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

Percentage Accurate: 98.2% → 100.0%

Time: 4.3s

Alternatives: 8

Speedup: 1.3×

• 20.3% 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: 98.2% 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, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. *-commutative 99.2%

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

   2. distribute-rgt-out-- 99.2%

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

   3. cancel-sign-sub-inv 99.2%

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

   4. metadata-eval 99.2%

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

   5. neg-mul-1 99.2%

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

   6. associate-+r+ 99.2%

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

   7. unsub-neg 99.2%

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

   8. +-commutative 99.2%

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

   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%

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

Alternative 2: 62.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+267}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+121} \lor \neg \left(x \leq 2.9 \cdot 10^{+154}\right) \land x \leq 1.6 \cdot 10^{+283}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e+267)
   (* x z)
   (if (<= x -7.5e-27)
     (* x y)
     (if (<= x 3.75e-6)
       (- z)
       (if (or (<= x 3.7e+121) (and (not (<= x 2.9e+154)) (<= x 1.6e+283)))
         (* x y)
         (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e+267) {
		tmp = x * z;
	} else if (x <= -7.5e-27) {
		tmp = x * y;
	} else if (x <= 3.75e-6) {
		tmp = -z;
	} else if ((x <= 3.7e+121) || (!(x <= 2.9e+154) && (x <= 1.6e+283))) {
		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 <= (-8.5d+267)) then
        tmp = x * z
    else if (x <= (-7.5d-27)) then
        tmp = x * y
    else if (x <= 3.75d-6) then
        tmp = -z
    else if ((x <= 3.7d+121) .or. (.not. (x <= 2.9d+154)) .and. (x <= 1.6d+283)) 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 <= -8.5e+267) {
		tmp = x * z;
	} else if (x <= -7.5e-27) {
		tmp = x * y;
	} else if (x <= 3.75e-6) {
		tmp = -z;
	} else if ((x <= 3.7e+121) || (!(x <= 2.9e+154) && (x <= 1.6e+283))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e+267:
		tmp = x * z
	elif x <= -7.5e-27:
		tmp = x * y
	elif x <= 3.75e-6:
		tmp = -z
	elif (x <= 3.7e+121) or (not (x <= 2.9e+154) and (x <= 1.6e+283)):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e+267)
		tmp = Float64(x * z);
	elseif (x <= -7.5e-27)
		tmp = Float64(x * y);
	elseif (x <= 3.75e-6)
		tmp = Float64(-z);
	elseif ((x <= 3.7e+121) || (!(x <= 2.9e+154) && (x <= 1.6e+283)))
		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 <= -8.5e+267)
		tmp = x * z;
	elseif (x <= -7.5e-27)
		tmp = x * y;
	elseif (x <= 3.75e-6)
		tmp = -z;
	elseif ((x <= 3.7e+121) || (~((x <= 2.9e+154)) && (x <= 1.6e+283)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e+267], N[(x * z), $MachinePrecision], If[LessEqual[x, -7.5e-27], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.75e-6], (-z), If[Or[LessEqual[x, 3.7e+121], And[N[Not[LessEqual[x, 2.9e+154]], $MachinePrecision], LessEqual[x, 1.6e+283]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000007e267 or 3.70000000000000013e121 < x < 2.89999999999999979e154 or 1.60000000000000005e283 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 83.8%

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

   4. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   if -8.5000000000000007e267 < x < -7.50000000000000029e-27 or 3.7500000000000001e-6 < x < 3.70000000000000013e121 or 2.89999999999999979e154 < x < 1.60000000000000005e283

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -7.50000000000000029e-27 < x < 3.7500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

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

      1. neg-mul-1 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+267}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+121} \lor \neg \left(x \leq 2.9 \cdot 10^{+154}\right) \land x \leq 1.6 \cdot 10^{+283}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-28} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.06e-28) (not (<= x 3.75e-6))) (* x (+ z y)) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.06e-28) || !(x <= 3.75e-6)) {
		tmp = x * (z + 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 <= (-1.06d-28)) .or. (.not. (x <= 3.75d-6))) then
        tmp = x * (z + 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 <= -1.06e-28) || !(x <= 3.75e-6)) {
		tmp = x * (z + y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.06e-28) or not (x <= 3.75e-6):
		tmp = x * (z + y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.06e-28) || !(x <= 3.75e-6))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.06e-28) || ~((x <= 3.75e-6)))
		tmp = x * (z + y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.06e-28], N[Not[LessEqual[x, 3.75e-6]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e-28 or 3.7500000000000001e-6 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if -1.06e-28 < x < 3.7500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

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

      1. neg-mul-1 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-28} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-29} \lor \neg \left(x \leq 0.46\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-29) (not (<= x 0.46))) (* x (+ z y)) (* z (+ x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-29) || !(x <= 0.46)) {
		tmp = x * (z + y);
	} 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 <= (-7d-29)) .or. (.not. (x <= 0.46d0))) then
        tmp = x * (z + y)
    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 <= -7e-29) || !(x <= 0.46)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-29) or not (x <= 0.46):
		tmp = x * (z + y)
	else:
		tmp = z * (x + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-29) || !(x <= 0.46))
		tmp = Float64(x * Float64(z + y));
	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 <= -7e-29) || ~((x <= 0.46)))
		tmp = x * (z + y);
	else
		tmp = z * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-29], N[Not[LessEqual[x, 0.46]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999995e-29 or 0.46000000000000002 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if -6.9999999999999995e-29 < x < 0.46000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-29} \lor \neg \left(x \leq 0.46\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-30} \lor \neg \left(x \leq 0.0036\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e-30) (not (<= x 0.0036))) (* x (+ z y)) (- (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-30) || !(x <= 0.0036)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - 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 <= (-4d-30)) .or. (.not. (x <= 0.0036d0))) then
        tmp = x * (z + y)
    else
        tmp = (x * z) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-30) || !(x <= 0.0036)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * z) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e-30) or not (x <= 0.0036):
		tmp = x * (z + y)
	else:
		tmp = (x * z) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e-30) || !(x <= 0.0036))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x * z) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e-30) || ~((x <= 0.0036)))
		tmp = x * (z + y);
	else
		tmp = (x * z) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e-30], N[Not[LessEqual[x, 0.0036]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e-30 or 0.0035999999999999999 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 98.7%

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

      1. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   if -4e-30 < x < 0.0035999999999999999

   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. distribute-rgt-out-- 100.0%

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

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

   5. Taylor expanded in y around 0 71.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-30} \lor \neg \left(x \leq 0.0036\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-5}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e-30)
   (+ (* x y) (* x z))
   (if (<= x 1.05e-5) (- (* x z) z) (* x (+ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-30) {
		tmp = (x * y) + (x * z);
	} else if (x <= 1.05e-5) {
		tmp = (x * z) - z;
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.4d-30)) then
        tmp = (x * y) + (x * z)
    else if (x <= 1.05d-5) then
        tmp = (x * z) - z
    else
        tmp = x * (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-30) {
		tmp = (x * y) + (x * z);
	} else if (x <= 1.05e-5) {
		tmp = (x * z) - z;
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e-30:
		tmp = (x * y) + (x * z)
	elif x <= 1.05e-5:
		tmp = (x * z) - z
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e-30)
		tmp = Float64(Float64(x * y) + Float64(x * z));
	elseif (x <= 1.05e-5)
		tmp = Float64(Float64(x * z) - z);
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e-30)
		tmp = (x * y) + (x * z);
	elseif (x <= 1.05e-5)
		tmp = (x * z) - z;
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e-30], N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-5], N[(N[(x * z), $MachinePrecision] - z), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.39999999999999975e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -5.39999999999999975e-30 < x < 1.04999999999999994e-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. distribute-rgt-out-- 100.0%

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

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

   5. Taylor expanded in y around 0 71.9%

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

   if 1.04999999999999994e-5 < x

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-5}:\\ \;\;\;\;x \cdot z - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-27} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e-27) (not (<= x 3.75e-6))) (* x y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e-27) || !(x <= 3.75e-6)) {
		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 <= (-8d-27)) .or. (.not. (x <= 3.75d-6))) 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 <= -8e-27) || !(x <= 3.75e-6)) {
		tmp = x * y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e-27) or not (x <= 3.75e-6):
		tmp = x * y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e-27) || !(x <= 3.75e-6))
		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 <= -8e-27) || ~((x <= 3.75e-6)))
		tmp = x * y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e-27], N[Not[LessEqual[x, 3.75e-6]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000003e-27 or 3.7500000000000001e-6 < x

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 58.0%

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

   if -8.0000000000000003e-27 < x < 3.7500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

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

      1. neg-mul-1 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-27} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.1% 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 99.2%

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

3. Taylor expanded in x around 0 33.7%

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

   1. neg-mul-1 33.7%

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

5. Simplified 33.7%

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

6. Final simplification 33.7%

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

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))