-83)))) {
		tmp = x * y;
	} 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 <= (-2.1d-25)) .or. (.not. (x <= (-6.2d-104))) .and. (x <= (-7.2d-125)) .or. (.not. (x <= 2.8d-83))) then
        tmp = x * y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-25) || (!(x <= -6.2e-104) && ((x <= -7.2e-125) || !(x <= 2.8e-83)))) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-25) or (not (x <= -6.2e-104) and ((x <= -7.2e-125) or not (x <= 2.8e-83))):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-25) || (!(x <= -6.2e-104) && ((x <= -7.2e-125) || !(x <= 2.8e-83))))
		tmp = Float64(x * y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-25) || (~((x <= -6.2e-104)) && ((x <= -7.2e-125) || ~((x <= 2.8e-83)))))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-25], And[N[Not[LessEqual[x, -6.2e-104]], $MachinePrecision], Or[LessEqual[x, -7.2e-125], N[Not[LessEqual[x, 2.8e-83]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000002e-25 or -6.19999999999999951e-104 < x < -7.2000000000000004e-125 or 2.8000000000000001e-83 < x

   1. Initial program 95.5%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.3%

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

   if -2.10000000000000002e-25 < x < -6.19999999999999951e-104 or -7.2000000000000004e-125 < x < 2.8000000000000001e-83

   1. Initial program 100.0%

      \[x \cdot y + \left(x - 1\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

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

      1. mul-1-neg 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-25} \lor \neg \left(x \leq -6.2 \cdot 10^{-104}\right) \land \left(x \leq -7.2 \cdot 10^{-125} \lor \neg \left(x \leq 2.8 \cdot 10^{-83}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

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 97.2%

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

   1. *-commutative 97.2%

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

   2. distribute-rgt-out-- 97.2%

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

   3. cancel-sign-sub-inv 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 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. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto x \cdot \left(y + z\right) - z \]
6. Add Preprocessing

Alternative 7: 36.2% 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. Add Preprocessing

3. Taylor expanded in x around 0 36.7%

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

   1. mul-1-neg 36.7%

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

5. Simplified 36.7%

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

6. Final simplification 36.7%

   \[\leadsto -z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))